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Lie group analysis for the effect of temperature-dependent fluid viscosity with thermophoresis and chemical reaction on MHD free convective heat and mass transfer over a porous stretching surface in the presence of heat source/sink |
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| Affiliation: | 1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan;2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah 21589, Saudi Arabia;3. School of Natural Sciences, National University of Science and Technology, Islamabad 44000, Pakistan;1. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China;2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;3. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia;1. Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor, Malaysia;2. School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia;3. Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania;1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China;2. College of Information and Control Engineering, Shandong Vocational University of Foreign Affairs, Rushan, Shandong, China;3. Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modeling, North-West University, Mafikeng Campus, Mmabatho, South Africa;4. School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China;5. Department of Mathematics, College of Science, Taif University, Taif 21944, Saudi Arabia |
| Abstract: | This paper concerns with a steady two-dimensional flow of an electrically conducting incompressible fluid over a vertical stretching sheet. The flow is permeated by a uniform transverse magnetic field. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. After finding three absolute invariants a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equation corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity to decrease with the increasing distance of the stretching sheet. At a particular point of the sheet the fluid velocity decreases with the decreasing viscosity but the temperature increases in this case. It is found that with the increase of magnetic field intensity the fluid velocity decreases but the temperature increases at a particular point of the heated stretching surface. Impact of thermophoresis particle deposition with chemical reaction in the presence of heat source/sink plays an important role on the concentration boundary layer. The results thus obtained are presented graphically and discussed. |
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