Heat transfer in laminar flow in a uniformly porous channel with an applied transverse magnetic field

Summary The steady laminar flow of an incompressible, viscous, and electrically conducting fluid between two parallel porous plates with equal permeability has been discussed by Terrill and Shrestha [6]. In this paper, using the solution of [6] for the velocity field, the heat transfer problems of (i) uniform wall temperature and (ii) uniform heat flux at wall are solved.For small suction Reynolds numbers we find that the Nusselt number, with increasing Reynolds number, increases for case (i) and decreases for (ii).Nomenclature stream function - 2h channel width - x, y distances measured parallel, perpendicular to the channel walls - U velocity of fluid in the x direction at x=0 - V constant velocity of suction at the wall - nondimensional distance, y/h - nondimensional distance, x/h - f() function defined in (1) - density - coefficient of kinematic viscosity - R suction Reynolds number, V h/ - Re channel Reynolds number, 4U h/ - B₀ magnetic induction - electrical conductivity - M Hartmann number, B₀h(/)^1/2 - K constant defined in (3) - A constant defined in (5) - 4R/Re - q local heat flux per unit area at the wall - k thermal conductivity - T temperature of the fluid - X –1/ ln(1–) - C_p specific heat at constant pressure - j current density - Pr Prandtl number, C_p/k - P mass transfer Péclet number, R Pr - Pe mass transfer Péclet number, P/ - T₀ temperature at x=0 - T_H() temperature in the fully developed region - T_h(X, ) temperature in the entrance region - Y_n() eigenfunctions, uniform wall temperature - _n eigenvalues - e() function defined by (24) - B_n 2/3_n² - A_n constants defined by (28) - a_2m constants defined by (30) - F_n() eigenfunctions, uniform wall heat flux - a_n, b_n, c_n, d_n, e_n constants defined by (45) and (48) - S a parameter, U²/q - h₁ heat transfer coefficient - T_m mean temperature - Nu Nusselt number - Nu_T Nusselt number, uniform wall temperature - Nu_q Nusselt number, uniform wall heat flux