On Combined Free and Forced Convection in Channels

Abstract

The heat-transfer problems of combined free and forced convection by a fully developed laminar flow in a vertical channel of constant axial wall temperature gradient with or without heat generations are approached by a new method. By introducing a complex function which is directly related to the velocity and temperature fields, the coupled momentum and energy equations are readily combinable to a Helmholtz wave equation in the complex domain. This greatly reduces the complexities of the problems. For illustrations, the cases of flows between parallel plates and in a rectangular channel are treated. It shows that this method is more direct and powerful than those of previous investigations.

Pressure work and viscous dissipation in the equations of thermal convection in a vertical channel

“…in which the temperature profile is given relative to the fixed wall temperature, indicated by subscript w. The solution (37) and (38) is mathematically similar to that obtained by Tao [14] for the case where a uniform streamwise temperature gradient is imposed. Without boundary constraints, pressure work would produce a vertical (adiabatic) lapse rate in the temperature: thus Tao's analysis with an imposed vertical temperature gradient but no pressure work replicates our analysis which includes pressure work but specifies vertically uniform temperature.…”

Flow Reversal of Fully Developed Mixed Convection in a Vertical Channel with Chemical Reaction

“…A combined forced and natural convective flow puts on the situation where an externally driven flow joins with an native buoyant flow and when both are prominent. One of the earliest studies on mixed convection in a vertical channel with uniform wall temperatures had been studied analytically by Tao [1]. Then Habchi and Acharya [2] studied mixed convection in a vertical channel with asymmetric walls heating, where one plate is heated and the other is adiabatic.…”

Multiple Solutions of Mixed Convective MHD Casson Fluid Flow in a Channel

“…Design of MHD power generators, nuclear waste processing, and distribution of chemical waste control are some most conspicuous applications among all. The problem of laminar fully developed mixed convection flow in a channel was followed back to 1960 by Tao [9]. Recently, Fersadou et al [10] investigated the problem of MHD mixed convection flow of nanofluid in a vertical porous channel numerically.…”