Lie symmetry analysis of flow and heat transfer in an inclined deformable channel under the influence of magnetic field during filtration process

Abstract

This project seeks to investigate the effects of dimensionless parameters affecting flow dynamics and heat distribution during ltration process which leads to optimal out flow (maximum permeates). The study carried out a detailed mathematical modeling process based on conservation of mass, momentum and energy to construct mathematical representation of flow and heat transfer during ltration process. Also dimensionless parameters that affect the flow dynamics and heat distribution are indicated based on the design of the filter. To understand the dynamics of underlying study better, basic governing partial di erential equations representing the internal flow and heat transfer are reduced to a system of ordinary di erential equations by using the Lie symmetry analysis. Thereafter, double perturbation is used to approximate solutions of velocity variation and heat distribution inside the lter chamber analytically. Results are presented graphically for e ects of parameter affecting the flow dynamics and heat distribution. Also analysis is carried out to obtain combination of parameters that lead to optimal ltration process.