## Abstract

This study compares the performance of three different nanofluids containing
aluminum oxide, copper oxide, and silicon dioxide nanoparticles dispersed in the
same base fluid, 60:40 ethylene glycol and water by mass, as coolant in
automobile radiators. The computational scheme adopted here is the
effectiveness-number of transfer unit (*ε* − NTU) method encoded
in matlab. Appropriate correlations of thermophysical properties for
these nanofluids developed from measurements are summarized in this paper. The
computational scheme has been validated by comparing the results of pumping
power, convective heat transfer coefficients on the air and coolant side,
overall heat transfer coefficient, effectiveness and NTU, reported by other
researchers. Then the scheme was adopted to compute the performance of
nanofluids. Results show that a dilute 1% volumetric concentration of
nanoparticles performs better than higher concentration. It is proven that at
optimal conditions of operation of the radiator, under the same heat transfer
basis, a reduction of 35.3% in pumping power or 7.4% of the surface area can be
achieved by using the Al_{2}O_{3} nanofluid. The CuO nanofluid
showed slightly lower magnitudes than the Al_{2}O_{3} nanofluid,
with 33.1% and 7.2% reduction for pumping power or surface area respectively.
The SiO_{2} nanofluid showed the least performance gain of the three
nanofluids, but still could reduce the pumping power or area by 26.2% or 5.2%.
The analysis presented in this paper was used for an automotive radiator but can
be extended to any liquid to gas heat exchanger.

## Introduction

With increasing demands for greater engine output, air conditioning (AC) capacity,
smaller hood space, and more stringent emission standards, the heat dissipation
requirements for automobiles have increased significantly over the past decades.
Automobiles use several heat exchangers to get rid of the heat: radiators,
condensers and evaporators for the AC, and oil coolers. Over the years steady
improvements have been made to increase the performance of these heat exchangers,
such as: different style of fin designs, increasing the number of fins and use of
different fin and tube materials. However, these improvements were made only to the
heat exchanger body, while the heat transfer fluid has remained unchanged.
Traditional coolants for automotive radiators inherently have poor thermal
conductivity. For example, 60:40 (by mass) ethylene glycol and water mixture (EG/W),
which is used in cold climates has a thermal conductivity of 0.36 W/mK at room
temperature 27 °C (300 K) whereas aluminum oxide (Al_{2}O_{3}) has a
thermal conductivity 36.0 W/mK, 100 times greater. Thus, mixing these two can bridge
the gap of thermal conductivity between fluids and solids. This is fulfilled by
nanofluids, which is a new generation of engineered fluid prepared by dispersing
nanometer size solid particles like Al_{2}O_{3} of average particle
size smaller than 100 nm, into a liquid denoted as the base fluid. Extensive
research on nanofluids in recent years has proven that by dispersing small volume of
nanoparticles in conventional heat transfer fluids, their thermal conductivity and
convective heat transfer can be enhanced [1–4]. Due to the higher thermal conductivity and diffusivity of
nanoparticles compared to liquids, they transport the heat from the low temperature
region to the high temperature region within the thermal boundary layer. The heat
transfer is also enhanced by the motion of the particles that generate microscale
turbulence and convection in the fluid surrounding the nanoparticles. Using a better
heat transfer fluid in automotive radiators could lead to a reduction in size and
pumping power, resulting in more efficient automobiles. With approximately 60
million cars produced yearly [5] in the world,
any reduction in the size and weight of the radiator can have substantial benefit
due to less metal and energy requirements reducing mining and environmental
effect.

Research on automotive radiators with single phase fluids is widely published in the literature. The most comprehensive research done in early years on a variety of heat transfer matrix geometries for radiators and other compact heat exchangers is due to Kays and London [6]. We have adopted from this reference the equations, analytic procedure and heat transfer matrix data in our analysis to study the performance of nanofluids in a radiator. Another authoritative work on heat exchanger design is by Fraas [7], which presents a detailed thermal and hydraulic analysis of a truck radiator. In our analysis herein, we have followed the design recommendations of coolant and air temperatures, pressure loss, pumping power from this reference. We have also verified the validity of our selected dimensional data for the heat transfer matrix that includes fin size, thickness, spacing and the flat tube dimensions using the information given by Kays and London and Fraas.

Ample research data exist on the thermal and hydraulic studies via experiments and theories on radiators in the publications of the Society of Automotive Engineers (SAE). They are for single phase coolants such as glycol/water mixtures or with pure water for applications in automobiles in tropical climate. However, very limited research has appeared in the literature thus far, using nanofluids as a coolant in automotive radiators. To the best of our knowledge, the present paper may be the first reported study that considers the thermal and hydraulic performance of three different nanofluids and compares their performance with the base fluid to evaluate their strengths and weaknesses.

We have collected the proper operational parameters, such as liquid and air temperatures, liquid, and air Reynolds number, acceptable pressure losses and the heat dissipation rate under which automobile radiators operate from several SAE papers, which are based on single phase coolants. Brief review of those papers follows from which we have selected the real-world values as input for our computation.

Fellague et al. [8]using a three-dimensional computational fluid dynamics code developed by the Ford Motor company presented a table of face velocities corresponding to three scenarios (idle, 30 mph, 60 mph), which generated radiator face velocities of 2.14 m/s, 3.00 m/s, and 4.84 m/s, respectively. These results indicate that the car velocity is about 5 times that of the radiator face velocity due blockage effects of the hood. Note that the face velocity is approach air velocity in the wind tunnel and the air velocity through the core of the radiator will be much higher. They adopted an air temperature of about 43 °C warming up to about 53 °C, a 10 °C temperature rise.

Gollin and Bjork [9] tested five radiators in a
wind tunnel to compare the performance of pure coolants: water; propylene glycol and
mixture coolants: EG/W; propylene glycol and water (PG/W) with mix ratios of 50:50
and 70:30. The five radiators were for: (1) Chrysler Minivan, (2) Ford Taurus, (3)
Ford Pick-up Truck, (4) Jeep Cherokee, and (5) Pontiac Bonneville with radiator core
area varying from 351 in^{2} to 525 in^{2}. They tested the
radiators with four air flow velocities within the range of 2–12 m/s (4.5–27 mph)
and the coolant flow rate of 0.38–2.28 kg/s (50–300 lbm/min) while maintaining a
nominal difference of 60 °C between the inlet temperatures of the air and coolant to
generate a practical set of experimental data. The most effective coolant was water
followed by 50:50 EG/W, 50:50 PG/W, 70:30 EG/W, 70:30 PG/W, and finally pure PG.

Beard and Smith [10] summarize analytical and wind tunnel test results for a typical 1.5 l car engine radiator, with the Reynolds number of coolant not exceeding 5000. They compared experimental and analytical values of heat dissipation. The coolant (water) side Reynolds number varied from 3900 to 9100 for a 3 in and 1 in core depth, respectively.

Eitel et al. [11] compared experimentally the performance of aluminum versus copper/brass radiator cores for heavy duty trucks. The volumetric flow was about 6000 l per hour corresponding to 0.42 m/s coolant velocity in the radiator tube. A maximum coolant temperature of 95 ± 3 °C was adopted in the test. For the same thermodynamic performance/conditions, the difference of inlet temperatures was 63.6 °C. The aluminum radiator with a mass of 9.4 kg was shown to be about 10% lighter compared to the copper/brass core radiator.

Liu et al. [12] present theoretical analysis for a heavy duty truck, 6-cyclinder,of 9.73 L displacement, turbocharged diesel engine with rating output of 206 W at a rated speed of 2400 rpm with intercooling. They limit the max coolant temperature to 95 °C. Liquid side Reynolds number ranged from 2200 to 10,000. Quantity of heat dissipated from the radiator is 116,771 kcal/h, whereas the quantity of heat rejection necessary for the engine is 112,000 kcal/h.

Cozzone [13] presented comparative results for a General Motors 1994 3.8 L V6 engine under dynamometer testing with PG/W and EG/W mixtures. They confirmed that the PG based coolant has improved heat transfer coefficient due to nuclear boiling.

Only a handful of publications have appeared in the literature thus far, studying the
performance of nanofluids in automobile radiators. Vasu et al. [14] carried out a theoretical study using the *ε*-NTU method with aluminum oxide at 4% volumetric concentration
dispersed in water and concluded a significant improvement in cooling capacity of
the nanofluid compared to pure water. This analysis is only applicable to regions of
the world, where ambient temperature remains above 0 °C throughout the year.

Leong et al. [15] performed a similar theoretical analysis, but considered nanofluids containing copper oxide with a concentration up to 2% dispersed in pure ethylene glycol (EG). However, pure EG is not used in radiators. For cold regions, a 50:50 EG/W mixture is used and for extreme cold regions, such as the interior Alaska a 60:40 EG/W mixture is used to guarantee a freeze protection down to − 48.3 °C. The mixture of EG/W is a better fluid from thermodynamics view point than pure EG. Leong et al. found 3.8% heat transfer enhancement over the base fluid at a 2% concentration for 6000 and 5000 air and coolant side Reynolds numbers, respectively.

Peyghambarzadeh et al. [16] performed an experimental study on aluminum oxide nanofluids with concentration ranging from 0% to 1.2% in pure ethylene glycol, pure water and ethylene glycol & water mixtures (5, 10, 20 vol.% EG) base fluids. They presented an impressive 40% increase in Nusselt Number at optimal conditions with nanofluids.

Vajjha et al. [17] carried out a computational
study on flat tubes of a radiator of a Chrysler Minivan using two different
nanoparticles Al_{2}O_{3} and CuO within a concentration range of
0–6% in 60:40 EG/W by mass, suitable for cold climates. From their analysis in the
laminar flow regime, they showed as much as 82.5% and 77.7% reduction in pumping
power for a constant heat transfer coefficient with 10% Al_{2}O_{3} and 6% CuO, respectively.

Some studies in the nanofluids literature show that there may not be a significant
enhancement in thermal conductivity and convective heat transfer by the addition of
nanoparticles to a fluid. For example, Gupta and Kumar [18] have conducted Brownian dynamic simulations and determined
that about a 6% increase in thermal conductivity of a nanofluid is possible. This
occurred at the highest concentration of nanoparticles and is below that predicted
by the effective medium theory. Yu et al. [19] expressed the figure of merit for nanofluids as the ratio of *h*_{nf}/*h*_{bf}. Yu et al.
[19] and Wu et al. [20] recommend that the comparison of convective heat transfer
coefficient on the basis of constant Reynolds number is misleading. Yu et al.
suggested that a constant pumping power criterion is the most stringent case for
comparing the heat transfer coefficient of nanofluids with that of the base fluid.
In this study, we have presented results in Sec. 5.2 (Fig. 9), which proves that on
the basis of equal pumping power, low concentration of nanofluids yield higher
convective heat transfer coefficient than the base fluid.

Observing the lack of data on the application of nanofluids in automotive radiators, we undertook the present research project. The automotive radiator modeled was for a Subaru vehicle. The reason for selecting this radiator is its ease in availability and low cost. We could dismantle part of it easily to make accurate measurements of fins and flat tubes. The radiator geometry is displayed in Fig. 2 under Sec. 3. It operates as a mixed (air side)/unmixed (liquid side) cross-flow compact heat exchanger, which uses a louvered serpentine fin design. It has selective cuts on the fins to influence mixing and turbulence in the boundary layer and promotes heat transfer. This type of radiator is used for engine sizes of 2.2–2.5 l 4-cylinder (137–165 hp), which is commonly used in compact cars.

### Project Objective.

A detailed computational study using matlab code was conducted to
compare the fluid dynamic and thermal performance of three nanofluids as heat
transfer mediums in an automotive radiator operating in the turbulent regime.
The three nanofluids were considered: aluminum oxide
(Al_{2}O_{3}), copper oxide (CuO), and silicon dioxide
(SiO_{2}) nanoparticles dispersed in the base fluid, EG/W 60:40 by
mass. This base fluid is commonly used in cold climates experienced in Alaska
and other circumpolar regions for its low freezing temperature around −48.3 °C
[21]. Using theoretical and empirical
correlations developed for nanofluid properties from the recent literature, we
investigated the effects of particle volumetric concentration, coolant and air
inlet temperatures and Reynolds number of air and coolant (EG/W &
nanofluids) on the thermal performance of the radiator. The objective is to
compare pumping power and surface area reduction on the basis of equal heat
dissipation with the base fluid and different nanofluids to conclusively
evaluate the benefit of nanofluids in automotive radiators.

## Thermodynamic Properties

Correlations for density, specific heat, dynamic viscosity, and thermal conductivity of the base fluid, air, and nanofluids are required for the computational analysis. Accurate data for properties of the base fluid and air are available in books. Correlations were developed from this data, by curve-fitting within a temperature range suitable for automobiles. These correlations were subsequently substituted in the computation scheme.

### Conventional Coolant—60:40 EG/W.

Traditional automotive coolant in cold regions is usually a 50:50 ethylene glycol
and water mixture, but in sub-arctic and arctic regions such as Alaska,
additional freezing protection is needed, therefore a 60:40 mixture by mass is
used. The base fluid properties data was obtained from the ASHRAE Fundamentals
Handbook [21] and curve fitted as a
function of temperature, over a range of 238 K
(−35 °C) ≤ *T* ≤ 398 K (125 °C) that will be encountered by an
automobile from starting to the fully operating condition. The thermophysical
property correlations presented in Table 1, except viscosity were modeled after Yaws [22], with the improvement that we expressed them in the
nondimensional form. The viscosity correlation follows the log-quadratic
empirical fit recommend by White [23] for
liquids. The subscript “0” refers to the fluid property at the standard
reference temperature of 273 K (*T*_{0}). All the
thermophysical correlations show a coefficient of determination *R*^{2}^{ }≈ 1 and an absolute error of less
than 0.1%, except for viscosity. To improve the accuracy of the viscosity
correlation, the temperature range was split into two segments
238 K ≤ *T* ≤ 273 K and 273 K ≤ T ≤ 398 K, achieving an error
of less than 0.9%.

Property | Correlation | Constants | R^{2} | Error |
---|---|---|---|---|

Density (kg/m^{3}) | $\rho \rho 0=A+B(TT0)+C(TT0)2$ | $\rho 0=1091.66kgm3$A = 0.9247 B = 0.2414 C = −0.1661 | 1 | 0.01% |

Viscosity (Pa · s) | $ln=(\mu \mu 0)=A+B(T0T)+C(T0T)2$ | $\mu 0=1.1\xd710-2kgm\xb7s$ | — | — |

238 K ≤ T ≤
273 K | A = 0.3707 B = −12.882 C = 12.513 | 1 | 0.19% | |

223 K ≤ T ≤
398 K | A = −4.976 B = −1.942 C = 6.9088 | 1 | 0.91% | |

Specific heat (J/kg · K) | $cpcp0=A+B(TT0)$ | $cp,0=3042.02Jkg\xb7K$A = 0.6185 B = 0.3814 | 1 | 0.01% |

Thermal conductivity (W/m · K) | $kk0=A+B(TT0)+C(TT0)2$ | $k0=0.342Wm\xb7K$A = −0.2939 B = 1.981 C = −0.6868 | 0.999 | 0.11% |

Property | Correlation | Constants | R^{2} | Error |
---|---|---|---|---|

Density (kg/m^{3}) | $\rho \rho 0=A+B(TT0)+C(TT0)2$ | $\rho 0=1091.66kgm3$A = 0.9247 B = 0.2414 C = −0.1661 | 1 | 0.01% |

Viscosity (Pa · s) | $ln=(\mu \mu 0)=A+B(T0T)+C(T0T)2$ | $\mu 0=1.1\xd710-2kgm\xb7s$ | — | — |

238 K ≤ T ≤
273 K | A = 0.3707 B = −12.882 C = 12.513 | 1 | 0.19% | |

223 K ≤ T ≤
398 K | A = −4.976 B = −1.942 C = 6.9088 | 1 | 0.91% | |

Specific heat (J/kg · K) | $cpcp0=A+B(TT0)$ | $cp,0=3042.02Jkg\xb7K$A = 0.6185 B = 0.3814 | 1 | 0.01% |

Thermal conductivity (W/m · K) | $kk0=A+B(TT0)+C(TT0)2$ | $k0=0.342Wm\xb7K$A = −0.2939 B = 1.981 C = −0.6868 | 0.999 | 0.11% |

### Air Properties.

The thermophysical properties of air as presented in Table 2 were curve-fitted using data from Çengel [24], which presents a broader temperature
range 223 K ≤ *T* ≤ 373 K than necessary for automotive radiator
application. The density correlation was derived from the ideal gas law. The
correlations for specific heat, viscosity, and thermal conductivity followed
models presented by Yaws [22], but in
nondimensional form. As observed for the base fluid correlations the coefficient
of determination *R*^{2}^{ }≈ 1 and the absolute
error associated with all the correlations are less than or equal to 0.3%.

Property | Correlation | Constants | R^{2} | Error |
---|---|---|---|---|

Density (kg/m^{3}) | $\rho \rho 0=A+B(T0T)$ | $\rho 0=1.292kgm3$ A = 0 B = 1 | 1 | 0.03% |

Viscosity (Pa · s) | $\mu \mu 0=A+B(TT0)+C(TT0)2$ | $\mu 0=1.73\xd710-5kgm\xb7s$ A = 0.05779
B = 1.11 C = −0.1681 | 0.9998 | 0.07% |

Specific heat (J/kg · K) | $cpcp0=A+B(TT0)+B(TT0)2+D(TT0)3$ | $cp,0=1006Jkg\xb7K$ A = 0.5984
B = 1.034 C = −0.8852
D = 0.2526 | 0.9793 | 0.30% |

Thermal conductivity (W/m · K) | $kk0=A+B(TT0)+C(TT0)2$ | $k0=0.02364Wm\xb7K$ A = 0.05054
B = 1.025 C = −0.07624 | 1 | 0.07% |

Property | Correlation | Constants | R^{2} | Error |
---|---|---|---|---|

Density (kg/m^{3}) | $\rho \rho 0=A+B(T0T)$ | $\rho 0=1.292kgm3$ A = 0 B = 1 | 1 | 0.03% |

Viscosity (Pa · s) | $\mu \mu 0=A+B(TT0)+C(TT0)2$ | $\mu 0=1.73\xd710-5kgm\xb7s$ A = 0.05779
B = 1.11 C = −0.1681 | 0.9998 | 0.07% |

Specific heat (J/kg · K) | $cpcp0=A+B(TT0)+B(TT0)2+D(TT0)3$ | $cp,0=1006Jkg\xb7K$ A = 0.5984
B = 1.034 C = −0.8852
D = 0.2526 | 0.9793 | 0.30% |

Thermal conductivity (W/m · K) | $kk0=A+B(TT0)+C(TT0)2$ | $k0=0.02364Wm\xb7K$ A = 0.05054
B = 1.025 C = −0.07624 | 1 | 0.07% |

### Nanofluid Properties.

For EG/W nanofluid with different nanoparticles suspensions, thermophysical properties data were not available in the literature. Therefore, a comprehensive properties measurement project was undertaken over a period of several years at the University of Alaska Fairbanks to develop general correlations for density, specific heat, thermal conductivity and viscosity of several EG/W based nanofluids.

#### Nanofluids Preparation and Characterization.

Several nanofluids were purchased from Alfa Aesar [25] as a concentrated aqueous suspension with average particle size in the range of 15–70 nm. The nanofluid was subjected to ultrasonication in two stages. In the first stage, the concentrated mother nanofluid (original fluid from manufacturer) was sonicated in a Branson Sonicator under a frequency of 40 kHz and a power of 185 W. The mother nanofluid was subjected to three sessions each of 2 h duration.

Using the density of nanoparticles (e.g., Al_{2}O_{3} particle density of 3600 kg/m^{3}) and that of the EG/W 60:40 at
room temperature of 25 °C is 1081 kg/m^{3}, it was calculated, how
much mass of the concentrated mother fluid will be added to form
concentrations of 1–6% by volume of nanoparticles in the EG/W base fluid.
Next, using a precision electronic mass balance the exact mass of the
concentrated mother nanofluid was measured by adding droplets of nanofluids
by a pipette. In the second phase, these dilute nanofluids in bottles were
sonicated in the ultrasonicator for 3 h, which has been found to be adequate
to break down the agglomerated particles. Then a small sample of the diluted
nanofluid is examined under the transmission electron microscope (TEM).
Figure 1 shows the TEM image of the
Al_{2}O_{3} nanofluid as an example. The particles are
perfectly spherical and vary in sizes from around 15 nm to about 70 nm. From
the particle size distribution, the average particle size of 45 nm specified
by the manufacturer seems to be accurate. No agglomeration of nanoparticles
was observed. Further details on the preparation of nanofluids,
ultrasonication process and characterization can be found from Refs. [3,26,27]. The sonicated
samples of nanofluid were used in the densometer, specific heat and thermal
conductivity apparatus and in the Brookfield viscometer for properties
measurement. The properties of nanoparticles are summarized in Table 3.

#### Density.

#### Specific Heat.

Vajjha and Das [26] conducted specific
heat measurements on three nanofluids (Al_{2}O_{3}, ZnO,
SiO_{2}) and developed a correlation given by Eq. (2), where the curve-fit
coefficients *A*, *B,* and *C* are shown in Table 4.

Nanofluid | A | B | C | Max. deviation % | Avg. absolute deviation % |
---|---|---|---|---|---|

Al_{2}O_{3} | 0.2432703 | 0.5179 | 0.4250 | 5 | 2.28 |

Nanofluid | A | B | C | Max. deviation % | Avg. absolute deviation % |
---|---|---|---|---|---|

Al_{2}O_{3} | 0.2432703 | 0.5179 | 0.4250 | 5 | 2.28 |

_{2}O

_{3}and ZnO nanoparticles were dispersed in 60:40 EG/W and the SiO

_{2}were dispersed in de-ionized water due to the gelling of the nanofluid. The authors used Eq. (3) presented by Xuan and Roetzl [30] to determine the specific heat for copper oxide and silicon dioxide dispersed in 60:40 ethylene glycol and water mixture.

#### Thermal Conductivity.

Vajjha and Das [3] experimentally determined the thermal conductivity of aluminum oxide, copper oxide, and zinc oxide nanofluids using the apparatus by PA Hilton that uses the steady state measurement technique. Koo and Kleinstreuer [1] had presented a thermal conductivity model for nanofluids that added a Brownian motion term to the conventional mixture conductivity model due to Maxwell. This is shown by Eq. (4). Following Koo and Kleinstreuer [1] model Vajjha and Das have developed similar correlations for nanoparticles dispersed in 60:40 EG/W mixture. The Eqs. (4) and (5) presented by them have an average deviation of 0.23%, 5.74%, and 1.97%, respectively, from the experimental data, for three nanofluids shown in Table 5. Sahoo [31] developed a correlation for silicon dioxide nanofluid using the same experimental setup. The correlations developed by these authors are given

Type of particles | β | Concentration |
---|---|---|

Al_{2}O_{3} | 8.4407 (100ϕ)^{−1.07304} | 1% ≤ ϕ ≤ 10% |

CuO | 9.881 (100ϕ)^{−0.9446} | 1% ≤ ϕ ≤ 6% |

SiO_{2} | 1.9526 (100ϕ)^{−1.4594} | 1% ≤ ϕ ≤ 10% |

Type of particles | β | Concentration |
---|---|---|

Al_{2}O_{3} | 8.4407 (100ϕ)^{−1.07304} | 1% ≤ ϕ ≤ 10% |

CuO | 9.881 (100ϕ)^{−0.9446} | 1% ≤ ϕ ≤ 6% |

SiO_{2} | 1.9526 (100ϕ)^{−1.4594} | 1% ≤ ϕ ≤ 10% |

#### Viscosity.

Vajjha et al. [28] proposed a
nondimensional correlation, Eq. (6) for three nanofluids (Al_{2}O_{3}, CuO,
SiO_{2}) dispersed in EG/W from 0 °C to 90 °C (Table 6) by combining the experimental data
from several researchers, Namburu et al. [32,33] and Sahoo et al.
[34]. The previous researchers
used Brookfield viscometer equipped with a computer controlled temperature
bath to measure viscosity of nanofluids.

Nanoparticle | A | B | Concentration |
---|---|---|---|

Al_{2}O_{3} | 0.983 | 12.959 | 1% ≤ ϕ ≤ 10% |

CuO | 0.9197 | 22.8539 | 1% ≤ ϕ ≤ 6% |

SiO_{2} | 1.0249 | 6.5972 | 1% ≤ ϕ ≤ 10% |

Nanoparticle | A | B | Concentration |
---|---|---|---|

Al_{2}O_{3} | 0.983 | 12.959 | 1% ≤ ϕ ≤ 10% |

CuO | 0.9197 | 22.8539 | 1% ≤ ϕ ≤ 6% |

SiO_{2} | 1.0249 | 6.5972 | 1% ≤ ϕ ≤ 10% |

## Automotive Radiator

The geometries of the automotive radiator used for computations in this study are those of a 1998 Subaru Forester or Impreza vehicle. The schematic geometry of the radiator is shown in Fig. 2. This radiator uses a serpentine-louvered fin design with a fin pitch of 24 fins/in (9.45 fins/cm). Table 7 lists the parameters and their values needed for the analysis of the performance of this radiator.

Parameter | Symbol | Unit | Value |
---|---|---|---|

Core matrix | Inline louvered fin | ||

Core geometry | L, _{r}H, _{r}D_{r} | m | 0.673 × 0.406 × 0.0163 |

Number of tubes | N | — | 52 |

Tube wall thickness | a | mm | 0.3302 |

Outside tube geometry | L, _{ot}H_{ot} | mm | 14.427 × 2.413 |

Inside tube geometry | L, _{it}H_{it} | mm | 13.767 × 1.753 |

Tube – Plate spacing | b_{c} | mm | 1.753 |

Tube and fin material | Aluminum (Alloy 2024-T6) | ||

Fin pitch | P | Fin/cm | 10.64 |

Fin – Plate spacing | b_{a} | mm | 6.35 |

Fin thickness | δ | mm | 0.152 |

Tube and fin thermal conductivity [24] | k_{f} | W/(m · K) | 177 |

Fin length | L_{f} | Mm | 3.175 |

Total transfer area/volume between plates^{a} | β | m^{2}/m^{3} | 2466 |

Fin area/total area^{a} | A_{ft} | — | 0.887 |

Air flow passage hydraulic diameter^{a} | D = 4_{h}_{,}_{a}r_{h}_{,}_{a} | mm | 1.423 |

Parameter | Symbol | Unit | Value |
---|---|---|---|

Core matrix | Inline louvered fin | ||

Core geometry | L, _{r}H, _{r}D_{r} | m | 0.673 × 0.406 × 0.0163 |

Number of tubes | N | — | 52 |

Tube wall thickness | a | mm | 0.3302 |

Outside tube geometry | L, _{ot}H_{ot} | mm | 14.427 × 2.413 |

Inside tube geometry | L, _{it}H_{it} | mm | 13.767 × 1.753 |

Tube – Plate spacing | b_{c} | mm | 1.753 |

Tube and fin material | Aluminum (Alloy 2024-T6) | ||

Fin pitch | P | Fin/cm | 10.64 |

Fin – Plate spacing | b_{a} | mm | 6.35 |

Fin thickness | δ | mm | 0.152 |

Tube and fin thermal conductivity [24] | k_{f} | W/(m · K) | 177 |

Fin length | L_{f} | Mm | 3.175 |

Total transfer area/volume between plates^{a} | β | m^{2}/m^{3} | 2466 |

Fin area/total area^{a} | A_{ft} | — | 0.887 |

Air flow passage hydraulic diameter^{a} | D = 4_{h}_{,}_{a}r_{h}_{,}_{a} | mm | 1.423 |

For simplicity, these surface geometry data (*β*, *A _{ft}*,
4

*r*) were taken from Kays and London [6] for a surface number of 27.03, which is the closest to the number of fins for this radiator.

_{h}_{,}_{a}### Surface Geometries.

Additional surface geometries are need for both the air and coolant side before performing an analysis. The equations below show how the surface geometries were calculated as presented by Kays and London [6].

Frontal area; *A _{fr}* (m

^{2})

Total transfer area/total exchanger volume; *α* (m^{2}/m^{3})

Total transfer area; *A _{t}* (m

^{2})

Free flow area/frontal area; *σ*

Free flow area; *A _{c}* (m

^{2})

Hydraulic diameter; *D _{h}* (

*m*)

## Thermal and Fluid Dynamic Calculations

The *ε* − NTU method was incorporated in Matlab coding to determine
thermal and fluid dynamic performance of the radiator. The method is outlined by
Kays and London [6] and Fig. 3 illustrates our implementation of the method.
The *ε* − NTU method usually does not require an iterative process,
but doing so provides better values for thermophysical properties of the fluid,
which gives a more accurate result, since nanofluids properties are sensitive to
temperature.

### Equations for the Air Side of the Radiator.

The following equations have been adopted from Kays and London [6]:

A correlation was developed for the Colburn Factor by curve-fitting the data from Kays and London [6] on inline louvered fins and is presented as below

### Equations for the Coolant Side of the Radiator

Nusselt number.

The thermal resistance of the tube wall
(*R _{t}* = (

*t*/

*kA*) = 1.80

*E*− 6

*K*/

*W*) was not included in the calculation. It is 100th of the mean values of either air (

*R*= 1/(

_{a}*η*

_{0}

*h*) = 6.37

_{a}A_{t}_{,}_{a}*E*− 4

*K*/

*W*) or coolant $(Rc=1/(hcAtc)=1.84E-4K/W)$ thermal resistance.

Friction factor

### Operational Parameters Selected as Inputs.

The real-world operational conditions of a radiator, such as inlet and outlet temperatures and flow rates for both coolant and air, must be used to derive meaningful results to compare performance of the radiator using different coolants. These practical data were collected from past literatures and summarized in Table 8 along with the current testing conditions.

Sources [7–10,15,37–40] | Test parameters used in computation | ||||
---|---|---|---|---|---|

Parameters | Min | Max | Min | Max | When held constant |

Air inlet temp (K) | 289 | 348 | 293 | 313 | 303 |

Coolant inlet temp (K) | 323 | 383 | 323 | 383 | 360 |

Air Reynolds numbers | 500 | 4000 | 500 | 2000 | 1000 |

Air mass flow rate (kg/s) | 0 | 20 | 1 | 4.6 | 2.3 |

Air face velocity (m/s) | 2 | 19 | 4 | 15 | 7.6 |

Coolant Reynolds number | 5000 | 7000 | 4500 | 6500 | 5500 |

Coolant mass flow rate (kg/s) | 0 | 3 | 1.8 | 2.5 | 2.08 |

Coolant flow velocity (m/s) | 0 | 3 | 1.38 | 1.96 | 1.6 |

Air - h (W/m_{a}^{2}K) | 200 | 267 | 139 | 350 | 221 |

Overall heat - U (W/m^{2}K) | 75 | 240 | 109 | 215 | 153 |

Q (kW) | 18 | 165 | 31 | 73 | 50 |

Sources [7–10,15,37–40] | Test parameters used in computation | ||||
---|---|---|---|---|---|

Parameters | Min | Max | Min | Max | When held constant |

Air inlet temp (K) | 289 | 348 | 293 | 313 | 303 |

Coolant inlet temp (K) | 323 | 383 | 323 | 383 | 360 |

Air Reynolds numbers | 500 | 4000 | 500 | 2000 | 1000 |

Air mass flow rate (kg/s) | 0 | 20 | 1 | 4.6 | 2.3 |

Air face velocity (m/s) | 2 | 19 | 4 | 15 | 7.6 |

Coolant Reynolds number | 5000 | 7000 | 4500 | 6500 | 5500 |

Coolant mass flow rate (kg/s) | 0 | 3 | 1.8 | 2.5 | 2.08 |

Coolant flow velocity (m/s) | 0 | 3 | 1.38 | 1.96 | 1.6 |

Air - h (W/m_{a}^{2}K) | 200 | 267 | 139 | 350 | 221 |

Overall heat - U (W/m^{2}K) | 75 | 240 | 109 | 215 | 153 |

Q (kW) | 18 | 165 | 31 | 73 | 50 |

Parameter | (a) | (b) | (c) | |||
---|---|---|---|---|---|---|

Fluid | Air | EG/W | Air | EG/W | Air | EG/W |

Inlet temperature (K) | 303.0 | 323.0 | 303.0 | 360.0 | 303.0 | 383.0 |

Outlet temperature (K) | 313.2 | 322.0 | 324.5 | 353.0 | 324.6 | 367.0 |

Average temperature (K) | 308.1 | 322.5 | 313.8 | 356.5 | 313.8 | 375.0 |

Reynolds number | 500 | 4500 | 1000 | 5500 | 2000 | 6500 |

Velocity (m/s) | 5.82 | 2.79 | 12.02 | 1.67 | 24.04 | 1.46 |

Volumetric flow rate (m^{3}/s) | 1.01 | 3.41 × 10^{−03} | 2.09 | 2.04 × 10^{−03} | 4.18 | 1.78 × 10^{−03} |

Mass flow rate (kg/s) | 1.16 | 3.64 | 2.35 | 2.13 | 4.69 | 1.83 |

Heat transfer coefficient (W/m^{2} K) | 130 | 5527 | 206 | 5266 | 321 | 5575 |

Thermal resistance (K/W) | 9.93 × 10^{−04} | 1.75 × 10^{−04} | 6.37 × 10^{−04} | 1.84 × 10^{−04} | 4.18 × 10^{−04} | 1.74 × 10^{−04} |

Thermal resistance ratio
(R/_{a}R)_{c} | 5.7 | 3.5 | 2.4 | |||

Overall heat trans. coef. (W/m^{2}K) | 108 | 153 | 212 | |||

Effectiveness | 0.51 | 0.38 | 0.27 | |||

NTU | 0.73 | 0.52 | 0.36 | |||

Heat dissipated (kW) | 11.8 | 50.9 | 101.9 | |||

Pressure loss (kPa) - Coolant | 34.97 | 11.54 | 8.25 | |||

Pumping power (W) - Coolant | 119.17 | 23.51 | 14.66 |

Parameter | (a) | (b) | (c) | |||
---|---|---|---|---|---|---|

Fluid | Air | EG/W | Air | EG/W | Air | EG/W |

Inlet temperature (K) | 303.0 | 323.0 | 303.0 | 360.0 | 303.0 | 383.0 |

Outlet temperature (K) | 313.2 | 322.0 | 324.5 | 353.0 | 324.6 | 367.0 |

Average temperature (K) | 308.1 | 322.5 | 313.8 | 356.5 | 313.8 | 375.0 |

Reynolds number | 500 | 4500 | 1000 | 5500 | 2000 | 6500 |

Velocity (m/s) | 5.82 | 2.79 | 12.02 | 1.67 | 24.04 | 1.46 |

Volumetric flow rate (m^{3}/s) | 1.01 | 3.41 × 10^{−03} | 2.09 | 2.04 × 10^{−03} | 4.18 | 1.78 × 10^{−03} |

Mass flow rate (kg/s) | 1.16 | 3.64 | 2.35 | 2.13 | 4.69 | 1.83 |

Heat transfer coefficient (W/m^{2} K) | 130 | 5527 | 206 | 5266 | 321 | 5575 |

Thermal resistance (K/W) | 9.93 × 10^{−04} | 1.75 × 10^{−04} | 6.37 × 10^{−04} | 1.84 × 10^{−04} | 4.18 × 10^{−04} | 1.74 × 10^{−04} |

Thermal resistance ratio
(R/_{a}R)_{c} | 5.7 | 3.5 | 2.4 | |||

Overall heat trans. coef. (W/m^{2}K) | 108 | 153 | 212 | |||

Effectiveness | 0.51 | 0.38 | 0.27 | |||

NTU | 0.73 | 0.52 | 0.36 | |||

Heat dissipated (kW) | 11.8 | 50.9 | 101.9 | |||

Pressure loss (kPa) - Coolant | 34.97 | 11.54 | 8.25 | |||

Pumping power (W) - Coolant | 119.17 | 23.51 | 14.66 |

## Results

### Verification of the Computational Scheme.

For verifying the accuracy of the Matlab script developed following the *ε* − NTU scheme described under Sec. 4, analyses of several test cases were performed. The
examples presented for truck radiator by Fraas [7] and an intercooler and regenerator by Kays and London [6] were computed using our code. A
comparison of important parameters such as pumping power, convective and overall
heat transfer coefficient, heat transfer rate, NTU and effectiveness obtained
from our computations agreed with the values presented by Fraas and Kays and
London within 1%. Additional verifications were performed using single phase
base fluid (EG/W 60:40) as coolant to prove that the computational scheme is
predicting results presented by other researchers for automotive radiators.

Shah and Sekulić [41] have presented that the maximum pumping power requirement of an automotive water pump for a midsize car should be around 300 W. Our calculations using the typical automobile input data for a Subaru radiator considered here are illustrated in Fig. 4, which shows a similar maximum pumping power requirement of 323 W at 323K with a Reynolds number of 6500 agreement.

Leong et al. [15]presented the air side
convective heat transfer coefficient to fall in the range of
200–260 W/m^{2}K for Re* _{a}* = 4000–6000.
The results of our computation are shown in Fig. 5, which predicts the air side convection of similar order of
magnitude. The difference is due to different fin designs; Leong et al. had
continuous plate fins, while we are using louvered-serpentine fins with a wide
range of air Reynolds number. The coolant Reynolds number has practically no
effect on the air convective heat transfer coefficient expect by the slight
change in thermophysical properties, therefore only one coolant Reynolds number
of Re

*= 5300 has been plotted for the air heat transfer coefficient. On overall heat transfer coefficient the air Reynolds number plays a more significant role than that of the coolant. This is due to the dominance of the air side thermal resistance. Oliet et al. [39] stated an upper bound of 240 W/m*

_{c}^{2}K and lower bound 110 W/m

^{2}K, for the overall heat transfer coefficient. Our computational results displayed in Fig. 5 show a close agreement within the bounds of 225–100 W/m

^{2}K.

In Fig. 6, we verify the ability of our computational scheme to predict the heat transfer rate properly. The effects of the coolant and air Reynolds numbers and the inlet temperature difference (ITD) have been examined on the heat transfer rate. As seen in the figure, the coolant Reynolds number has little effect on the heat transfer rate, while air Reynolds number show significant effect on the heat transfer rate, while the ITD plays an important role as expected, being the driving force for heat transfer. Our method predicts a maximum heat transfer rate of about 110 kW and a minimum of 12 KW. As a confirmation of these results, this range encompasses the values presented by other researchers. Computations by Maplesoft [42] for a radiator predicts 70.7 kW and Ecer et al. [37] predicted a range of 18–32 kW. Kreul [38] presented an approximation that the maximum heat transfer rate for our Subaru with an engine power of 135 hp, a heat dissipation of 95 kW. Our computation predicts a close value of 100 kW as the maximum heat dissipation for our modeled Subaru radiator.

In Fig. 7, we present the NTU and effectiveness values for comparison with those reported by Shah and Sekulić [41] and Maplesoft [42]. Shah stated the NTU and effectiveness for automotive radiators were approximately, 0.5% and 40%, respectively, which fall in the middle of our computed results shown in Fig. 7. Maplesoft's values of 0.9% and 50% for NTU and effectiveness respectively are at the upper region of our calculations. This may be due to the fact that their analysis is based on 50:50 EG/W, whereas our analysis is based on 60:40 EG/W. It is well-known that the thermophysical properties of 50:50 mixture is superior to those of 60:40 mixture as water has superior thermal properties than the EG.

Table 9 summarizes the thermal and fluid dynamic performance of the base fluid EG/W (60:40) in an automotive radiator for three operational scenarios: idling, city and highway, which correspond to the lowest, medium and highest performance cases. The idle scenario operates at the lowest ITD of 20 K and Reynolds number for air (500) and coolant (4500), which shows the lowest heat dissipation of 11.8 kW with the highest value of pumping power 120 W. The city or medium performance case shows an ITD of 57 K with reasonable Reynolds number of 1000 and 5500 for air and coolant, respectively. Here, we attain mid-level performance with dissipating 50.9 kW with a pumping power cost of 23.5 W. The highest or highway performance case shows the highest ITD of 80 K with the probably the upper range Reynolds numbers for air (2000) and the coolant (6500). At this case the heat transfer rate is at its maximum dissipation of 102 kW with the pumping power at the lowest value of 14.7 W. The three cases illustrated here prove the computational scheme's ability to predict the correct trend of the thermal and fluid dynamic performance of a radiator.

### Nanofluids Performance Evaluation.

After verifying the successful prediction of the developed computation scheme for base fluid, it was applied to evaluate performance of different nanofluids. The objective was to determine the optimal conditions for nanofluids to obtain the best performance. Four parameters can be varied to evaluate the performance of nanofluids:

Volumetric concentration:

*T*= 303_{i}_{,}_{a}*K*;*T*= 360_{i}_{,}_{c}*K*; Re= 1000; Re_{a}= 5500;_{c}*ϕ*= 1 − 6%Coolant inlet temperature:

*T*= 303_{i}_{,}_{a}*K*;*T*= 323–383_{i}_{,}_{c}*K*; Re= 1000; Re_{a}= 5500;_{c}*ϕ*= 1%Coolant Reynolds number:

*T*= 303_{i}_{,}_{a}*K*;*T*= 360_{i}_{,}_{c}*K*; Re= 1000; Re_{a}= 4500 − 6500;_{c}*ϕ*= 1%Air Reynolds numbers:

*T*= 303_{i}_{,}_{a}*K*;*T*= 360_{i}_{,}_{c}*K*; Re= 500–2000; Re_{a}= 5500;_{c}*ϕ*= 1%

The performance of nanofluids is then compared on two bases: constant surface area and constant pumping power, while maintaining equal heat dissipation. Using nanofluids in a heat exchanger can either decrease the pumping power of the current system or decrease the required surface area of the heat exchanger for a future system, for equal heat transfer rate of the base fluid. Using the following numerical scheme will determine the amount nanofluids can reduce the pumping power by:

- (1)
Assume initial mass flow rate ($m\xb7bf=m\xb7nf$) for nanofluid.

- (2)
Use the

*ε*− NTU analysis scheme outline in Sec. 4. - (3)
Determine mass flow rate of nanofluid for equal heat transfer: $Qbf=(m\xb7cp\Delta T)nf$

- (4)
Repeat process (1–4) with new mass flow rate until no noticeable change in mass flow rate is observed.

The second analysis using constant pumping power determines how much we can reduce the required surface area. This was accomplished using the following numerical scheme:

- (1)
Assume same heat transfer area (tube length) for nanofluids as base fluids

- (2)
Use the analysis scheme outline in Sec. 4.

- (3)
Determine heat transfer area required for same heat transfer rate as base fluid: NTU

_{bf}= (*UA*/*C*_{min})_{nf} - (4)
With new heat transfer area, calculate the required tube length of the heat exchanger

- (5)
Determine the maximum flow rate at which the nanofluid can perform with equal pumping power: $Wbf=(V\xb7\Delta P)nf$

- (6)
Repeat analysis (1–5) until no noticeable changes in tube length and flow rate are observed.

#### Performance Analysis on the Effects of Volumetric Concentration.

**Parameters:***T _{i}_{,}_{a}* = 303 K;

*T*= 360 K; Re

_{i}_{,}_{c}*= 1000; Re*

_{a}*= 5500;*

_{c}*ϕ*= 1–6%

The effects of volumetric concentration of nanoparticles on the performance of nanofluids are examined in Figs. 8 and 9. It is noted in nanofluid literature that increasing the particle concentration increases viscosity and thermal conductivity. An increase in viscosity will increase the Prandtl number but decrease the Reynolds number influencing heat transfer and pumping power. While an increase in thermal conductivity will increase the convection coefficient if the Nusselt number is maintained the same. These two properties are what make nanofluids thermal performance better than base fluid but can also hinder the performance.

##### Constant surface area and heat transfer rate.

Under equal heat dissipation, nanofluids will perform at a much lower
Reynolds as shown in Fig. 8. With a
1% concentration we see the Reynolds number drop as much as 25% compared
to the base fluid. Increasing the particle concentration will continue
to lower the nanofluids Reynolds number due to the increase in viscosity
of the fluid. SiO_{2} nanofluid, which has the least increase on
viscosity of the three nanofluids, shows the least amount of change but
reduces the Reynolds number by as much as 20%. The CuO Reynolds number
is much more affected by the particle concentration due to CuO having a
stronger effect on viscosity than Al_{2}O_{3}.

We can also observe in Fig. 8 that
increasing the concentration above 1% shows diminishing performance and
above 3% even Al_{2}O_{3} and SiO_{2} nanofluids
do not show a reduction in pumping power over the base fluid. This
analysis agrees with the earlier published results of Vajjha and Das
[27] that the particle
volumetric concentration is 1%, may be the optimal concentration for
nanofluids. The 1% concentration seems to increase the thermal
conductivity sufficiently, without increasing the viscosity much.

*E*is the friction power expended per unit of surface area, and for a given

*E*value, higher the heat transfer coefficient (

*h*), better thermal performance of the heat exchanger.

We have generated a similar plot following Kays and London, shown in Fig. 9 to compare the performance
between three nanofluids with a concentration of 1–3% and the base
fluid. The convective heat transfer coefficients were calculated from
Eq. (25)–(27) and friction factor
from Eqs. (33) and (34). From Fig. 9 we notice the 1%
Al_{2}O_{3} and CuO concentration provide the
highest heat transfer coefficients for a given *E* value,
but as we increase the concentration the performance diminishes. The
Al_{2}O_{3} nanofluid shows mild change with
increasing the concentration, while CuO nanofluid is greatly affected by
particle concentration, with losing about half of its performance gain
from 1% to 2% concentration. The SiO_{2} nanofluid is the least
influenced with increasing concentration, only diminishing the
performance minutely. From this analysis, we also reconfirm the thermal
performance gain of these three nanofluids lays within the concentration
range of 1–3%, with the exception of CuO which showed a diminished
performance, below the base fluid, at 3%.

#### Performance Analysis on the Effects of Coolant Inlet Temperatures.

**Parameters:***T _{i}_{,}_{a}* = 303 K;

*T*= 323–383 K; Re

_{i}_{,}_{c}*= 1000; Re*

_{a}*= 5500;*

_{c}*ϕ*= 1%

The next parameter analysis examines the effects of the coolant inlet temperature on the performance of nanofluid. Nanofluids' viscosity like base fluid is greatly affected by temperature, but unlike base fluid nanofluid thermal conductivity is significantly enhanced by temperature due to the Brownian motion of nanoparticles. Due to this significant change in thermophysical properties, exploring the performance of nanofluid in heat exchangers at various temperatures is necessary.

##### Constant surface area and heat transfer rate.

In Fig. 10, the reductions in
pumping power and volumetric flow rate for 1% concentration of
nanoparticles under the same surface area and heat transfer rate are
shown. The nanofluids exhibit better thermal performance at higher
temperatures. Lower volumetric flow by all three nanofluids, as much as
18%, in comparison to the base fluid achieve the same objective. In Fig. 10,
Al_{2}O_{3} shows the best performance with a
significant pumping power reduction of about 36%. For
Al_{2}O_{3} nanofluid, changing the inlet
temperature from 323 K to 383 K reduces the pumping power 33% and 36%,
respectively. Even, the SiO_{2} nanofluid observed to be the
lowest performer among the three nanofluids, promises a volumetric flow
reduction of 12% and pumping power reduction of about 27%. This
nanofluid maintains nearly constant characteristic over the coolant
inlet temperature range, because it has the least variation of viscosity
and thermal conductivity among the three nanofluids.

##### Constant pumping power and heat transfer rate.

Next, we examine how temperature affects the heat transfer performance of
nanofluid under a constant pumping power condition. From Fig. 11, we see the heat transfer
coefficient of nanofluids increase dramatically from about 19–30%,
18–29%, and 14–19% for Al_{2}O_{3}, CuO, and
SiO_{2}, respectively. This is due to the increase in
thermal conductivity from the Brownian motion with increase in coolant
inlet temperature. Furthermore, the viscosity decreases with an increase
in temperature causing the Reynolds number to rise, which leads to an
increase in Nusselt number from Eq. (26). The thermal performance of
Al_{2}O_{3} and CuO nanofluids are close. The
SiO_{2} nanofluid lags behind the other two, however, still
showing a significant performance 20% more than the base fluid.

With such high increases in the convective heat transfer coefficient, we
see a moderate increase in the overall heat transfer coefficient in Fig. 11. This is due to the fact
that the air side thermal resistance of the convective film is found to
be about 3.5 times greater than that on the coolant side. The overall
heat transfer coefficient increases by as much as 6% for either
Al_{2}O_{3} or CuO. This gain in the overall heat
transfer, translates to about 5.5% reduction in surface area of the
radiator at the higher coolant temperature for same heat transfer rate
and pumping power as the base fluid.

#### Performance Analysis on the Effects of Coolant Reynolds Number.

**Parameters**: *T _{i}_{,}_{a}* = 303 K;

*T*= 360 K; Re

_{i}_{,}_{c}*= 1000; Re*

_{a}*= 4500–6500;*

_{c}*ϕ*= 1%

The following analysis finds a specific flow regime where the performance gain using nanofluids is the highest by studying the effects of the coolant Reynolds number.

##### Constant surface area and heat transfer rate.

Computations carried out in the practical coolant Reynolds number range for the automotive radiator are shown in Fig. 12 to evaluate the effect on the volumetric flow rate and pumping power performance for three nanofluids. We observe as the Reynolds number is increased the performance gain of nanofluid diminishes from 40% reduction in pumping power to 32%. The diminishing effect influences all three nanofluids in the same proportion. The higher velocity associated with higher Reynolds number causes the pumping power to raise, because it is proportional to the cubic power of the velocity, thereby reducing the pumping power savings. Hence, the lower range of turbulent flow regime is desirable to gain the maximum benefit from using nanofluids.

##### Constant pumping power and heat transfer rate.

The effects of the coolant Reynolds number on convective heat transfer
coefficient, overall heat transfer coefficient and subsequently
determining the surface area reduction are studied next. From the Fig. 12, we noticed that nanofluids
performance diminished with increasing Reynolds number. We observe a
similar trend in Fig. 13 for heat
transfer coefficient gain. For Al_{2}O_{3} nanofluid,
the heat transfer enhancement is 31% at 4500 Reynolds number and 23% at
6500 Reynolds number, which is a significant enhancement in
performance.

Now, looking at the overall heat transfer coefficient performance in Fig. 13, one observes a reduction
in performance from 6.5% to 4%. This is due to two factors: diminishing
performance in heat transfer coefficient and the increasing difference
of thermal resistance between the air and the coolant side. The thermal
resistance ratio
(*R _{a}*/

*R*) starts at 2.8 for coolant Reynolds number of 4500 and increases to about 4.1 at Reynolds number of 6500. The higher the thermal resistance ratio the lower the impact of increasing the coolant heat transfer coefficient will have on the overall heat transfer coefficient. From this analysis, we conclude that nanofluids could save up to 6.2%, 6% or 4.7% using Al

_{c}_{2}O

_{3}, CuO or SiO

_{2}respectively in surface area reduction for the radiator.

#### Performance Analysis on the Effects of Air Reynolds Number.

**Parameters**: *T _{i}_{,}_{a}* = 303 K;

*T*= 360 K; Re

_{i}_{,}_{c}*= 500–2000; Re*

_{a}*= 5500;*

_{c}*ϕ*= 1%

##### Constant surface area and heat transfer rate.

As expected no appreciable change in the performance of nanofluids with varying the air Reynolds number from 500 to 2000 was noticed. Only a slight change in the performance ≤ 1% occurred due to the change in the average temperature of the nanofluid.

##### Constant pumping power and heat transfer rate.

The air Reynolds number plays a more vital role when looking at overall
heat transfer coefficient as shown in Fig. 14. We present how the coolant side heat transfer
coefficient and overall heat transfer coefficient are affected by the
air Reynolds number. The coolant heat transfer coefficient stays
relatively constant over the range of air Reynolds number with only very
marginal change, which is due to slight temperature change for the
coolant, but the overall heat transfer coefficient shows considerable
change. This is due to the change in the thermal resistance ratio
(*R _{a}*/

*R*) which decreases from 5.2 at Re

_{c}*= 500 to 2.3 at Re*

_{a}*= 2000, due to the increase in the air side convective heat transfer coefficient.*

_{a}As explained in Constant Pumping Power and Heat Transfer Rate Section,
the higher the resistance ratio the smaller the change in overall heat
transfer coefficient will be obtained from nanofluids. The reverse is
also true, the lower the thermal resistance ratio the greater the impact
of nanofluids on the overall heat transfer coefficient. The overall heat
transfer coefficient gain increased from 3.5% to 6.6% for
Al_{2}O_{3}. This trend is also true for the area
reduction possible with nanofluids, as evidenced in Fig. 15, where we observe changes from
3.3% to 6%, 3.2% to 5.9% or 2.4% to 4.4% for
Al_{2}O_{3}, CuO, and SiO_{2}, respectively.

### Performance Summary of Nanofluids.

From the knowledge of the analyses performed in preceding sections, we determined
the best case scenario for nanofluids performance gain when: *T _{i}_{,}_{c}* = 383 K;
Re

*= 2000; Re*

_{a}*= 5500, and*

_{c}*ϕ*= 1%. Using these parameters we performed the computations and summarized the performance of nanofluids in Fig. 16 (patterned bars). It is possible to save as much as 35.3% in pumping using Al

_{2}O

_{3}nanoparticles at a concentration of 1% or reduce the surface area/weight of the radiator by as much as 7.4%. As evidenced in earlier sections, and illustrated in Fig. 16 once again, Al

_{2}O

_{3}nanofluid out-performs the other nanofluids, but is closely matched by CuO nanofluid, which achieves savings in pumping power and area of 33.1% or 7.2%, respectively. Although not as spectacular, even SiO

_{2}nanofluid promises reduction in pumping power and surface area on the basis of equal heat transfer in comparison to the base fluid.

Furthermore, to achieve a comprehensive comparison, we analyzed a worst case
scenario for nanofluids using the following parameters: *T _{i}_{,}_{c}* = 323 K;
Re

*= 500; Re*

_{a}*= 6500, and*

_{c}*ϕ*= 1% presented the results in Fig. 16 (solid bars). It was found that, even for the worst case operational parameters, nanofluids prove their superior performance over the base fluid with reduction in the pumping power by 28.7%, 25.7%, or 21.6% for Al

_{2}O

_{3}, CuO, and SiO

_{2}, respectively. The percentage reduction in surface area is now a modest amount in the range of 1.1–1.5% for Al

_{2}O

_{3}. This is due to the dominance of the air side thermal resistance; the thermal resistance ratio (

*R*/

_{a}*R*) changes from 2.0 for the best case scenario to 8.5 for the worst case scenario.

_{c}### Material and Financial Reductions Estimation.

Consider aluminum oxide nanofluid of 1% volumetric concentration and use a conservative value of reducing the surface area of the radiator by 4%.The reduction in surface area is proportional to the reduction in radiator length and weight. The typical weight of the aluminum Subaru radiator examined in this study is approximately 15 pounds (6.8 kg). According to International Organization of Motor Vehicle Manufactures [5], approximately 60 million cars are produced worldwide yearly with the average cost of aluminum in 2012 $0.98 per pound[43]. We can then calculate the amount of material and cost saved by reducing the surface area of the radiator by 4%.

Amount of aluminum saved each year = (60 × 10

^{6})(15) (0.04) = 36 million poundsMoney saved = (3.6 × 10

^{7})(0.98) ≈ $35.3 million per year

This does not include lowering mining cost and lowering the impact on the environment.

## Conclusion

A detailed computational study was performed for an automotive radiator with three
different nanoparticles, Al_{2}O_{3}, CuO, and SiO_{2},
dispersed in the base fluid, EG/W 60:40 by mass. Realistic operational parameter
ranges were selected and used in computations for the inlet temperatures, air, and
coolant Reynolds number, from real world data presented by past researchers. The
computational scheme is based on the well-known *ε* − NTUmethod
encoded in matlab.

Several validation studies were performed with the computational scheme with the base fluid and the following parameters: pumping power, convective and overall heat transfer coefficients, heat dissipation, effectiveness, and NTU agreed with the results of previous researchers.

After the code validation, nanofluids performance comparisons were conducted
examining the effects of different parameters (volumetric concentration, coolant
inlet temperature, and air and coolant Reynolds numbers) to determine the most
optimal condition for nanofluids. From the analysis, it was determined that the
nanofluids have a superior performance gain at 1% volumetric concentration, higher
coolant inlet temperature, low turbulent flow regime in the tube preferably around
Re* _{c}* ≤ 5500 and air side Reynolds number around
Re

*≥ 1000. At the most optimal conditions of operation it is possible to reduce 35.3% in pumping power or increase the convective heat transfer coefficient by 29%, which in turn reduces the surface area by 7.4% using Al*

_{a}_{2}O

_{3}nanofluid. The CuO nanofluid showed slightly lower magnitudes than the Al

_{2}O

_{3}nanofluid, with 33.1% and 7.2% reduction for pumping power or surface area, respectively. The SiO

_{2}nanofluid had the least performance gain of the three nanofluids, but still could reduce the pumping power and surface area by 26.2% or 5.2%.

## Acknowledgment

Financial support from Alaska NASA and NSF EPSCoR and the Mechanical Engineering Department of University of Alaska Fairbanks is gratefully acknowledged.

*a*=tube wall thickness (m)

*A*=_{c}free flow area (m

^{2})*A*=_{ft}fin area/total area

*A*=_{fr}frontal area (m

^{2})*A*=_{t}heat transfer area (m

^{2})*A*,*B*,*C*,… =dimensionless curve-fit constants

*b*=plate spacing (m)

*C*=heat capacity rate (W/K)

*C** =capacity ratio

*c*=_{p}specific heat (J/kg · K)

*D*=depth (m)

*D*=_{h}hydraulic diameter (4

*r*, m)_{h}*d*=_{p}particle diameter (m)

*f*=friction factor

*h*=heat transfer coefficient (W/m

^{2}· K)*H*=height (m)

*j*=_{a}Colburn factor

*k*=thermal conductivity (W/m · K)

*L*=length (m)

- $m\xb7$ =
mass flow rate (kg/s)

*N*=number of tubes

- Nu =
Nusselt number

- NTU =
number transfer units

*P*=fin pitch (fins/cm)

- Pr =
Prandtl number

*Q*=heat dissipation (W)

*r*=_{h}hydraulic radius

*R*^{2}=coefficient of determination

- Re =
Reynolds number

*T*=temperature (K)

*T*_{0}=reference temp. (273 K)

*U*=overall heat transfer coefficient (W/m

^{2}· K)*V*=velocity (m/s)

- $V\xb7$ =
volumetric flow rate (m

^{3}/s)*V*=_{r}volume of radiator (m

^{3})- $W\xb7$ =
pumping power (W)

*α*=total transfer area/total exchanger volume (m

^{2}/m^{3})*β*=total transfer area/volume between plates (m

^{2}/m^{3})*δ*=fin thickness (m)

- Δ
*P*= pressure drop (Pa)

*ε*=heat exchanger effectiveness

*η*=fin efficiency

*η*_{0}=surface effectiveness

*κ*=Boltzmann constant (1.38 × 10

^{−23}*J*/K)*μ*=viscosity (Pa · s)

*ρ*=density (kg/m

^{3})*σ*=free flow area/frontal area

*ϕ*=volumetric concentration