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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Computation of Internal Heat Source, Viscous Dissipation and Mass Flow Effects on Mono-Diffusive Thermo-Convective Stability in a Horizontal Porous Medium

Discontinuity, Nonlinearity, and Complexity 13(3) (2024) 517--529 | DOI:10.5890/DNC.2024.09.010

K. V. Muhammed Rafeek$^{1}$, G. Janardhana Reddy$^{1}$, Anjanna Matta$^{2}$, O. Anwar B\'{e}g$^{3}$

$^{1}$ Laboratory on Computational Fluid Dynamics, Department of Mathematics, Central University of Karnataka, Kalaburagi, India

$^{2}$ Department of Mathematics, Faculty of Science & Technology, The ICFAI Foundation for Higher Education, Hyderabad, India

$^{3}$ Multi-physical Engineering Sciences, Aeronautical/ Mechanical Engineering Department, School of Science, Engineering and Environment, Salford University, Manchester M54WT, UK

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Abstract

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.

Acknowledgments

The first author wishes to express his gratitude to the Department of Science and Technology, Government of India for the granting of DST-Inspire Fellowship (IF190169) and to the Central University of Karnataka for providing the research facilities. This research of the third author was supported by the DST-SERB, Govt. of India (Grant no. TAR/2018/001290).

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