Nonlinear steady Darcy-Bard convection problem: Revisit using the heatlines approach
Darcy-Bard convection; Heat transport; Heatlines or heat function; Number of Bard cells; Onset of convection; Rectangular enclosure
The classical problem of Darcy-Bard convection(DBC) in enclosures is revisited using the method of heatlines to have a better perspective of the problem. General aspect ratio is chosen in the analysis which helps in obtaining the results of four different types of enclosures, viz., tall, square, shallow and very shallow. Three different water saturated porous media(WSPM) and their actual thermophysical properties are used in the computation of the results. The method of heatlines facilitates the observation of fluid and heat flow lines in order to have a good understanding of the dynamics. The neo-classical approach not only accurately predicts the critical Darcy-Rayleigh and wave numbers but also picturizes the heat flow of the problem in the most natural way. The Galerkin method is used in the paper for the normal and convective modes of convection yields accurate analytical results in the heatlines formulation. Theoretical expression to calculate the number of Bard cells that form in the system at onset is obtained by linear theory, and ranges of aspect ratio at which unicellular, two-cellular and multicellular convection are possible are determined and documented. The weakly non-linear stability analysis is performed to determine the heat transport. Among four considered enclosures, maximum heat transport is achieved in the case of a square enclosure. Out of three chosen WSPM, the water-saturated glass balls porous medium and the water-saturated aluminium-foam porous medium show most stable and least stable behaviours. Results obtained from the heatlines approach are validated by comparing with the results of the classical DBC problem in the case of a very shallow enclosure. From the study, we conclude that the square enclosure with water-saturated aluminium-foam porous medium has possible application in heat removal systems. 2025 The Physical Society of the Republic of China (Taiwan)
Lakshmi, K.M.; Siddheshwar, P.G.; Laroze, D.; Dz, P.
Chinese Journal of Physics;Volume;94;pp.328-346
Restricted Access; Hardcopy may be available in the library
https://doi.org/10.1016/j.cjph.2025.01.032 https://www.scopus.com/pages/publications/85217428595?origin=resultslist
Lakshmi K.M., Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal, India; Siddheshwar P.G., Centre for Mathematical Needs, Department of Mathematics, Christ University, Hosur Road, Bengaluru, 560029, India; Laroze D., Instituto de Alta Investigaci, Universidad de Tarapac Casilla 7D, Arica, 1000000, Chile; Dz P., Departamento de Ciencias Ficas, Universidad de La Frontera, Casilla 54-D, Temuco, Chile