Numerical Simulation of Steady/Unsteady MHD Flow over a Non-linear Stretching/Shrinking Sheet with Variable Liquid Characteristics

Abstract

This dissertation is divided into two parts. The first part describes the work on magnetohydrodynamics boundary layer flow past a non-linear stretching surface in the presence of variable fluid characteristics. The second part is associated with the study of unsteady magnetohydrodynamics (MHD) stagnation point flow of bio-nanofluid near a shrinking/stretching surface. We use the relevant similarity transformation to convert the partial differential equations (PDEs) of the concerned problem into ordinary differential equation (ODEs). The shooting method has been used to obtain the numerical results of reduced coupled ODEs of the concerned problem. The acquired results from shooting method are compared with the bvp4c MATLAB solver. We also present a new numerical technique, namely, simplified finite difference method (SFDM) in our study and present some useful results by using it. Graphs are plotted to perceive the influence of several pertinent parameters on the fluid flow field while considering constant and variable fluid properties together. The current analysis of the first part describes the boundary layer flow with variable liquid properties past a non-linear stretching surface. Most of the studies were given on constant fluid properties. Whereas very few discuss the variable fluid properties in their study. To bridge this gap between constant and variable liquid properties. The comparison of constant and variable fluid characteristics is made in our study. The obtained results of constant and variable fluid properties are compared through graphs and tables. It is determined that the obtained results are different for variable and constant fluid characteristics. The heat and mass transfer rates in constant fluid properties are higher than the variable fluid properties. The wall resistance coefficient rises for changeable liquid characteristics when compare to constant liquid characteristics. It is also noted that width of boundary layer in Case B (variable fluid properties) is different compared to Case A (constant fluid properties). In the second part of the thesis, we investigate the unsteady MHD stagnation point bio-nanofluid flow past a shrinking/stretching surface. The flow modeled PDEs are first reduced to non-linear coupled ODEs by appropriate transformation. The numerical outcomes of the reduced coupled ODEs are obtained through shooting and bvp4c method. We noticed an excellent resemblance between the present numerical results and the published results in the literature. It is found that boundary layer thickness is different in stretching sheet case when compared to shrinking sheet case also density of motile microorganism declines for raising values of Nb, Lb and Pe.