The Solution of Temperature Development in the Entrance Region of an MHD Channel by the B. G. Galerkin Method

Abstract

The general mathematical problem of MHD thermal entrance regions is formulated for a parallel plate channel by including Joule heating, viscous dissipation, and the effect of axial conduction. The associated eigenvalue problem is solved by the B. G. Galerkin method and the results are presented for constant wall temperature and constant wall heat flux conditions. It is shown that the particular method has distinct computational advantages over the classical form of solutions. The constant wall temperature case is investigated by employing the solutions of the eigenvalue problem and it is concluded that the axial conduction has considerable effect on the temperature development for low values of Peclet number.

Effects of viscous dissipation and fluid axial heat conduction on heat transfer for non-Newtonian fluids in ducts with uniform wall temperature

“…At a very large value of z*, the fully developed condition is reached. For ducts with uniform wall temperature the fully developed temperature is a function of y* alone [3][4][5]14]. Under this condition, h fd is analytically obtained as…”

“…However, their mathematical models and solution methods are different from the present work. LeCroy and Eraslan [5] and Lahjomri et al [6] treated a thermally developing laminar Hartman flow, and Min et al [7] and Nield et al [8] concerned a thermally developing flow of Bingham plastic and a porous medium, respectively.…”

“…Among the numerous literature on laminar heat transfer in ducts subjected to uniform wall temperature, to the authors' knowledge, the effects of both viscous dissipation and fluid axial heat conduction are discussed in [1][2][3][4][5][6][7][8].…”

Viscous Dissipation and Fluid Axial Heat Conduction Effect on the Heat Transfer to a Laminar Non-Newtonian Fluid Flow in Cylindrical Annular Duct with an Axially Moving Core

“…The thermal boundary condition at the outlet are not known explicitly. At the outlet or at the downstream infinity �𝜕𝜕 * 𝛽 𝛽�, the fluid temperature gradient in regard to the axial coordinate will tend to vanish, that is �𝜕𝜕𝜕𝜕 � /𝜕𝜕𝜕𝜕 * � 0� [26], [23], [36], [37] and the temperature at the outlet is a particular solution of the energy equation Eq. ( 7) as - 129 -…”