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Heat Transfer Research
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Heat Transfer Research

DOI: 10.1615/HeatTransRes.2019028547
pages 1383-1416

NUMERICAL SOLUTION OF NATURAL-CONVECTION FLOW IN ENCLOSURES: AN IMPLICIT VORTICITY BOUNDARY CONDITION TYPE METHOD

Nagesh Babu Balam
Efficiency of Buildings Group, C.S.I.R.-Central Building Research Institute, Roorkee, India-247667
Akhilesh Gupta
Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, 247667, India

ABSTRACT

This paper presents a numerical method for solving viscous incompressible Navier-Stokes equations and their application to natural-convection flow. A generalized solution methodology based on the existing vorticity-stream function methods has been developed to show that the vorticity boundary condition being implemented is explicit in nature. A novel two-dimensional numerical solution method of vorticity-stream function formulation is proposed by implementing vorticity boundary conditions implicitly. The developed method is applied to various types of two-dimensional boundaries encountered in natural-convection flows such as: a) regular (square/rectangular) boundary enclosures, b) nonrectangular/irregular boundary enclosures, c) boundary with obstructions. The results obtained match closely with standard reference results available in the literature demonstrating the second-order overall accuracy. Convergence behavior of implicit vorticity boundary conditions shows that the present method exhibits faster convergence and better stability over the conventional vorticity-stream function formulation. The present method requires solution of only one Poisson equation per each iteration time step, thus reducing the overall complexity of the algorithm equivalent to solving a heat conduction-type Poisson problem.

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