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 Articles 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/. Title A name given to the resource BrinkmanBard Convection with Rough Boundaries and Third-Type Thermal Boundary Conditions Subject The topic of the resource asymptotic analysis; Biot number; BrinkmanBard convection; DarcyRayleigh number; generalized Lorenz model; Maclaurin series; Robin boundary condition; rough boundaries; slip Darcy number Description An account of the resource The BrinkmanBard convection problem is chosen for investigation, along with very general boundary conditions. Using the Maclaurin series, in this paper, we show that it is possible to perform a relatively exact linear stability analysis, as well as a weakly nonlinear stability analysis, as normally performed in the case of a classical free isothermal/free isothermal boundary combination. Starting from a classical linear stability analysis, we ultimately study the chaos in such systems, all conducted with great accuracy. The principle of exchange of stabilities is proven, and the critical Rayleigh number, (Formula presented.), and the wave number, (Formula presented.), are obtained in closed form. An asymptotic analysis is performed, to obtain (Formula presented.) for the case of adiabatic boundaries, for which (Formula presented.). A seemingly minimal representation yields a generalized Lorenz model for the general boundary condition used. The symmetry in the three Lorenz equations, their dissipative nature, energy-conserving nature, and bounded solution are observed for the considered general boundary condition. Thus, one may infer that, to obtain the results of various related problems, they can be handled in an integrated manner, and results can be obtained with great accuracy. The effect of increasing the values of the Biot numbers and/or slip Darcy numbers is to increase, not only the value of the critical Rayleigh number, but also the critical wave number. Extreme values of zero and infinity, when assigned to the Biot number, yield the results of an adiabatic and an isothermal boundary, respectively. Likewise, these extreme values assigned to the slip Darcy number yield the effects of free and rigid boundary conditions, respectively. Intermediate values of the Biot and slip Darcy numbers bridge the gap between the extreme cases. The effects of the Biot and slip Darcy numbers on the HopfRayleigh number are, however, opposite to each other. In view of the known analogy between Bard convection and TaylorCouette flow in the linear regime, it is imperative that the results of the latter problem, viz., BrinkmanTaylorCouette flow, become as well known. 2023 by the authors. Creator An entity primarily responsible for making the resource Siddheshwar P.G.; Narayana M.; Laroze D.; Kanchana C. Source A related resource from which the described resource is derived Symmetry, Vol-15, No. 8 Publisher An entity responsible for making the resource available Multidisciplinary Digital Publishing Institute (MDPI) Date A point or period of time associated with an event in the lifecycle of the resource 2023-01-01 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.3390/sym15081506" target="_blank" rel="noreferrer noopener">https://doi.org/10.3390/sym15081506</a> <br /><br /><a href="https://www.scopus.com/inward/record.uri?eid=2-s2.0-85168920179&amp;doi=10.3390%2Fsym15081506&amp;partnerID=40&amp;md5=eb92adebdcb72fd9c088f09536177206" target="_blank" rel="noreferrer noopener">https://www.scopus.com/inward/record.uri?eid=2-s2.0-85168920179&amp;doi=10.3390%2fsym15081506&amp;partnerID=40&amp;md5=eb92adebdcb72fd9c088f09536177206</a> Rights Information about rights held in and over the resource All Open Access; Gold Open Access; Green Open Access Relation A related resource ISSN: 20738994 Format The file format, physical medium, or dimensions of the resource Online Language A language of the resource English Type The nature or genre of the resource Article Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Siddheshwar P.G., Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India; Narayana M., Department of Mathematics, The University of the West Indies, Mona Campus, 7, Kingston, Jamaica; Laroze D., Instituto de Alta Investigaci, Universidad de Tarapac Casilla 7 D, Arica, 1000000, Chile; Kanchana C., Instituto de Alta Investigaci, Universidad de Tarapac Casilla 7 D, Arica, 1000000, Chile