Approximate closed-form solution of free convection flow past a vertical cone

Abstract

This paper presents a technique to find the closed-form solution of the boundary-value problem representing free convection flow past a vertical cone. Partial differential equations that govern the flow are converted into nonlinear ordinary differential equations with the aid of similarity transformations. First, a numerical solution is obtained with the help of the bvp4c package of MATLAB, and then utilizing the numerical solution, the closed-form solution is obtained. The accuracy of the closed-form solution is analyzed by the residual technique. Graphs of the residuals of the governing equations indicate that our approximate closed-form solution closely matches the exact solution.