Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Faculty Publications Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Creator An entity primarily responsible for making the resource Kruthik, P.S.; Idris, Ruwaidiah; Siddheshwar, P.G. Title A name given to the resource STUDY OF THE LINEAR AND NONLINEAR REGIMES OF NATURAL CONVECTION WITH WEAK OR DOMINATING INTERNAL HEAT GENERATION FOR RIGID-FREE BOUNDARIES Date A point or period of time associated with an event in the lifecycle of the resource 01-01-2025 Source A related resource from which the described resource is derived Journal of Porous Media;Volume;28;Issue;9;pp.21-39 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1615/JPorMedia.2025056500" target="_blank" rel="noreferrer noopener">https://doi.org/10.1615/JPorMedia.2025056500</a> <br /><br /><a href="https://www.scopus.com/pages/publications/105004989484?origin=resultslist" target="_blank" rel="noreferrer noopener">https://www.scopus.com/pages/publications/105004989484?origin=resultslist</a> Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant 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 Description An account of the resource 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,. Subject The topic of the resource BrinkmanBard convection; DarcyBard convection; internal heat generation; linear stability analysis; Maclaurin series; natural convection; nonlinear stability analysis; RayleighBard convection; single-term Galerkin method Publisher An entity responsible for making the resource available Begell House Inc. Relation A related resource ISSN: 1091028X; CODEN: JPMEF Language A language of the resource English Type The nature or genre of the resource Article Rights Information about rights held in and over the resource Restricted Access; Hardcopy may be available in the library Format The file format, physical medium, or dimensions of the resource online