the influence of heat transfer on peristaltic transport of mhd second grade fluid through porous medium in a vertical asymmetric channel

In this paper, we study the influence of heat transfer on the peristaltic transport of an incompressible magnetohydrodynamic second grade fluid in vertical symmetric and asymmetric channels. the channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. the flow is investigated in the wave frame of reference moving with velocity of the wave. perturbation solutions are obtained for the stream function, temperature and pressure gradient under long wave length assumption. pressure difference and frictional force are discussed through numerical integration. the influence of various parameters of interest on the flow are discussed and also the graphical results are obtained for different wave forms.