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Parallel numerical computation of mixed convection in a square enclosure with multiple heat sources on Anucluster

Mixed convection in a square cavity

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Abstract

The coupled nonlinear partial differential equations modelling the influence of multiple heat sources on the mixed convection process in a fluid saturated vertical porous square enclosure have been solved numerically by Galerkin finite element method in conjuction with the Krylov Solver BICGM. Detailed parallel numerical computations, based on the message passing libraries from ANULIB, have been carried out on an eight noded ANUCLUSTER to assess the influence of flow governing paremeters such as Rayleigh number and suction/injection velocity on mixed convection process. The obtained results have been analysed for heat and mass transfer in the form of isotherm, streamline and velocity vector plots. Local, cumulative and global heat fluxes have been calculated in the form of corresponding versions of Nusselt number. Computations have also been carried out for the case natural convection due the multiple hot sources. Nusselt numbers from mixed convection process are compared with those from natural convection process. Efficiency and speedup of the parallel computations on ANUCLUSTER have also been assessed and presented.

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Abbreviations

\(V_{inj}\) :

Suction/injection velocity

D :

Width of the inlet and outlet

\(Q_{\xi }\) :

Cumulative heat flux along all hot bodies

\(Q_{\xi _{i}}\) :

Cumulative heat flux along \( i{\text {th}}\) hot body

\(Nu_{\partial \Omega _s^i}\) :

Nusselt number along the edges of \(i{\text{th}}\) hot body

\(N_i\) :

Interpolation function

Ra :

Rayleigh number

T :

Non-dimensional fluid temperature

U, V :

Velocity components along the x and y directions

W :

Weight function

\(W_1\) :

Injection window

\(W_2\) :

Suction window

X, Y :

Non-dimensional Cartesian coordinates

\(\Gamma \) :

Boundary of domain

\(\Omega \) :

Domain of interest

\(\Omega _s^{i}\) :

\(i{\text{th}}\) hot body source

\(\Omega _s^{i,j}\) :

\(j{\text{th}}\) side of \(i{\text{th}}\) hot body source

\(\psi \) :

Non-dimensional stream function

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Acknowledgments

This work has been carried out under the SERB,DST, Govt. of India sponsored project. The authors are thankful to SERB,DST, Govt. of India for providing the SRA fellowship to the third author.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    B. V. Rathish Kumar, Mohit Nigam, Priti Kumari & Parul Sharma

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  1. B. V. Rathish Kumar
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Correspondence to B. V. Rathish Kumar.

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Kumar, B.V.R., Nigam, M., Kumari, P. et al. Parallel numerical computation of mixed convection in a square enclosure with multiple heat sources on Anucluster. Int J Adv Eng Sci Appl Math 7, 96–105 (2015). https://doi.org/10.1007/s12572-015-0131-4

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