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

Integral transform solution of natural convection in a cylinder cavity with uniform internal heat... 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/approachGITT 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.FindingsGITT 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/valueThe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

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

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References (36)

Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
0961-5539
DOI
10.1108/hff-08-2017-0294
Publisher site
See Article on Publisher Site

Abstract

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/approachGITT 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.FindingsGITT 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/valueThe 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.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Sep 25, 2018

Keywords: Natural convection; GITT technique; Hybrid computational methodology; Vertical cylinder

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