Vorticity-Velocity Method for the Graetz Problem and the Effect of Natural Convection in a Horizontal Rectangular Channel With Uniform Wall Heat Flux

[+] Author and Article Information
F. C. Chou, G. J. Hwang

Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China

J. Heat Transfer 109(3), 704-710 (Aug 01, 1987) (7 pages) doi:10.1115/1.3248145 History: Received August 16, 1985; Online October 20, 2009


Numerical solutions given by a vorticity-velocity method are presented for combined free and forced laminar convection in the thermal entrance region of a horizontal rectangular channel without the assumptions of large Prandtl number and small Grashof number. The channel wall is heated with a uniform wall heat flux. Typical developments of temperature profile, secondary flow, and axial velocity at various axial positions in the entrance region are presented. Local friction factor and Nusselt number variations are shown for Rayleigh numbers Ra = 104 , 3×104 , 6×104 , and 105 with the Prandtl number as a parameter. The solution for the limiting case of large Prandtl number and small Grashof number obtained from the present study confirms the data of existing literature. It is observed that the large Prandtl number assumption is valid for Pr = 10 when Ra ≤ 3×104 but for a larger Prandtl number when the Rayleigh number is higher.

Copyright © 1987 by ASME
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