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Heat Transfer Research
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ISSN Imprimer: 1064-2285
ISSN En ligne: 2162-6561

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Heat Transfer Research

DOI: 10.1615/HeatTransRes.2019028547
Forthcoming Article

Numerical solution to natural convection flow in enclosures – An implicit vorticity boundary condition type method

Nagesh Babu Balam
CSIR - Central Building Research Institute
Akhilesh Gupta
Indian Institute of Technology, Roorkee


This paper presents a numerical method for solving viscous incompressible Navier-stokes equations and its application to natural convection flow. A generalised solution methodology based on existing Vorticity – Streamfunction methods is developed to show that the vorticity boundary condition being implemented is explicit in nature. A novel numerical solution method of Vorticity – Streamfunction formulation is proposed by implementing the Vorticity boundary conditions implicitly. The developed method is applied over various types of boundaries encountered in natural convection flows such as a)Regular (square/rectangular) boundary enclosures, b) Non rectangular/Irregular boundary enclosures, c)Boundary with obstructions. The results obtained closely match with standard reference results available in literature demonstrating the 2nd order overall accuracy. Convergence behaviour of implicit vorticity boundary conditions show that present method exhibits faster convergence and better stability over conventional Vorticity – Streamfunction formulation. The present method requires solution of only one Poisson equation per each iteration time step, hence reducing the overall complexity of the algorithm equivalent to solving a heat conduction type Poisson problem.