Electro-magneto-hydrodynamic flow and radiative heat transfer of the non-Newtonian fluids through a porous micro-channel

This problem deals with steady driven pressure flow and heat transfer of electromagneto-hydrodynamic micro-pump of third-grade fluids between two micro-parallel plates embedded in a porous medium. The effects of thermal radiation and electrokinetics have been taken into account. The flow forced by the Lorentz force, produced by the interaction of a vertical magnetic field and an externally horizontal imposed electrical field, is assumed to be unidirectional and one dimensional. Based upon the velocity field, the thermally fully developed heat transfer with radiation effect is analyzed by taking the viscous dissipation, the volumetric heat generation due to the Joule heating effect and the electromagnetic couple effect into account. Analytical solutions using the perturbation method are obtained in series forms, under the assumption that the third-grade non-Newtonian parameter has small values. Using the homotopy perturbation method, approximate analytical solutions for any values of the third-grade non-Newtonian parameter were obtained. The effects of the permeability of the porous medium K, the dimensionless electrical strength parameter H, the Hartmann number Ha, the non-Newtonian parameter Lambda, the constant pressure P, the thermal radiation Nr, and the non-dimensional parameter Brinkman number gamma1 on the velocity and temperature are investigated graphically and discussed in detail.