The onset of convection in a binary fluid saturated anisotropic porous layer |
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| Authors: | MS Malashetty Mahantesh Swamy |
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| Affiliation: | 1. Department of Engineering, University of Sannio, Piazza Roma 21, 82100 Benevento, Italy;2. Department of Theoretical Mechanics, Tomsk State University, 634050 Tomsk, Russia;3. Department of Nuclear and Thermal Power Plants, Tomsk Polytechnic University, 634050 Tomsk, Russia;4. Department of Applied Mathematics, Defence Institute of Advanced Technology (Deemed University), Pune - 411025, India;5. Department of Mathematics, Central University of Karnataka, Kalaburagi - 585 367, Karnataka, India;1. School of Civil Engineering, Shandong University, Jinan 250061, China;2. Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China;3. Department of Mathematics, Government First Grade College for Women, Hassan 573201, India;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. Departamento de Fíisica y Matemática Aplicada, Universidad de Navarra, 31080 Pamplona, Spain;2. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile;3. Departamento de Ciencias Físicas, Universidad de La Frontera, Casilla 54 D, Temuco, Chile;4. Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile;1. Department of Mathematics, Faculty of Sciences, Banaras Hindu University, Varanasi 221005, India;2. Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow 226025, India |
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| Abstract: | The double diffusive convection in a horizontal fluid saturated anisotropic porous layer, which is heated and salted from below, is studied analytically. The generalized Darcy model is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes and frequency of oscillations are obtained analytically using linear theory. The effect of anisotropy parameters, solute Rayleigh number, Lewis number and Prandtl number on the stationary, oscillatory and finite amplitude convection is shown graphically. The transient behavior of the Nusselt and Sherwood numbers is studied, by solving numerically a fifth order Lorenz type system using Runge–Kutta method. Some of the convection systems previously reported in the literature are shown to be special cases of the system presented in this study. |
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