Abstract
The focus of this paper is to study the effects of stagnation point flow and porous medium on ferrofluid flow over a variable thicked sheet. Heat transfer analysis is discussed by including thermal radiation. Suitable transformations are applied to convert partial differential equations to ordinary differential equations. Convergent results for series solutions are calculated. The impact of numerous parameters on velocity and temperature is displayed for series solutions. Graphical behavior for skin friction coefficient and Nusselt number is also analyzed. Numerical values of Nusselt number are tabulated depending upon various parameters
Issue Section:
Porous Media
References
1.
Selimefendigil
,
F.
, and
Oztop
,
H. F.
, 2014
, “
Effect of a Rotating Cylinder in Forced Convection of Ferrofluid Over a Backward Facing Step
,” Int. J. Heat Mass Transfer
, 71, pp. 142
–148
.10.1016/j.ijheatmasstransfer.2013.12.0422.
Abbas
,
Z.
, and
Sheikh
,
M.
, 2017
, “
Numerical Study of Homogeneous–Heterogeneous Reactions on Stagnation Point Flow of Ferrofluid With Non-Linear Slip Condition
,” Chin. J. Chem. Eng.
,
25
(1
), pp. 11
–17
.10.1016/j.cjche.2016.05.0193.
Sheikholeslami
,
M.
,
Rashidi
,
M. M.
, and
Ganji
,
D. D.
, 2015
, “
Effect of Non-Uniform Magnetic Field on Forced Convection Heat Transfer of Image–Water Nanofluid
,” Comput. Methods Appl. Mech. Eng.
,
294
, pp. 299
–312
.10.1016/j.cma.2015.06.0104.
Ram
,
P.
, and
Sharma
,
K.
, 2011
, “
Revolving Ferrofluid Flow Under the Influence of MFD Viscosity and Porosity With Rotating Disk
,” J. Electromagn. Anal. Appl.
,
3
(9
), pp. 378
–386
.10.4236/jemaa.2011.390605.
Sheikholeslami
,
M.
, and
Shehzad
,
S. A.
, 2017
, “
Thermal Radiation of Ferrofluid in Existence of Lorentz Forces Considering Variable Viscosity
,” Int. J. Heat Mass Transfer
,
109
, pp. 82
–92
.10.1016/j.ijheatmasstransfer.2017.01.0966.
Zeeshan
,
A.
,
Majeed
,
A.
, and
Ellahi
,
R.
, 2016
, “
Effect of Magnetic Dipole on Viscous Ferro-Fluid Past a Stretching Surface With Thermal Radiation
,” J. Mol. Liq.
,
215
, pp. 549
–554
.10.1016/j.molliq.2015.12.1107.
Hayat
,
T.
,
Qayyum
,
S.
,
Imtiaz
,
M.
,
Alzahrani
,
F.
, and
Alsaedi
,
A.
, 2016
, “
Partial Slip Effect in Flow of Magnetite Fe3O4 Nanoparticles Between Rotating Stretchable Disks
,” J. Magn. Magn. Mater.
,
413
, pp. 39
–48
.10.1016/j.jmmm.2016.04.0258.
Majeed
,
A.
,
Zeeshan
,
A.
, and
Ellahi
,
R.
, 2016
, “
Unsteady Ferromagnetic Liquid Flow and Heat Transfer Analysis Over a Stretching Sheet With the Effect of Dipole and Prescribed Heat Flux
,” J. Mol. Liq.
,
223
, pp. 528
–533
.10.1016/j.molliq.2016.07.1459.
Sheikholeslami
,
M.
, and
Rokni
,
H. B.
, 2017
, “
Nanofluid Two Phase Model Analysis in Existence of Induced Magnetic Field
,” Int. J. Heat Mass Transfer
,
107
, pp. 288
–299
.10.1016/j.ijheatmasstransfer.2016.10.13010.
Turkyilmazoglu
,
M.
, 2012
, “
Exact Analytical Solutions for Heat and Mass Transfer of MHD Slip Flow in Nanofluids
,” Chem. Eng. Sci.
,
84
, pp. 182
–187
.10.1016/j.ces.2012.08.02911.
Rashidi
,
M. M.
,
Nasiri
,
M.
,
Khezerloo
,
M.
, and
Laraqi
,
N.
, 2016
, “
Numerical Investigation of Magnetic Field Effect on Mixed Convection Heat Transfer of Nanofluid in a Channel With Sinusoidal Walls
,” J. Magn. Magn. Mater.
,
401
, pp. 159
–168
.10.1016/j.jmmm.2015.10.03412.
Sheremet
,
M. A.
,
Pop
,
I.
, and
Roşca
,
N. C.
, 2016
, “
Magnetic Field Effect on the Unsteady Natural Convection in a Wavy-Walled Cavity Filled With a Nanofluid: Buongiorno's Mathematical Model
,” J. Taiwan Inst. Chem. Eng.
,
61
, pp. 211
–222
.10.1016/j.jtice.2015.12.01513.
Hayat
,
T.
,
Khan
,
M. I.
,
Waqas
,
M.
,
Alsaedi
,
A.
, and
Farooq
,
M.
, 2017
, “
Numerical Simulation for Melting Heat Transfer and Radiation Effects in Stagnation Point Flow of Carbon–Water Nanofluid
,” Comput. Methods Appl. Mech. Eng.
,
315
, pp. 1011
–1024
.10.1016/j.cma.2016.11.03314.
Awais
,
M.
,
Malik
,
M. Y.
,
Bilal
,
S.
,
Salahuddin
,
T.
, and
Hussain
,
A.
, 2017
, “
Magnetohydrodynamic (MHD) Flow of Sisko Fluid Near the Axisymmetric Stagnation Point Towards a Stretching Cylinder
,” Results Phys.
,
7
, pp. 49
–56
.10.1016/j.rinp.2016.10.01615.
Mabood
,
F.
,
Shafiq
,
A.
,
Hayat
,
T.
, and
Abelman
,
S.
, 2017
, “
Radiation Effects on Stagnation Point Flow With Melting Heat Transfer and Second Order Slip
,” Results Phys.
,
7
, pp. 31
–42
.10.1016/j.rinp.2016.11.05116.
Turkyilmazoglu
,
M.
, and
Pop
,
I.
, 2013
, “
Exact Analytical Solutions for the Flow and Heat Transfer Near the Stagnation Point on a Stretching/Shrinking Sheet in a Jeffrey Fluid
,” Int. J. Heat Mass Transfer
,
57
(1
), pp. 82
–88
.10.1016/j.ijheatmasstransfer.2012.10.00617.
Jalilpour
,
B.
,
Jafarmadar
,
S.
,
Ganji
,
D. D.
,
Shotorban
,
A. B.
, and
Taghavifar
,
H.
, 2014
, “
Heat Generation/Absorption on MHD Stagnation Flow of Nanofluid Towards a Porous Stretching Sheet With Prescribed Surface Heat Flux
,” J. Mol. Liq.
,
195
, pp. 194
–204
.10.1016/j.molliq.2014.02.02118.
Khan
,
W. A.
, and
Pop
,
I.
, 2010
, “
Flow Near the Two-Dimensional Stagnation Point on an Infinite Permeable Wall With a Homogeneous–Heterogeneous Reaction
,” Commun. Nonlinear Sci. Numer. Simul.
,
15
(11
), pp. 3435
–3443
.10.1016/j.cnsns.2009.12.02219.
You
,
L. H.
,
Tang
,
Y. Y.
,
Zhang
,
J. J.
, and
Zheng
,
C. Y.
, 2000
, “
Numerical Analysis of Elastic-Plastic Rotating Disks With Arbitrary Variable Thickness and Density
,” Int. J. Solids Struct.
,
37
(52
), pp. 7809
–7820
.10.1016/S0020-7683(99)00308-X20.
Subhashini
,
S. V.
,
Sumathi
,
R.
, and
Pop
,
I.
, 2013
, “
Dual Solutions in a Thermal Diffusive Flow Over a Stretching Sheet With Variable Thickness
,” Int. Commun. Heat Mass Transfer
,
48
, pp. 61
–66
.10.1016/j.icheatmasstransfer.2013.09.00721.
Farooq
,
M.
,
Anjum
,
A.
,
Hayat
,
T.
, and
Alsaedi
,
A.
, 2016
, “
Melting Heat Transfer in the Flow Over a Variable Thicked Riga Plate With Homogeneous-Heterogeneous Reactions
,” J. Mol. Liq.
,
224
, pp. 1341
–1347
.10.1016/j.molliq.2016.10.12322.
Bayat
,
M.
,
Rahimi
,
M.
,
Saleem
,
M.
,
Mohazzab
,
A. H.
,
Wudtke
,
I.
, and
Talebi
,
H.
, 2014
, “
One Dimensional Analysis for Magneto-Thermo-Mechanical Response in a Functionally Graded Annular Variable-Thickness Rotating Disk
,” Appl. Math. Modell.
,
38
(19–20
), pp. 4625
–4639
.10.1016/j.apm.2014.03.00823.
Wahed
,
M. S. A.
,
Elbashbeshy
,
E. M. A.
, and
Emam
,
T. G.
, 2015
, “
Flow and Heat Transfer Over a Moving Surface With Non-Linear Velocity and Variable Thickness in a Nanofluids in the Presence of Brownian Motion
,” Can. J. Phys.
,
254
, pp. 49
–62
.10.1016/j.amc.2014.12.08724.
Xun
,
S.
,
Zhao
,
J.
,
Zheng
,
L.
,
Chen
,
X.
, and
Zhang
,
X.
, 2016
, “
Flow and Heat Transfer of Ostwald-De Waele Fluid Over a Variable Thickness Rotating Disk With Index Decreasing
,” Int. J. Heat Mass Transfer
,
103
, pp. 1214
–1224
.10.1016/j.ijheatmasstransfer.2016.08.06625.
Rashidi
,
M. M.
,
Pour
,
S. A. M.
, and
Abbasbandy
,
S.
, 2011
, “
Analytic Approximate Solutions for Heat Transfer of a Micropolar Fluid Through a Porous Medium With Radiation
,” Commun. Nonlinear Sci. Numer. Simul.
,
16
(4
), pp. 1874
–1889
.10.1016/j.cnsns.2010.08.01626.
Hayat
,
T.
,
Imtiaz
,
M.
,
Alsaedi
,
A.
, and
Mansoor
,
R.
, 2014
, “
MHD Flow of Nanofluids Over an Exponentially Stretching Sheet in a Porous Medium With Convective Boundary Conditions
,” Chin. Phys. B
,
23
(5
), p. 054701
.10.1088/1674-1056/23/5/05470127.
Hayat
,
T.
, and
Abbas
,
Z.
, 2008
, “
Heat Transfer Analysis on the MHD Flow of a Second Grade Fluid in a Channel With Porous Medium
,” Chaos, Solitons Fractals
,
38
, pp. 556
–567
.10.1016/j.chaos.2006.12.00428.
Ellahi
,
R.
, and
Afzal
,
S.
, 2009
, “
Effects of Variable Viscosity in a Third Grade Fluid With Porous Medium: An Analytic Solution
,” Commun. Nonlinear Sci. Numer. Simul.
,
14
(5
), pp. 2056
–2072
.10.1016/j.cnsns.2008.05.00629.
Mabood
,
F.
,
Shateyi
,
S.
,
Rashidi
,
M. M.
,
Momoniat
,
E.
, and
Freidoonimehr
,
N.
, 2016
, “
MHD Stagnation Point Flow Heat and Mass Transfer of Nanofluids in Porous Medium With Radiation, Viscous Dissipation and Chemical Reaction
,” Adv. Powder Technol.
,
27
(2
), pp. 742
–749
.10.1016/j.apt.2016.02.03330.
Makinde
,
O. D.
, and
Animasaun
,
I. L.
, 2016
, “
Thermophoresis and Brownian Motion Effects on MHD Bioconvection of Nanofluid With Nonlinear Thermal Radiation and Quartic Chemical Reaction Past an Upper Horizontal Surface of a Paraboloid of Revolution
,” J. Mol. Liq.
,
221
, pp. 733
–743
.10.1016/j.molliq.2016.06.04731.
Rashidi
,
M. M.
,
Ganesh
,
N. V.
,
Hakeem
,
A. K. A.
, and
Ganga
,
B.
, 2014
, “
Buoyancy Effect on MHD Flow of Nanofluid Over a Stretching Sheet in the Presence of Thermal Radiation
,” J. Mol. Liq.
,
198
, pp. 234
–238
.10.1016/j.molliq.2014.06.03732.
Hayat
,
T.
,
Imtiaz
,
M.
,
Alsaedi
,
A.
, and
Kutbi
,
M. A.
, 2015
, “
MHD Three-Dimensional Flow of Nanofluid With Velocity Slip and Nonlinear Thermal Radiation
,” J. Magn. Magn. Mater.
,
396
, pp. 31
–37
.10.1016/j.jmmm.2015.07.09133.
Hayat
,
T.
,
Imtiaz
,
M.
,
Alsaedi
,
A.
, and
Ahmad
,
B.
, 2016
, “
Convective Flow of Carbon Nanotubes Between Rotating Stretchable Disks With Thermal Radiation Effects
,” Int. J. Heat Mass Transfer
,
101
, pp. 948
–957
.10.1016/j.ijheatmasstransfer.2016.05.11434.
Abbasbandy
,
S.
, and
Shivanian
,
E.
, 2011
, “
Predictor Homotopy Analysis Method and Its Application to Some Nonlinear Problems
,” Commun. Nonlinear Sci. Numer. Simul.
,
16
(6
), pp. 2456
–2468
.10.1016/j.cnsns.2010.09.02735.
Abbasbandy
,
S.
,
Shivanian
,
E.
, and
Vajravelu
,
K.
, 2011
, “
Mathematical Properties of Image-Curve in the Frame Work of the Homotopy Analysis Method
,” Commun. Nonlinear Sci. Numer. Simul.
,
16
(11
), pp. 4268
–4275
.10.1016/j.cnsns.2011.03.03136.
Abbasbandy
,
S.
, and
Shirzadi
,
A.
, 2011
, “
A New Application of the Homotopy Analysis Method: Solving the Sturm–Liouville Problems
,” Commun. Nonlinear Sci. Numer. Simul.
,
16
(1
), pp. 112
–126
.10.1016/j.cnsns.2010.04.00437.
Ellahi
,
R.
,
Raza
,
M.
, and
Vafai
,
K.
, 2012
, “
Series Solutions of Non-Newtonian Nanofluids With Reynolds Model and Vogel's Model by Means of the Homotopy Analysis Method
,” Math. Comput. Modell.
,
55
(7–8
), pp. 1876
–1891
.10.1016/j.mcm.2011.11.04338.
Kumari
,
M.
,
Pop
,
I.
, and
Nath
,
G.
, 2010
, “
Transient MHD Stagnation Flow of a Non-Newtonian Fluid Due to Impulsive Motion From Rest
,” Int. J. Non-Linear Mech.
,
45
(5
), pp. 463
–473
.10.1016/j.ijnonlinmec.2010.01.00239.
Esmaeilpour
,
M.
, and
Ganj
,
D. D.
, 2010
, “
Solution of the Jeffery-Hamel Flow Problem by Optimal Homotopy Asymptotic Method
,” Comput. Math. Appl.
,
59
(11
), pp. 3405
–3411
.10.1016/j.camwa.2010.03.02440.
Imtiaz, M., Alsaedi, A., Shafiq, A.,
and Hayat
,
T.
, 2017
, “
Impact of Chemical Reaction on Third Grade Fluid Flow With Cattaneo-Christov Heat Flux
,” J. Mol. Liq.
,
229
, pp. 501
–507
.10.1016/j.molliq.2016.12.10341.
Mushtaq
,
A.
,
Khan
,
J. A.
,
Mustafa
,
M.
,
Hayat
,
T.
, and
Alsaedi
,
A.
, 2018
, “
Consequences of Convection-Radiation Interaction for Magnetite-Water Nanofluid Flow Due to a Moving Plate
,” Therm. Sci.
, 22(1), pp. 443
–451
.https://pdfs.semanticscholar.org/ec3e/b6c4181542a66004d25b36a378c8c08002fd.pdf42.
Turkyilmazoglu
,
M.
, 2017
, “
Magnetohydrodynamics Two-Phase Dusty Fluid Flow and Heat Model Over Deforming Isothermal Surfaces
,” Phys. Fluids
,
29
(1
), p. 013302
.10.1063/1.496592643.
Turkyilmazoglu
,
M.
, 2015
, “
Anomalous Heat Transfer Enhancement by Slip Due to Nanofluids in Circular Concentric Pipes
,” Int. J. Heat Mass Transfer
,
85
, pp. 609
–614
.10.1016/j.ijheatmasstransfer.2015.02.01544.
Turkyilmazoglu
,
M.
, 2015
, “
A Note on the Correspondence Between Certain Nanofluid Flows and Standard Fluid Flows
,” ASME J. Heat Transfer
,
137
(2
), p. 024501
.10.1115/1.402880745.
Turkyilmazoglu
,
M.
, 2018
, “
Convergence Accelerating in the Homotopy Analysis Method: A New Approach
,” Adv. Appl. Math. Mech.
,
10
(4
), pp. 925
–947
.10.4208/aamm.OA-2017-019646.
Turkyilmazoglu
,
M.
, 2017
, “
Parametrized Adomian Decomposition Method With Optimum Convergence
,” Trans. Modell. Comput. Simul.
,
27
(4
), pp. 1
–22
.Copyright © 2019 by ASME
You do not currently have access to this content.