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Title: Numerical solution of natural-convection flow in enclosures: An implicit vorticity boundary condition type method
Authors: Balam N.B.
Gupta, Akhilesh Kumar
Published in: Heat Transfer Research
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 bett er 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. © 2019 by Begell House, Inc.
Citation: Heat Transfer Research (2019), 50(14): 1383-1416
Issue Date: 2019
Publisher: Begell House Inc.
Keywords: Fi nite diff erence method
Implicit boundary
Natural convection
Navier-Stokes equation
Stream function
ISSN: 10642285
Author Scopus IDs: 57193856184
Author Affiliations: Balam, N.B., Efficiency of Buildings Group, C.S.I.R.-Central Building Research Institute, Roorkee, 247667, India
Gupta, A., Mechanical and Industrial Engineering Department, Indian Institute of Technology, Roorkee, 247667, India
Corresponding Author: Balam, N.B.; CSIR-Central Building Research InstituteIndia; email:
Appears in Collections:Journal Publications [ME]

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