Computation of Internal Heat Source, Viscous Dissipation and Mass Flow Effects on Mono-Diffusive Thermo-Convective Stability in a Horizontal Porous Medium - Rafeek, K. V. Muhammed; Reddy, G. Janardhana; Matta, Anjanna; Bég, O. Anwar (Discontinuity, Nonlinearity, and Complexity, 2026)
A physical model is developed to investigate the combined effects of internal heat source, mass flow and viscous dissipation on the Hadley-Prats flow in an infinite parallel horizontal porous layer with the inclined temperature gradient. Following non-dimensionalization of the model, a linear instability analysis is conducted and the basic steady state solution is derived. Transverse or longitudinal roll disturbances are examined. The eigenvalue problem is solved using Runge-Kutta and shooting methods to determine the eigenvalues as the vertical values of the thermal Rayleigh number R_z for both cases of disturbances i.e. longitudinal and transverse rolls. The critical wave number and critical vertical thermal Rayleigh number R_z are identified for different thermo physical parameters. The conceptual study is constructed to comprehend the consequence of the viscous dissipation of the mono-diffusive instability analysis of Hadley-Prats flow thermal convection in the fluid saturated infinite horizontal porous layer. The simulations show that increased internal heat generation causes efficient destabilisation in all areas, since it raises the overall temperature of the system. Higher values of horizontal Rayleigh number R_x, and with viscous dissipation generally result in a decrease in critical vertical Rayleigh number and therefore flow destabilization in the porous medium. Physical interpretation of the numerical solutions relating to the linear instability analysis is presented.