Electromagnetohydrodynamic flow and heat transfer of third grade fluids between two micro-parallel plates

Abstract

Electromagnetohydrodynamic micro-pump of third grade fluids between two micro-parallel plates is performed in this paper. 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. Analytical solutions of velocity and temperature are obtained by perturbation techniques under the assumption of small non-Newtonian behavior and the Chebyshev spectral collocation method is used to solve the same problem numerically. Analytical solutions are contrasted with the numerical solutions within admissible parameter range and the agreements are excellent. The effects of Hartmann number Ha (the ratio of magnetic forces to viscous forces), non-Newtonian parameter Λ (the dimensionless parameter related to the non-Newtonian behavior), the dimensionless electrical strength parameter H and the non-dimensional parameter γ1 (that is, Brinkman number, the ratio of heat produced by viscous dissipation to heat transported by molecular conduction) on the velocity and temperature are investigated graphically and discussed in detail. In addition, the dependence of Nusselt number (the strength of convective heat exchange) on corresponding parameters is presented. Results show that Nusselt number decreases with Hartmann number Ha and increases with dimensionless parameters H and γ1.