Computational investigation of free convection flow inside inclined square cavities

Authors

  • Mariya Helen
    Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, India.
  • Prabhakar V
    Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, India.

Keywords:

Penalty finite element analysis, inclined square cavities, thermal distribution, fluid distortion, Mathematica, hybrid function, numerical integration, COMSOL

Abstract

The temperature and fluid profiles of flow inside tilted square cavities are analysed with two different cases of thermal boundary conditions, (1) Isothermally cold sidewalls of the cavity and the hot bottom wall kept parallel to the insulated top wall, (2) Hot left wall, cold right wall, insulated top and bottom walls. The Galerkin finite element method with penalty parameter is used to solve the nonlinear coupled system of partial differential equations governing the flow and thermal fields. The method is further used to solve the Poisson equation for stream function. The results are presented in terms of isotherms and streamlines. The Gaussian rule with the hybrid function formed from the block-pulse function and Lagrange polynomial is implemented for the evaluation of the definite integrals present in the residual equations.  Attempting to affix the hybrid methods in the integration part for solving Finite Element Method (FEM) turned efficacious as the convergence is achieved for streamlines and isotherms with the existing results. The tilted square cavities with inclination angles Deg 0 to Deg 90 and Rayleigh number ranging between 10^3  and 10^5 for Pr=0.71  (air) are investigated. The source code for the finite element analysis is written in Mathematica. The results thus obtained are found to be competent with those of COMSOL, the Software for Multiphysics Simulation.

Dimensions

L. Viorel & N. Anisoara, “Numerical modelling of fluid flow and heat transfer in a corrugated channel for heat exchanger applications”, Procedia Manufacturing 22 (2018) 634.

A. Omri, J. Orfi & S.B. Nasrallah, “Natural convection effects in solar stills”, Desalination 183 (2005) 73.

G.D. Mey, M. Wojcik, J. Pilarski, M. Lasota, J. Banaszczyk, B. Vermeersch, A. Napieralski & M.D. Paepe, “Chimney effect on natural convection cooling of a transistor mounted on a cooling fin”, Journal of Electronic Packaging 131 (2009) 14501.

M. Sabour, M. Ghalambaz, & A Chamkha, “Natural convection of nanofluids in a cavity: criteria for enhancement of nanofluids”, International Journal of Numerical Methods for Heat and Fluid Flow 27 (2017) 1504.

K.Wisam, B.Hussama, K. Khanafera, H.J. Salema & Sheard GJ, “Natural convection heat transfer utilizing nanofluid in a cavity with a periodic side-wall temperature in the presence of a magnetic field”,International Communications in Heat and Mass Transfer 104 (2019) 127.

N. Nabipour, M. Babanezhad, A.T.Nakhjirin, & S. Shirazian, “Prediction of Nanofluid Temperature Inside the Cavity by Integration of Grid Partition Clustering Categorization of a Learning Structure with the Fuzzy

System”,International Communications in Heat and Mass Transfer 5 (2020) 3571.

A.J. Chamkha, “Hydromagnetic combined convection flow in a vertical lid-driven cavity with internal generation or absorption”,An International Journal of Computation and Methodology 41 (2002) 529.

C.S.N. Azwadi, M.Y.M Fairus & Syhrullail.S, “Virtual Study of Natural convection Heat transfer in an Inclined square cavity”,Journal of Applied Sciences 10 (2010) 331.

M.K Das & K.S.K Reddy, “Conjugate natural convection heat transfer in an inclined square cavity containing a conducting block”,International Journal of Heat and Mass Transfer 49 (2006) 4987.

A.K. Singh, S. Roy, T. Basak, “Analysis of Bejan’s heatlines on visualization of heat flow and thermal mixing in tilted square cavities”, International Journal of Heat and Mass Transfer 55 (2012) 2965.

J.K. Mariya Helen Mercy & V. Prabhakar, “Study of fluid flow inside closed cavities using computational numerical methods”,International Journal for Simulation and Multidisciplinary Design Optimization 12 (2012) 1.

J. Rasoul & P. Prinos, “Natural convection in an inclined enclosure”, International Journal of Numerical Methods for Heat & Fluid Flow 12 (1997) 438.

F. Xu, J.C. Patterson, C. Lei, “Natural convection in a differentially Heated cavity with a square obstruction on the sidewall”,Australian Journal of Mechanical Engineering 4 (2015) 77.

Bendaraa et al, “Numerical Study of Natural Convection in Square Cavity Using Lattice Boltzmann Method: Obstacles Effect”, IOP Conf. Ser: Mater. Sci. Eng 948 (2020) 1.

J. Vierendeels, B. Merci & E.Dick, “Benchmark solutions for the natural convective heat transfer problem in a square cavity with large horizontal temperature di erences”,International Journal of Numerical Methods for Heat & Fluid Flow 13 (2003) 1057.

R.C. Mohapatra, “Study on Natural Convection in a Square Cavity with Wavy right vertical wall Filled with Viscous Fluid”,Journal of Mechanical and Civil Engineering 14 (2017) 32.

J.N. Reddy, An Introduction to the Finite Element Method, United States of America, McGraw-Hill, New York (1993).

Victor Oboni Atabo, Solomon Ortwer Adee, “A New Special 15-Step Block Method for Solving General Fourth Order Ordinary Differential Equations”,J. Nig. Soc. Phys. Sci.3 (2021) 308.

Mark I. Modebei, Olumide O. Olaiya, Ignatius P. Ngwongwo, “Computational study of a 3-step hybrid integrators for third order ordinary differential equations with shift of three o -step points”,J. Nig. Soc. Phys.

Sci.3 (2021) 459.

V. J. Shaalini, S. E. Fadugba, “A New Multi-Step Method for Solving Delay Differential Equations using Lagrange Interpolation”,J. Nig. Soc. Phys. Sci.3 (2021) 159.

Friday Obarhua, Oluwasemire John Adegbor, “An Order Four Continuous Numerical Method for Solving General Second Order Ordinary Differential Equations”,J. Nig. Soc. Phys. Sci.3 (2021) 42.

Olumide O. Olaiya, Rasaq A. Azeez, Mark I. Modebei, “Efficient Hybrid Block Method For The Numerical Solution Of Second-order Partial Differential Problems via the Method of Lines”,J. Nig. Soc. Phys. Sci.3 (2021) 26.

H.R. Marzban, H.R. Tabrizidooz & M. Razzaghi, “Hybrid functions for nonlinear initial value problems with applications to Lane-Emden type equations”,Physics Letters A 372 (2008) 5883.

H.R. Marzban, S.M. Hoseini & M. Razzaghi, “Solution of Volterra’s population model via block-pulse functions and lagrange interpolating polynomials”, Math Methods Appl Sci, 32 (2009) 127.

Siraj-Ul-Islam, I. Aziz & F. Haq, “A comparative study of numerical integration based on Haar wavelets and hybrid functions”,Computers and Mathematics with Applications, 59 (2009) 2026.

I. Aziz, Siraj-Ul-Islam, & W. Khan, “Quadrature rules for numerical integration based on haar wavelets and hybrid functions”,Computers and Mathematics with Applications, 61 (2011) 2770.

G. Uma, V. Prabhakar & S. Hariharan, “Numerical integration using hybrid of block-pulse functions and Lagrange polynomial”,International Journal of Pure and Applied Mathematics, 106 (2016) 33.

H.R. Marzban, H.R. Tabrizidooz & M.Razzaghi, “Solution of variational problems via hybrid of block-pulse and Lagrange interpolating”,ET Control Theory Appl, 3 (2009) 1363.

Larry J.Segerlind, Applied finite element analysis, United States of America, John Wiley & Sons, New York (1984).

Published

2022-05-29

How to Cite

Computational investigation of free convection flow inside inclined square cavities. (2022). Journal of the Nigerian Society of Physical Sciences, 4(2), 231-241. https://doi.org/10.46481/jnsps.2022.637

Issue

Volume 4, Issue 2, May 2022

Section

Original Research
Copyright & Licensing

Copyright (c) 2022 Journal of the Nigerian Society of Physical Sciences

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How to Cite

Computational investigation of free convection flow inside inclined square cavities. (2022). Journal of the Nigerian Society of Physical Sciences, 4(2), 231-241. https://doi.org/10.46481/jnsps.2022.637

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