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

Abstract

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.

Onset of secondary flow and enhancement of heat transfer in horizontal convergent and divergent channels heated from below

“…From the review of literature, it appears that the results obtained for the critical Rayleigh number for the initiation of the plume, the number of plume produced and the heat transfer characteristic between the experiments with water and the ones with air are different. Numerical studies were also performed to study the occurrence and the structure of the secondary flow and the enhancement of heat transfer in both the developing and fully developed regions [17][18][19][20][21][22][23]. The trends obtained in general are consistent with the experimental observations.…”

Mixed convection heat transfer in horizontal rectangular ducts with radiation effects

“…Therefore, the computations with grid distribution of 51 Â 51(1 Â 10 À5 -2 Â 10 À4 ) are considered to be sufficiently accurate to describe the flow and heat transfer in a horizontal rectangular duct. As a partial verification of the computational procedure, results were initially obtained for convection heat transfer in a horizontal rectangular duct without thermal radiation effect and compared with those of Chou and Hwang [8]. The Nusselt number and friction factor were found to agree within 2%.…”

“…Massive amount of works, both theoretical and experimental, have been done on mixed convection heat transfer in internal laminar or turbulent flows [1][2][3][4][5][6][7][8]. Cheng et al [9], Ou et al [10] and Cheng and Ou [11] employed the assumption of large Prandtl number to study the mixed convection heat transfer in the thermal entrance region of horizontal rectangular channels.…”

Mixed Convection in a Horizontal Square Packed-Sphere Channel Under Axially Uniform Heating Peripherally Uniform Wall Temperature

“…Notably, all of the above works pertain to the thermally fully developed region. The thermal boundary conditions on the treated entrance problems have included uniform wall heat flux through the wall in the axial and peripheral directions [13,14] or isothermal ducts [15,16]. Literature on the packed-sphere channel in the entrance region is very limited.…”