MHD Accelerated Flow of Maxwell Fluid in a Porous Medium and Rotating Frame

The magnetohydrodynamic (MHD) and rotating flow of Maxwell fluid induced by an accelerated plate is investigated. The Maxwell fluid saturates the porous medium. Both constant and variable accelerated cases are considered. Exact solution in each case is derived by using Fourier sine transform. Many interesting available results in the relevant literature are obtained as the special cases of the present analysis. The graphical results are presented and discussed. 1. Introduction Several fluids including butter, cosmetics and toiletries, paints, lubricants, certain oils, blood, mud, jams, jellies, shampoo, soaps, soups, and marmalades have rheological characteristics and are referred to as the non-Newtonian fluids. The rheological properties of all these fluids cannot be explained by using a single constitutive relationship between stress and shear rate which is quite different than the viscous fluids [1, 2]. Such understanding of the non-Newtonian fluids forced researchers to propose more models of non-Newtonian fluids. In general, the classification of the non-Newtonian fluid models is given under three categories which are called the differential, the rate, and the integral types [3]. Out of these, the differential and rate types have been studied in more detail. In the present analysis we discuss the Maxwell fluid which is the subclass of rate-type fluids which take the relaxation phenomenon into consideration. It was employed to study various problems due to its relatively simple structure. Moreover, one can reasonably hope to obtain exact solutions from Maxwell fluid. This motivates us to choose the Maxwell model in this study. The exact solutions are important as these provide standard reference for checking the accuracy of many approximate solutions which can be numerical or empirical in nature. They can also be used as tests for verifying numerical schemes that are being developed for studying more complex flow problems [4–9]. On the other hand, these equations in the non-Newtonian fluids offer exciting challenges to mathematical physicists for their exact solutions. The equations become more problematic, when a non-Newtonian fluid is discussed in the presence of MHD and porous medium. Despite this fact, various researchers are still making their interesting contributions in the field (e.g., see some recent studies [1–15]). Few investigations which provide the examination of non-Newtonian fluids in a rotating frame are also presented [1–19]. Such studies have special relevance in meteorology, geophysics, and astrophysics. To the best of our