Integral transform solution of natural convection in a cylinder cavity with uniform internal heat generation

Abstract

Purpose The purpose of this study is to propose the generalised integral transform technique to investigate the natural convection behaviour in a vertical cylinder under different boundary conditions, adiabatic and isothermal walls and various aspect ratios. Design/methodology/approach GITT was used to investigate the steady-state natural convection behaviour in a vertical cylinder with internal uniformed heat generation. The governing equations of natural convection were transferred to a set of ordinary differential equations by using the GITT methodology. The coefficients of the ODEs were determined by the integration of the eigenfunction of the auxiliary eigenvalue problems in the present natural convection problem. The ordinary differential equations were solved numerically by using the DBVPFD subroutine from the IMSL numerical library. The convergence was achieved reasonably by using low truncation orders. Findings GITT is a powerful computational tool to explain the convection phenomena in the cylindrical cavity. The convergence analysis shows that the hybrid analytical–numerical technique (GITT) has a good convergence performance in relatively low truncation orders in the stream-function and temperature fields. The effect of the Rayleigh number and aspect ratio on the natural convection behaviour under adiabatic and isothermal boundary conditions has been discussed in detail. Originality/value The present hybrid analytical–numerical methodology can be extended to solve various convection problems with more involved nonlinearities. It exhibits potential application to solve the convection problem in the nuclear, oil and gas industries.