group transformations. M. Bhuvaneswari and S. Sivasankaran. Citation: AIP Conference Proceedings 1605, 440 (2014); doi: 10.1063/1.4887629. View online: ...
Free convection flow in an inclined plate with variable thermal conductivity by scaling group transformations M. Bhuvaneswari and S. Sivasankaran Citation: AIP Conference Proceedings 1605, 440 (2014); doi: 10.1063/1.4887629 View online: http://dx.doi.org/10.1063/1.4887629 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1605?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Rotation effects on coupled heat and mass transfer by unsteady MHD free convection flow in a porous medium past an infinite inclined plate AIP Conf. Proc. 1605, 410 (2014); 10.1063/1.4887624 Parametric study on hydromagnetic flow and heat/mass transfer past a semi-infinite inclined plate in the presence of variable thermal conductivity and reactive index: A group theory approach AIP Conf. Proc. 1440, 754 (2012); 10.1063/1.4704285 Thermal convection below a conducting lid of variable extent: Heat flow scalings and two-dimensional, infinite Prandtl number numerical simulations Phys. Fluids 15, 455 (2003); 10.1063/1.1533755 Comments on ``Laminar Free Convection Flow on a Vertical Plate'' Phys. Fluids 10, 1120 (1967); 10.1063/1.1762236 Free Convection between Two Vertical Plates in the Presence of an Inclined Temperature Gradient J. Chem. Phys. 23, 1742 (1955); 10.1063/1.1742452
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Free Convection Flow in an Inclined Plate with Variable Thermal Conductivity by Scaling Group Transformations M. Bhuvaneswari and S. Sivasankaran Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia, Abstract. The Lie group analysis of natural convection flow over an inclined semi-infinite plate with variable thermal conductivity is studied. The fluid thermal conductivity is assumed to vary as a linear function of temperature. A scaling group of transformation is applied to the governing partial differential equations and then used to reduce them to a system of ordinary differential equations. Numerical solutions of the ordinary differential equations are also obtained. From the numerical results it is found that the momentum and thermal boundary layer thicknesses increase with thermal conductivity parameter. The velocity increases and temperature decreases with increasing the Grashof number. Keywords: Lie groups; Natural convection; Thermal conductivity; Inclined plate. PACS: 47.55.pb; 44.20.+b; 47.15.Cb.
INTRODUCTION The study of natural convection flow of an incompressible viscous fluid past a heated surface has attracted the interest of many researchers due to many applications such as cooling of nuclear reactors, the boundary layer control in aerodynamics, crystal growth, food processing and cooling towers. In this paper, symmetry methods are applied to the boundary layer problem. Symmetry groups are invariant transformations which do not alter the structural form of the equation under investigation. The advantage of symmetry method is that it can be applied successfully to non-linear equations. Lie group of transformations map a given differential equation to itself. The differential equations remain invariant under some continuous group of transformations usually known as symmetries of a differential equation. Yurusoy and Pakdemirli [1] studied the boundary layer equations for Newtonian / non-Newtonian fluids by using Lie group method. Kalpakides and Balassas [2] also studied the free convective boundary layer problem using Lie group analysis. Radiative and magnetic effects on free convection and mass transfer flow past a flat plate are studied by Ibrahim et al. [3]. They obtained similarity reductions and found analytical and numerical solutions using scaling symmetry. Sivasankaran et al. [4] investigated the radiation effects on free convection past an inclined semiinfinite surface using Lie group analysis. They found that the thermal and momentum boundary layer thicknesses increase by increasing the radiation parameter. Lee et al. [5] examined the natural convective flow with radiation over an inclined semi-infinte plate in a porous medium. They observed that velocity increases and temperature decreases by increasing porosity parameter. Bhuvaneswari et al. [6] studied heat and mass transfer of an incompressible viscous fluid past a semi-infinite inclined surface with first-order homogeneous chemical reaction. Numerical solutions on heat transfer of the polar fluid on steady flow through a vertical infinite plate have been analyzed by Ferdows et al. [7]. They found that velocity decreases on increasing the material parameter and spin gradient viscosity parameter. Radiation and natural convection flow of a heat generating fluid over an inclined surface embedded in a porous medium is investigated by Bhuvaneswari et al. [8]. It is found that the local Nusselt number increases with the porosity and conduction–radiation parameter. Most of the existing studies are based on the constant physical properties of the fluid. However it is known that these physical properties change with temperature. To accurately predict the results, it is necessary to take into account this variation of physical properties. Hence, the present work investigates the effect of variable thermal conductivity on natural convection past an inclined plate using Lie group analysis.
MATHEMATICAL ANALYSIS Consider the heat transfer by natural convection in laminar boundary layer flow of an incompressible viscous fluid along an inclined semi-infinite plate with an acute angle D from the vertical. The surface is
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