Effects of LTNE on Two-Component Convective Instability in a Composite System with Thermal Gradient and Heat Source

Varalakshmi K. Balaji, Manjunatha Narayanappa (), Ramalingam Udhayakumar, Ghada AlNemer (), Sumithra Ramakrishna and Gangadharaih Yeliyur Honnappa
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Varalakshmi K. Balaji: Department of Mathematics, School of Applied Sciences, REVA University, Bengaluru 560064, India
Manjunatha Narayanappa: Department of Mathematics, School of Applied Sciences, REVA University, Bengaluru 560064, India
Ramalingam Udhayakumar: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, India
Ghada AlNemer: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Sumithra Ramakrishna: Department of Mathematics, Nrupathunga University, Bengaluru 560064, India
Gangadharaih Yeliyur Honnappa: Department of Mathematics, RV Institute of Technology & Management, Bengaluru 560076, India

Mathematics, 2023, vol. 11, issue 20, 1-17

Abstract: An analytical study is conducted to examine the influence of thermal gradients and heat sources on the onset of two-component Rayleigh–Bènard (TCRB) convection using the Darcy model. The study takes into account the effects of local thermal non-equilibrium (LTNE), thermal profiles, and heat sources. The composite structure is horizontally constrained by adiabatic stiff boundaries, and the resulting solution to the problem is obtained using the perturbation approach. The various physical parameters have been thoroughly examined, revealing that the fluid layer exhibits dominance in the two-layer configuration. It has been observed that the parabolic profile demonstrates greater stability in comparison to the step function. Conversely, in the setup where the porous layer dominates, the step function plays a crucial role in maintaining stability. The porous layer, model (iv), exhibits greater stability in the predominant combined structure, while the linear configuration is characterized by higher instability.

Keywords: heat source; LTNE; two component; thermal gradients; Rayleigh–Bènard convection; corrected internal Rayleigh numbers; perturbation approach (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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