Lie Symmetry Analysis of MHD Thermosolutal Marangoni Convection with Heat Generation and First Order Chemical Reaction /
Saad Zubair
- 86p. Soft Copy 30cm
The purpose of this research is to study the combined effects of Magnetohydrodynamic (MHD), Marangoni convection, heat generation, thermosolutal transport and chemical reaction of first order for a fluid system. These flows play a potent role in many applications of realworld such as cooling systems, heat exchangers, chemical and material processing, buildings and HVAC’s, power generation, food processing, aerospace and automotive, geothermal systems, thermal energy storage and many more. The equations modeling these flows are nonlinear partial differential equation which in general are very complex and challenging to solve. The considered flow equations are transformed into less complex ordinary differential equations by using an approach called Lie symmetry transformations. This mathematical technique helps in the reduction of variables of the system, thereby decreasing complexity of the system which often results in a set of solvable equations. This reduction of variables yields nonlinear equations of ordinary type that (in general) do not possess exact solutions, however computational cost involved in generating approximate solutions for the reduced equations decreases enormously. Through these solutions a better understanding of the system and the physical parameters that affect the system is established. This thesis employs Homotopy Perturbation Method that is an analytical approach for obtaining analytical approximate solutions for the flow and heat transfer considered by imposing the said physical constraints. MAPLE is used to develop the code for Homotopy Perturbation Method and for generating Lie similarity transformations. Using MAPLE, the reduction is performed, and graphs are obtained showing the influence of various variable parameters like Prandtl number, Hartmann number, Schmid number, rate of chemical reaction and the coefficient of heat generation corresponding to the temperature, velocity and concentration profiles. Lie control parameters are involved in these similarity solutions that are obtained in this thesis. These parameters are shown to influence the flow dynamics like the physical parameters. This control characterization of the fluid flow and heat transfer considered here has not been presented earlier.