ItemArticle

STUDY OF THE LINEAR AND NONLINEAR REGIMES OF NATURAL CONVECTION WITH WEAK OR DOMINATING INTERNAL HEAT GENERATION FOR RIGID-FREE BOUNDARIES

Title
STUDY OF THE LINEAR AND NONLINEAR REGIMES OF NATURAL CONVECTION WITH WEAK OR DOMINATING INTERNAL HEAT GENERATION FOR RIGID-FREE BOUNDARIES
Creator
Kruthik, P.S.; Idris, Ruwaidiah; Siddheshwar, P.G.
Description
The paper presents the linear and non-linear regimes of natural convection in the presence of uniform internal heat generation for rigid-free boundaries. A linear stability analysis followed by nonlinear stability analysis is carried out for using a novel procedure. The eigenvalue of the two problems are different. The first one has Rayleigh number based on internal heat generation as the eigenvalue while the second, which is of the classical Bard type, has a buoyancyRayleigh number. The critical Rayleigh number in both problems is initially determined using the single-term Galerkin method, followed by a refinement of the value by the Maclaurin series method. The findings indicate that the system becomes stable with increasing values of the porous parameter and the Brinkman number. The percentage relative error in the eigenvalue obtained by the single-term Galerkin method relative to that obtained by the Maclaurin series method is presented. In the second natural convection problem, we have two Rayleigh numbers, viz., the weak internal Rayleigh number, RI, and the external Rayleigh number, Ra. The effect of RI on Rac is to reduce it in the case of a heat source and increase it in the case a of heat sink. Additionally, conditions facilitating the transition from Brinkman Bard convection to DarcyBard convection are presented. The GinzburgLandau equation is obtained for both the problems and the scaled Lorenz model is derived in the case of second problem. The solution from the GinzburgLandau equation is used to plot for the amplitude and results are illustrated. 2025 by Begell House,.
Source
Journal of Porous Media;Volume;28;Issue;9;pp.21-39
Date
01-01-2025
Publisher
Begell House Inc.
Subject
BrinkmanBard convection; DarcyBard convection; internal heat generation; linear stability analysis; Maclaurin series; natural convection; nonlinear stability analysis; RayleighBard convection; single-term Galerkin method
Coverage
Kruthik P.S., Special Interest Group for Modelling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, Kuala Nerus, Terengganu, 21030, Malaysia; Idris R., Special Interest Group for Modelling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, Kuala Nerus, Terengganu, 21030, Malaysia; Siddheshwar P.G., Centre for Mathematical Needs, Department of Mathematics, CHRIST University, Bengaluru, 560029, India
Rights
Restricted Access; Hardcopy may be available in the library
Relation
ISSN: 1091028X; CODEN: JPMEF
Format
online
Language
English
Type
Article

Citation

Kruthik, P.S.; Idris, Ruwaidiah; Siddheshwar, P.G., “STUDY OF THE LINEAR AND NONLINEAR REGIMES OF NATURAL CONVECTION WITH WEAK OR DOMINATING INTERNAL HEAT GENERATION FOR RIGID-FREE BOUNDARIES,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 19, 2026, https://archives.christuniversity.in/items/show/23346.

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