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TECHNICAL PAPERS

# Mixed Convection From a Heated Square Cylinder to Newtonian and Power-Law Fluids

[+] Author and Article Information
A. K. Dhiman, N. Anjaiah

Department of Chemical Engineering,  Indian Institute of Technology, Kanpur 208016, India

R. P. Chhabra1

Department of Chemical Engineering,  Indian Institute of Technology, Kanpur 208016, Indiachhabra@iitk.ac.in

V. Eswaran

Department of Mechanical Engineering,  Indian Institute of Technology, Kanpur 208016, India

1

Corresponding author.

J. Fluids Eng 129(4), 506-513 (Sep 28, 2006) (8 pages) doi:10.1115/1.2436586 History: Received May 10, 2006; Revised September 28, 2006

## Abstract

Steady laminar mixed convection flow and heat transfer to Newtonian and power-law fluids from a heated square cylinder has been analyzed numerically. The full momentum and energy equations along with the Boussinesq approximation to simulate the buoyancy effects have been solved. A semi-explicit finite volume method with nonuniform grid has been used for the range of conditions as: Reynolds number 1–30, power-law index: 0.8–1.5, Prandtl number 0.7–100 $(Pe⩽3000)$ for Richardson number 0–0.5 in an unbounded configuration. The drag coefficient and the Nusselt number have been reported for a range of values of the Reynolds number, Prandtl number, and Richardson number for Newtonian, shear-thickening $(n>1)$ and shear-thinning $(n<1)$ fluids. In addition, detailed streamline and isotherm contours are also presented to show the complex flow field, especially in the rear of the cylinder. The effects of Prandtl number and of power-law index on the Nusselt number are found to be more pronounced than that of buoyancy parameter $(Ri⩽0.5)$ for a fixed Reynolds number in the steady cross-flow regime $(Re⩽30)$.

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## Figures

Figure 1

Schematics of the flow across a square cylinder

Figure 2

Streamline profiles for Re=5 and 30, Ri=0.5, and Pr=1 at different values of n

Figure 3

Isotherm profiles for Re=5 and 30, Ri=0.5, and Pr=1 at different values of n

Figure 4

Streamline profiles for Re=30, for Ri=0.25, and 0.5 at different Prandtl numbers

Figure 5

Isotherm profiles for Re=30, for Ri=0.25, and 0.5 at different Prandtl numbers

Figure 6

Variation of CD and CL with Re at different Ri and Pr. The dashed line presents the results for Ri=0 case.

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