magnetohydrodynamics fluid flow and heat transfer over a permeable shrinking sheet with joule dissipation: analytical approach

A laminar, two dimensional, steady boundary layer newtonian conducting fluid flow passes over a permeable shrinking sheet in the presence of a uniform magnetic field is investigated. the governing equations have converted to ordinary nonlinear differential equations (ode) by using appropriate similarity transformations. the main idea is to transform ode with infinite boundary condition into other sets of variables in a way that infinite boundary condition becomes a finite boundary condition. the effects of physical parameters affecting the velocity and temperature are shown. the results show that with increasing the magnetic and suction parameters, the normal velocity component of fluid increases over the sheet whereas the tangential velocity component of fluid decreases. moreover, when the suction parameter, the prandtl and eckert numbers increase, the rate of the heat transfer increases. however, when the magnetic parameter increases, the rate of heat transfer reduces. finally, the solution shows that the results of the analytical method using a special technique have an excellent agreement with numerical solutions.