Effectiveness of radiation and Joule heating on hydromagnetic Carreau fluid through microfluidic channels with slip boundary conditions

In the present article, the fundamental flows (such as both the plates are moving in the opposite directions, lower plate is moving with constant velocity and other is at rest, and both the plates are moving in the direction of the flow) of magnetohydrodynamic Carreau fluid with slip boundary conditions have been considered. The effects of radiation and Joule heating are also considered in the energy equation. The physical situation is carried out in Cartesian coordinate system in all the mentioned problems. Using appropriate non-dimensional quantities, the governing differential equations have been non-dimensionalized. The approximate analytical solutions of the non-dimensional system of differential equations have been presented using regular perturbation method. It is observed from our investigation that, the velocity decreases with increasing values of magnetic parameter, the trend is reversed in the case of applied constant pressure gradient. The temperature is an increasing function of Brinkman number and radiation parameter.