Heat transfer by magnetohydrodynamic laminar flow in circular pipe

This paper presents the influence of magnetic field on heat due to viscous and electrical dissipations for an incompressible, viscous, electrically conducting fluid through a circular pipe in the presence of an applied (transverse) uniform magnetic field. The walls of the pipe are assumed to be non-conducting and kept at uniform temperature gradient in one case and at a constant temperature gradient in another case. The heat equation governing the present problem is solved exactly in hypergeometric series. The temperature at the centre of the pipe T_e, unweighted mean temperature T_m and weight mean temperature T_M are calculated. The temperature profiles are shown graphically for different values of Hartmann number M, Brinkman number B_r and a non-dimensional number S. Numerical calculations are made for the Nusselt number and are entered in the table.