Analytical solution to the problem of heat transfer in an MHD flow inside a channel with prescribed sinusoidal wall heat flux

An MHD laminar flow through a two dimensional channel subjected to a uniform magnetic field and heated at the walls of the conduit over the whole length with a sinusoidal heat flux of vanishing mean value or not, is studied analytically. General expressions of the temperature distribution and of the local and mean Nusselt numbers are obtained by using the technique of linear operators in the case of negligible Joule and viscous dissipation and by taking into account the axial conduction effect. The principal results show that an increase of the local Nusselt number with Hartmann number is observed, and, far from the inlet section, the average heat transfer between the fluid and the walls shows a significant improvement at all values of Hartmann number used when the frequency of the prescribed sinusoidal wall heat flux is increasing in the case of vanishing mean value of the heat flux and this is true especially at low Peclet numbers.