Viscous dissipation and thermoconvective instabilities in a horizontal porous channel heated from below |
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| Authors: | A Barletta L Storesletten |
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| Affiliation: | 1. Dipartimento di Ingegneria Energetica, Nucleare e del Controllo, Ambientale (DIENCA), Università di Bologna, Via dei Colli 16, I–40136 Bologna, Italy;2. Department of Mathematics, University of Agder, Serviceboks 422, 4604 Kristiansand, Norway;1. Petroleum Exploration and Production Research Institute of SINOPEC, Beijing 100083, China;2. State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China;1. Universidade Federal de Santa Catarina, Departamento de Engenharia Química e de Alimentos, 88040-970 Florianópolis, Brazil;2. Universidade Federal de Santa Catarina, Campus Blumenau, 89065-300 Blumenau, Brazil;3. Università del Sannio, Facoltà di Ingegneria, 82100 Benevento, Italy;1. Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India;2. Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India;3. Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits-2050, Johannesburg, South Africa |
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| Abstract: | A linear stability analysis of the basic uniform flow in a horizontal porous channel with a rectangular cross section is carried out. The thermal boundary conditions at the impermeable channel walls are: uniform incoming heat flux at the bottom wall, uniform temperature at the top wall, adiabatic lateral walls. Thermoconvective instabilities are caused by the incoming heat flux at the bottom wall and by the internal viscous heating. Linear stability against transverse or longitudinal roll disturbances is investigated either analytically by a power series formulation and numerically by a fourth order Runge-Kutta method. The special cases of a negligible effect of viscous dissipation and of a vanishing incoming heat flux at the bottom wall are discussed. The analysis of these special cases reveals that each possible cause of the convective rolls, bottom heating and viscous heating, can be the unique cause of the instability under appropriate conditions. In all the cases examined, transverse rolls form the preferred mode of instability. |
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