MHD free-forced convection and mass transfer flow through temperature stratified high-porosity medium from a vertical plate with power-law variation wall temperature in the presence of hall and ion-slip currents

Abstract

Considerable research efforts have been devoted to the study of MHD free-force convection and mass transfer flow through temperature stratified high porosity medium from a vertical plate with power-law variation wall temperature in the presence of Hall and ion-slip currents under various flow conditions. A magnetic field is applied perpendicular to the plates. Various configurations have been considered for the plates. The whole system is rotated with a constant angular velocity Ω. The Hall and ion-slip currents effect has also been put into consideration. The effects of changing various parameters on the velocity, temperature and concentration distributions have been discussed. However, finding exact solutions of nonlinear problems is very difficult. In particular, obtaining an exact analytic solution of a given nonlinear problem is often more complicated as compared to that of a numerical solution, despite the availability of high performance supercomputers and software which provide efficient ways to perform high quality symbolic computations. In our analysis, the primary focus has been shown on the study of the physical and mathematical structure of fluid models. Method of explicit and implicit finite difference method, Nachtsheim-Swigert iteration technique are used as main tools for numerical approach while the perturbation technique is used for the analytical approach. The studies of the flow feature mentioned above are made in different sections taking different aspects of the flow that are of practical importance. The non-dimensional coupled partial differential equations of the momentum, energy and concentration equations are derived by considering suitable usual transformation and similarity variables. Also stability analysis has been derived for conversed solutions. In section 4.1 of chapter 4, the similarity solutions have been obtained for one dimensional unsteady MHD free convection and mass transfer flow through a vertical oscillatory porous plate in a rotating porous medium with Hall, ion-slip currents and heat source. Two cases are considered, (a) analytical solution with perturbation technique, (b) numerical solution by implicit finite difference method. In section 4.2 of chapter 4 and section 5.1, 5.2 of chapter 5, similarity solutions have been obtained by finite difference method (implicit and explicit). The numerical solutions for the velocity profiles, temperature distributions as well as concentration distributions are obtained using implicit finite difference method for the effects of the various important parameters entering into the problem in case of the one dimensional problem. Also the shear stress, Nusselt number as well as Sherwood number have been computed by implicit finite difference method in case of one dimensional flow. Further the above mentioned flow problem has been considered for two dimensional case, unsteady MHD free convective flow. The local and average shear stresses as well as Nusselt number and Sherwood number have been computed by explicit finite difference technique in case of two dimensional flows. In both cases the stability conditions and convergence criteria of the explicit finite difference scheme have been analyzed for finding the restriction of the values of various parameters to get more accuracy. In chapter 6, similarity equations of the corresponding momentum and energy equations are derived by introducing a time dependent length scale which in fact plays the role of a similarity parameter. The suction velocity is taken to be inversely proportional to this parameter. In Chapter 7, the flow structures of stratification fluid models are investigated in detail and some new exact solutions have been obtained. The ambient temperature has been assumed to be an increasing function with the distance along the plate. The heat transfer changes significantly with the stratification and magnetic parameters. In Chapter 8, power-law variation wall temperature along vertical plate, in the presence of Hall and ion-slip currents are discussed. The plate surface has a power-law variation wall temperature and is permeable to allow for possible fluid with wall suction or blowing, velocity varied according to a power-law. The Nachtsheim-Swigert iteration technique has been used Chapter6, Chapter 7 and Chapter 8. The effects on the velocities, temperature, concentration, local and average shear stresses, Nusselt and Sherwood numbers of the various important parameters entering into the problems separately are discussed for each problem with the help of graphs and tables. Finally, in Chapter 9, a general discussion on the overall results of the problems considered in the dissertation is sorted out.