Natural convection flow along a vertical circular cone with uniform surface temperature and surface heat flux in a thermally stratified medium

Abstract

The problem of laminar natural convection from a vertical circular cone maintained at either a uniform surface temperature or a uniform surface heat flux, and placed in a thermally stratified medium is considered. The governing non‐similarity boundary layer equation for uniform surface temperature are analyzed by using two distinct solution methodologies; namely, (i) a finite difference method and (ii) a local non‐similarity method. For uniform surface heat flux case, the solutions of the governing non‐similarity boundary layer equations are obtained by using three distinct solution methodologies, namely, (i) a finite difference method, (ii) a series solution method and (iii) an asymptotic solution method. The solutions are presented in terms of local skin‐friction and local Nusselt number for different values of Prandtl number and are displayed graphically. Effects of variations in the Prandtl number and stratification parameter on the velocity and temperature profiles are also shown graphically. Solutions obtained by finite difference method are compared with the other methods and found to be in excellent agreement.

Transient Free Convective Flow over a Vertical Cone Embedded in a Thermally Stratified Medium

“…The governing boundary layer equations are solved using an implicit finitedifference scheme of Crank-Nicolson type for various values of the Prandtl number Pr and stratification parameter. In order to check the accuracy of the numerical results, the present results are compared with the available results of Hering [15] and Hossian et al [27]. Results are found to be in excellent agreement.…”

“…Thus, the velocity and temperature profiles for a cone with uniform surface temperature when Pr 0.7 and stratification parameter 0.4 S are compared with the non-similarity solutions of Hossain et al [27] when the Prandtl number of Pr 0.7 and the stratification parameter of 0.4 S . These profiles are displayed in Fig.…”

“…Numerical results were presented for two values of the Prandtl number of 0.72 (air) and 6.0 (water) and for different values of the semi vertical angle and stratification parameter. Recently, Hossain et al [27] studied non-similarity solutions for the problem of steady, laminar, natural convective flow and heat transfer from a vertical circular cone immersed in a thermally stratified medium with either a uniform surface temperature or a uniform surface heat flux. A finite-difference method, a series solution method and an asymptotic solution have been obtained for the non-similarity boundary layer equations.…”

Transient Laminar MHD Free Convective Flow past a Vertical Cone with Non-Uniform Surface Heat Flux

“…Use of heat flux sensors can lead to improvements in efficiency, system safety and mod-eling. The studies [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] have considered problems of flow past a vertical cone/frustum of a cone in the case of uniform/non-uniform surface heat flux with porous/non-porous medium. Recently, Bapuji et al [31] have numerically studied the problem of transient natural convection from a vertical cone with non-uniform surface heat flux using an implicit finite-difference method.…”

Viscous Dissipation Effects on Natural Convection from a Vertical Plate with Uniform Surface Heat Flux Placed in a Thermally Stratified Media

“…They also used the perturbation series expansion and local nonsimilarity methods. Recently, a nonsimilarity analysis has been presented by Hossain et al [11] on the effect of uniform surface temperature and surface heat flux on the natural convection flow of a viscous incompressible fluid from a vertical cone placed in a thermally stratified medium. In this analysis, perturbation solutions are obtained appropriate to two extreme regimes of the cone and also finite difference solutions for the entire flow regime for fluid of different Prandtl number and different stratification conditions.…”