Abstract
Natural convection effects of the numerical solution for unsteady, laminar, free convection flow over an incompressible viscous fluid past a non-isothermal vertical cone with surface temperature T′w(x) = T′∞ + axn varying as power function of distance from the apex (x = 0) is presented here. The dimensionless governing equations of the flow that are unsteady, coupled and non-linear partial differential equations are solved by an efficient, accurate and unconditionally stable finite difference scheme of Crank-Nicolson type. The velocity and temperature fields have been studied for various parameters Prandtl number, semi vertical angle 0◦ < φ < 90◦ and n. The local as well as average skin-friction and Nusselt number are also presented and analyzed graphically. The present results are compared with available results in literature and are found to be in good agreement.
Highlights
Natural convection flows under influence of gravitational force have been investigated most extensively because they occur frequently in nature as well as in science and engineering applications
Merk and Prins [1, 2] developed the general relation for similar solutions on iso-thermal axisymmetric forms and they showed that the vertical cone has such a solution in steady state
Braun et al [3] obtained similar solutions for isothermal axi-symmetric bodies with closed lower ends, and integral methods are used for obtaining heat transfer results for a wide range of Prandtl numbers
Summary
Natural convection flows under influence of gravitational force have been investigated most extensively because they occur frequently in nature as well as in science and engineering applications. Since 1953, several authors have developed similarity solutions for axi-symmetrical problems for natural convection laminar flow over a vertical cone in steady state. Braun et al [3] obtained similar solutions for isothermal axi-symmetric bodies (i.e., cone, parabolic-nosed, flat-nosed bodies) with closed lower ends, and integral methods are used for obtaining heat transfer results for a wide range of Prandtl numbers. Numerical solutions of the transformed boundary layer equations are obtained for both isothermal and linear surface temperature with Prandtl number 0.7 They noticed from the velocity and temperature profiles that the dimensionless tangential-flow function for the iso-thermal cone attains 22 % greater than that for the cone with linear surface temperature distribution. Pop and Grosan et al [11] analyzed the steady laminar mixed convection boundary-layer flow over a vertical isothermal cone for fluids of any P r for the both cases of buoyancy assisting and buoyancy opposing flow conditions. The resulting non-similarity boundary-layer equations are solved numerically using the Keller-box scheme for fluids of any P r from very small to extremely large values (0.001 ≤ P r ≤ 10000)
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