Comments on “heat transfer in a square porous cavity in presence of square solid block”

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Abstract

Purpose: The purpose of this paper is to discuss the need to attend correctly to the accuracy and the manner in which the value of the streamfunction is determined when two or more impermeable boundaries are present. This is discussed within the context of the paper by Nandalur et al. (2019), which concerns the effect of a centrally located conducting square block on convection in a square sidewall-heated porous cavity. Detailed solutions are also presented which allow the streamfunction to take the natural value on the surface of the internal block. Design/methodology/approach: Steady solutions are obtained using finite difference methods. Three different ways in which insulating boundary conditions are implemented are compared. Detailed attention is paid to the iterative convergence of the numerical scheme and to its overall accuracy. Error testing and Richardson’s extrapolation have been used to obtain very precise values of the Nusselt number. Findings: The assumption that the streamfunction takes a zero value on the boundaries of both the cavity and the embedded block is shown to be incorrect. Application of the continuity-of-pressure requirement shows that the block and the outer boundary take different constant values. Research limitations/implications: The Darcy–Rayleigh number is restricted to values at or below 200; larger values require a finer grid. Originality/value: This paper serves as a warning that one cannot assume that the streamfunction will always take a zero value on all impermeable surfaces when two or more are present. A systematic approach to accuracy is described and recommended.

Original languageEnglish
JournalInternational Journal of Numerical Methods in Heat and Fluid Flow
Early online date23 Sep 2019
DOIs
Publication statusE-pub ahead of print - 23 Sep 2019

Keywords

  • Accuracy
  • Convection
  • Embedded solid block
  • Finite differences
  • Nonlinear flow
  • Porous media
  • Square cavity

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics

Cite this

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title = "Comments on “heat transfer in a square porous cavity in presence of square solid block”",
abstract = "Purpose: The purpose of this paper is to discuss the need to attend correctly to the accuracy and the manner in which the value of the streamfunction is determined when two or more impermeable boundaries are present. This is discussed within the context of the paper by Nandalur et al. (2019), which concerns the effect of a centrally located conducting square block on convection in a square sidewall-heated porous cavity. Detailed solutions are also presented which allow the streamfunction to take the natural value on the surface of the internal block. Design/methodology/approach: Steady solutions are obtained using finite difference methods. Three different ways in which insulating boundary conditions are implemented are compared. Detailed attention is paid to the iterative convergence of the numerical scheme and to its overall accuracy. Error testing and Richardson’s extrapolation have been used to obtain very precise values of the Nusselt number. Findings: The assumption that the streamfunction takes a zero value on the boundaries of both the cavity and the embedded block is shown to be incorrect. Application of the continuity-of-pressure requirement shows that the block and the outer boundary take different constant values. Research limitations/implications: The Darcy–Rayleigh number is restricted to values at or below 200; larger values require a finer grid. Originality/value: This paper serves as a warning that one cannot assume that the streamfunction will always take a zero value on all impermeable surfaces when two or more are present. A systematic approach to accuracy is described and recommended.",
keywords = "Accuracy, Convection, Embedded solid block, Finite differences, Nonlinear flow, Porous media, Square cavity",
author = "Rees, {D A S}",
year = "2019",
month = "9",
day = "23",
doi = "10.1108/HFF-04-2019-0313",
language = "English",
journal = "International Journal of Numerical Methods in Heat and Fluid Flow",
issn = "0961-5539",
publisher = "Emerald Group Publishing Ltd.",

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AB - Purpose: The purpose of this paper is to discuss the need to attend correctly to the accuracy and the manner in which the value of the streamfunction is determined when two or more impermeable boundaries are present. This is discussed within the context of the paper by Nandalur et al. (2019), which concerns the effect of a centrally located conducting square block on convection in a square sidewall-heated porous cavity. Detailed solutions are also presented which allow the streamfunction to take the natural value on the surface of the internal block. Design/methodology/approach: Steady solutions are obtained using finite difference methods. Three different ways in which insulating boundary conditions are implemented are compared. Detailed attention is paid to the iterative convergence of the numerical scheme and to its overall accuracy. Error testing and Richardson’s extrapolation have been used to obtain very precise values of the Nusselt number. Findings: The assumption that the streamfunction takes a zero value on the boundaries of both the cavity and the embedded block is shown to be incorrect. Application of the continuity-of-pressure requirement shows that the block and the outer boundary take different constant values. Research limitations/implications: The Darcy–Rayleigh number is restricted to values at or below 200; larger values require a finer grid. Originality/value: This paper serves as a warning that one cannot assume that the streamfunction will always take a zero value on all impermeable surfaces when two or more are present. A systematic approach to accuracy is described and recommended.

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