Thermal Analysis of the Effect of Non-Linear Thermal Radiation and Non-Uniform Internal Heat Generation on a MHD Combustible Third-Grade Fluid Flowing Through a Vertically Positioned Darcy Porous Channel

Abstract

This study presents the thermal analysis of a magnetohydrodynamic combustible third-grade fluid flowing through a Darcy porous channel that is vertically positioned and subjected to the combined effect of Darcy Forchheimer inertia, non-linear thermal radiation and non-uniform internal heat generation/absorption. The fluid layer in contact with the channel walls is subjected to asymmetric slip conditions and constant temperature boundaries. The coupled non-linear system of ordinary differential equations arising from the phenomena are subjected to the procedure of nondimensionalization. The resulting dimensionless equations are then solved numerically by Two-Point Taylor Polynomial Iterative Linearization Technique with Legendre nodes (TTPILT). The methodology associated with the numerical approach begins with the linearization of non-linear terms in the governing equations, followed by the application of the Legendre nodes collocation technique to iteratively obtain solutions. The iterative process continues until convergence to the desired solution is achieved. The accuracy of the method is validated by comparing the obtained results with those generated using the spectral Chebyshev collocation method, which shows good agreement. Graphical illustrations of the fluid velocity and temperature profiles are provided and discussed. The findings on flow characteristics and thermal behavior have significant implications for the design and optimization of thermodynamic systems. In particular, the thermal analysis offers valuable insights for developing energy-efficient systems with optimal performance.