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 electro-kinetics 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 \(\mathit{Ha}\), the non-Newtonian parameter Lambda, the constant pressure \(P\), the thermal radiation \(\mathit{Nr}\), and the non-dimensional parameter Brinkman number gamma1 on the velocity and temperature are investigated graphically and discussed in detail.

这个问题涉及稳定的驱动压力流和埋在多孔介质中的两个微型平行板之间的电磁流体动力微型泵的三级流体的传热。已经考虑了热辐射和电动势的影响。由洛伦兹力强迫的流动，是由垂直磁场和外部水平施加的电场的相互作用所产生的，被认为是单向的和一维的。基于速度场，通过考虑粘性耗散，焦耳热效应和电磁耦合效应产生的体积热量，分析了具有辐射效应的热充分发展的热传递。使用摄动法的分析溶液以串联形式获得，假设三级非牛顿参数的值较小。使用同伦摄动法，获得了三级非牛顿参数的任何值的近似解析解。多孔介质渗透性的影响\（K \），无量纲电气强度参数\（H \），哈特曼数\（\ mathit {Ha} \），非牛顿参数Lambda，恒压\（P \），热辐射\ （\ mathit {Nr} \）以及速度和温度上的无量纲参数Brinkman数gamma1进行了图形化研究，并进行了详细讨论。