Research Article
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Year 2024, Volume: 4 Issue: 1, 86 - 109, 31.03.2024
https://doi.org/10.53391/mmnsa.1382516

Abstract

References

  • [1] Saury, D., Rouger, N., Djanna, F. and Penot, F. Natural convection in an air-filled cavity: experimental results at large Rayleigh numbers. International Communications in Heat and Mass Transfer, 38(6), 679-687, (2011).
  • [2] Sajjadi, H., Gorji, M., Kefayati, G.H.R., Ganji, D.D. and Shayan Nia, M. Numerical analysis of turbulent natural convection in a square cavity using Large-Eddy simulation in lattice Boltzmann method. Iranian Journal of Science & Technology Transactions of Mechanical Engineering, 35(M2), 33-143, (2011).
  • [3] Shati, A.K.A., Blakey, S.G. and Beck, S.B.M. A dimensionless solution to radiation and turbulent natural convection in square and rectangular enclosures. Journal of Engineering Science and Technology, 7(2), 257-279, (2012).
  • [4] Durand-Estebe, B., Lebot, C., Arquis, E. and Mancos, J. Validation of turbulent natural convection in a square cavity for application of CFD modeling to heat transfer and fluid flow in a data center. In Proceedings, Biennial Conference on Engineering Systems Design and Analysis (ESDA), pp. 111-127, Nantes, France, (2012, July).
  • [5] Choi, S.K. and Kim, S.O. Turbulence modeling of natural convection in enclosures: a review. Journal of Mechanical Science and Technology, 26, 283-297, (2012).
  • [6] Jani, S., Mahmoodi, M. and Amini, M. Magnetohydrodynamic free convection in a square cavity heated from below and cooled from other walls. International Journal of Mechanical, Industrial Science and Engineering, 7(4), 750-755, (2013).
  • [7] Butler, C., Newport, D. and Geron, M. Natural convection experiments on a heated horizontal cylinder in a differentially heated square cavity. Experimental Thermal and Fluid Science, 44, 199-208, (2013).
  • [8] Xin, S., Salat, J., Joubert, P., Sergent, A., Penot, F. and Le Quéré, P. Resolving the stratification discrepancy of turbulent natural convection in differentially heated air-filled cavities. Part III: A full convection–conduction–surface radiation coupling. International Journal of Heat and Fluid Flow, 42, 33-48, (2013).
  • [9] Carvalho, P.H.S. and De Lemos, M.J.S. Turbulent free convection in a porous square cavity using the thermal equilibrium model. International Communications in Heat and Mass Transfer, 49, 10-16, (2013).
  • [10] Kefayati, G.H. Lattice Boltzmann simulation of natural convection in a nanofluid-filled inclined square cavity at presence of magnetic field. Scientia Iranica, 20(5), 1517-1527, (2013).
  • [11] Bahoosh, R., Mohamadi, F. and Karimi, M. Numerical investigation of natural convection in a square cavity with tilting walls. Journal of Thermophysics and Heat Transfer, 29(4), 725-731, (2014).
  • [12] Jani, S., Mahmoodi, M., Amini, M. and Jam, J.E. Numerical investigation of natural convection heat transfer in a symmetrically cooled square cavity with a thin fin on its bottom wall. Thermal Science, 18(4), 1119-1132, (2014).
  • [13] Asad, M.F.A., M., Oreyeni, T., Yavuz, M. and Olanrewaju, P.O. Analytic simulation of MHD boundary layer flow of a chemically reacting upper-convected Maxwell fluid past a vertical surface subjected to double stratifications with variable properties. The European Physical Journal Plus, 137, 813, (2022).
  • [14] Islam, T., Yavuz, M., Parveen, N. and Asad, M.F.A. Impact of non-uniform periodic magnetic field on unsteady natural convection flow of nanofluids in square enclosure. Fractal and Fractional, 6(2), 101, (2022).
  • [15] Asad, M.F.A., Yavuz, M., Alam, M.N., Sarker, M.M.A. and Bazighifan, O. Influence of fin length on magneto-combined convection heat transfer performance in a lid-driven wavy cavity. Fractal and Fractional, 5(3), 107, (2021).
  • [16] Sajjadi, H. and Kefayati, R. Lattice Boltzmann simulation of turbulent natural convection in tall enclosures. Thermal Science, 19(1), 155-166, (2015).
  • [17] Miroshnichenko, I. and Sheremet, M. Comparative study of standard k − ϵ and k − ϵ turbulence models by giving an analysis of turbulent natural convection in an enclosure. In EPJ Web of Conferences, 82, 1-4, (2015).
  • [18] Zineddine, D.A., Tabet, S. and Azzi, A. Natural convection in partially heated square cavity. Mechanics, 22(2), 119-124, (2016).
  • [19] Zhao, B. and Tian, Z. High-resolution high-order upwind compact scheme-based numerical computation of natural convection flows in a square cavity. International Journal of Heat and Mass Transfer, 98, 313-328, (2016).
  • [20] Aithal, S.M. Turbulent natural convection in a square cavity with a circular cylinder. Journal of Thermo physics and Heat Transfer, 30(4), 843-853, (2016).
  • [21] Adnani, M., Meziani, B., Ourrad, O. and Zitoune, M. Natural convection in a square cavity: numerical study for different values of prandtl number. Fluid Dynamics and Material Processing, 12(1), 1-14, (2016).
  • [22] Benchabi, R. and Lanani, A. Two-Dimensional numerical simulation of natural convection in a square cavity. Mechanics, 23(4), 545-551, (2017).
  • [23] Solomon, A.B., van Rooyen, J., Rencken, M., Sharifpur, M. and Meyer, J.P. Experimental study on the influence of the aspect ratio of square cavity on natural convection heat transfer with Al2O3/Water nanofluids. International Communications in Heat and Mass Transfer, 88, 254-261, (2017).
  • [24] Yang, G., Iacovides, H., Craft, T. and Apsley, D. RANS modelling for temperature variance in conjugate heat transfer. In Proceedings 5th World Congress on Mechanical, Chemical, and Material Engineering, pp. 15-17, Lisbon, Portugal, (2019, August).
  • [25] Razera, A.L., da Fonseca, R.J.C., Isoldi, L.A., Dos Santos, E.D., Rocha, L.A.O. and Biserni, C. A constructal approach applied to the cooling of semi-elliptical blocks assembled into a rectangular channel under forced convection. International Journal of Heat and Mass Transfer, 184, 122293, (2022).
  • [26] Selimefendigil, F. and Öztop, H.F. Optimization of convective heat transfer performance for fluid flow over a facing step by using an elliptic porous object. Case Studies in Thermal Engineering, 27, 101233, (2021).
  • [27] Khatamifar, M., Lin, W. and Dong, L. Transient conjugate natural convection heat transfer in a differentially-heated square cavity with a partition of finite thickness and thermal conductivity. Case Studies in Thermal Engineering, 25, 100952, (2021).
  • [28] Devi, T.S., Lakshmi, C.V., Venkatadri, K. and Reddy, M.S. Influence of external magnetic wire on natural convection of non-Newtonian fluid in a square cavity. Partial Differential Equations in Applied Mathematics, 4, 100041, (2021).
  • [29] Wen, X., Wang, L.P. and Guo, Z. Development of unsteady natural convection in a square cavity under large temperature difference. Physics of Fluids, 33, 084108, (2021).
  • [30] Goswami, N., Randive, P.R. and Pati, S. Natural convection from a pair of heated cylinders in a square cavity with non-uniform temperature on the side walls. Journal of The Institution of Engineers (India): Series C, 102, 389-396, (2021).
  • [31] El, H.M. and Lafdaili, Z. Turbulent natural-convection heat transfer in a square cavity with nanofluids in presence of inclined magnetic field. Thermal Science, 26(4), 3201-3213, (2022).
  • [32] Turkyilmazoglu, M. Exponential nonuniform wall heating of a square cavity and natural convection. Chinese Journal of Physics, 77, 2122-2135, (2022).
  • [33] Bilal, S., Khan, N.Z., Shah, I.A., Awrejcewicz, J., Akgül, A. and Riaz, M.B. Numerical study of natural convection of power law fluid in a square cavity fitted with a uniformly heated T-fin. Mathematics, 10(3), 342, (2022).
  • [34] Sondur, S.R., Meuris, B. and Mescher, A.M. Benchmarked simulations of natural convection airflow in a square cavity. Numerical Heat Transfer, Part A: Applications, 84(4), 297-314, (2023).
  • [35] Asad, M.F.A., Alam, M.N., Tunç, C. and Sarker, M.M.A. Heat transport exploration of free convection flow inside enclosure having vertical wavy walls. Journal of Applied and Computational Mechanics, 7(2), 520-527, (2021).
  • [36] Asad, M.F.A., Alam, M.N., Rashad, A.M. and Sarker, M.M.A. Impact of undulation on magneto-free convective heat transport in an enclosure having vertical wavy sides. International Communications in Heat and Mass Transfer, 127, 105579, (2021).
  • [37] Hossain, M.S., Asad, M.F.A., Mallik, M.S.I., Yavuz, M., Alim, M.A. and Khairul Basher, K.M. Numerical study of the effect of a heated cylinder on natural convection in a square cavity in the presence of a magnetic field. Mathematical and Computational Applications, 27(4), 58, 1-17, (2022).
  • [38] Asad, M.F.A., Alam, M.N., Ahmad, H., Sarker, M.M.A., Alsulami, M.D. and Gepreel, K.A. Impact of a closed space rectangular heat source on natural convective flow through triangular cavity. Results in Physics, 23, 104011, (2021).
  • [39] Hossain, M.S., Sarder, C.K., Hoque, K.E., Bangalee, M.Z.I., Billah, M.M. and Uddin, M.A. Finite element simulation on MHD free convection in a square enclosure with elliptical shaped obstacle. Ganit: Journal of Bangladesh Mathematical Society, 43(1), 63-75, (2023).
  • [40] Hossain, M.S., Alim, M.A. and Andallah, L.S. Numerical simulation of MHD natural convection flow within porous trapezoidal cavity with heated triangular obstacle. International Journal of Applied and Computational Mathematics, 6, 166, (2020).
  • [41] Hossain, M.S. and Alim, M.A. MHD free convection within trapezoidal cavity with nonuniformly heated bottom wall. International Journal of Heat and Mass Transfer, 69, 327–336, (2014).
  • [42] Hossain, M.S., Alim, M.A. and Andallah, L.S. Numerical investigation of natural convection flow in a trapezoidal cavity with non-uniformly heated triangular block embedded inside. Journal of Advances in Mathematics and Computer Science, 28(5), 1-30, (2018).
  • [43] Taylor, C. and Hood, P. A numerical solution of the Navier-Stokes equations using the finite element technique. Computers & Fluids, 1(1), 73-100, (1973).
  • [44] Reddy J.N. An introduction to the finite element method. In Dynamics of Earth’s Fluid System. McGraw-Hill: New York, (1985).
  • [45] Rahman, M.M., Alim, M.A. and Mamun, M.A.H. Finite element analysis of mixed convection in a rectangular cavity with a heat-conducting horizontal circular cylinder. Nonlinear Analysis: Modelling and Control, 14(2), 217-247, (2009).

Free convection at different locations of adiabatic elliptic blockage in a square enclosure

Year 2024, Volume: 4 Issue: 1, 86 - 109, 31.03.2024
https://doi.org/10.53391/mmnsa.1382516

Abstract

The numerical simulation of free convection flow within a square-shaped enclosure for various orientations of elliptic blockage (EB) is performed in the present study. The bottom wall of the cavity remains uniformly heated, where the left and right (side) walls as well as the boundary wall of the elliptic blockage are insulated and the top wall remains at a cool temperature. As $Pr$ remains constant, the effects of different values of $Ra$ have a great influence on overall fluid flow and temperature gradient for three different locations: bottom elliptic blockage (BEB), center elliptic blockage (CEB) and top elliptic blockage (TEB), as a mass flow circulation has been identified, and a state of equilibrium has been established within the fluid flow simulations along with the isotherm contours. The outcomes of the numerical analysis are presented with the streamlines, isotherms, and variations of the average Nusselt number.

References

  • [1] Saury, D., Rouger, N., Djanna, F. and Penot, F. Natural convection in an air-filled cavity: experimental results at large Rayleigh numbers. International Communications in Heat and Mass Transfer, 38(6), 679-687, (2011).
  • [2] Sajjadi, H., Gorji, M., Kefayati, G.H.R., Ganji, D.D. and Shayan Nia, M. Numerical analysis of turbulent natural convection in a square cavity using Large-Eddy simulation in lattice Boltzmann method. Iranian Journal of Science & Technology Transactions of Mechanical Engineering, 35(M2), 33-143, (2011).
  • [3] Shati, A.K.A., Blakey, S.G. and Beck, S.B.M. A dimensionless solution to radiation and turbulent natural convection in square and rectangular enclosures. Journal of Engineering Science and Technology, 7(2), 257-279, (2012).
  • [4] Durand-Estebe, B., Lebot, C., Arquis, E. and Mancos, J. Validation of turbulent natural convection in a square cavity for application of CFD modeling to heat transfer and fluid flow in a data center. In Proceedings, Biennial Conference on Engineering Systems Design and Analysis (ESDA), pp. 111-127, Nantes, France, (2012, July).
  • [5] Choi, S.K. and Kim, S.O. Turbulence modeling of natural convection in enclosures: a review. Journal of Mechanical Science and Technology, 26, 283-297, (2012).
  • [6] Jani, S., Mahmoodi, M. and Amini, M. Magnetohydrodynamic free convection in a square cavity heated from below and cooled from other walls. International Journal of Mechanical, Industrial Science and Engineering, 7(4), 750-755, (2013).
  • [7] Butler, C., Newport, D. and Geron, M. Natural convection experiments on a heated horizontal cylinder in a differentially heated square cavity. Experimental Thermal and Fluid Science, 44, 199-208, (2013).
  • [8] Xin, S., Salat, J., Joubert, P., Sergent, A., Penot, F. and Le Quéré, P. Resolving the stratification discrepancy of turbulent natural convection in differentially heated air-filled cavities. Part III: A full convection–conduction–surface radiation coupling. International Journal of Heat and Fluid Flow, 42, 33-48, (2013).
  • [9] Carvalho, P.H.S. and De Lemos, M.J.S. Turbulent free convection in a porous square cavity using the thermal equilibrium model. International Communications in Heat and Mass Transfer, 49, 10-16, (2013).
  • [10] Kefayati, G.H. Lattice Boltzmann simulation of natural convection in a nanofluid-filled inclined square cavity at presence of magnetic field. Scientia Iranica, 20(5), 1517-1527, (2013).
  • [11] Bahoosh, R., Mohamadi, F. and Karimi, M. Numerical investigation of natural convection in a square cavity with tilting walls. Journal of Thermophysics and Heat Transfer, 29(4), 725-731, (2014).
  • [12] Jani, S., Mahmoodi, M., Amini, M. and Jam, J.E. Numerical investigation of natural convection heat transfer in a symmetrically cooled square cavity with a thin fin on its bottom wall. Thermal Science, 18(4), 1119-1132, (2014).
  • [13] Asad, M.F.A., M., Oreyeni, T., Yavuz, M. and Olanrewaju, P.O. Analytic simulation of MHD boundary layer flow of a chemically reacting upper-convected Maxwell fluid past a vertical surface subjected to double stratifications with variable properties. The European Physical Journal Plus, 137, 813, (2022).
  • [14] Islam, T., Yavuz, M., Parveen, N. and Asad, M.F.A. Impact of non-uniform periodic magnetic field on unsteady natural convection flow of nanofluids in square enclosure. Fractal and Fractional, 6(2), 101, (2022).
  • [15] Asad, M.F.A., Yavuz, M., Alam, M.N., Sarker, M.M.A. and Bazighifan, O. Influence of fin length on magneto-combined convection heat transfer performance in a lid-driven wavy cavity. Fractal and Fractional, 5(3), 107, (2021).
  • [16] Sajjadi, H. and Kefayati, R. Lattice Boltzmann simulation of turbulent natural convection in tall enclosures. Thermal Science, 19(1), 155-166, (2015).
  • [17] Miroshnichenko, I. and Sheremet, M. Comparative study of standard k − ϵ and k − ϵ turbulence models by giving an analysis of turbulent natural convection in an enclosure. In EPJ Web of Conferences, 82, 1-4, (2015).
  • [18] Zineddine, D.A., Tabet, S. and Azzi, A. Natural convection in partially heated square cavity. Mechanics, 22(2), 119-124, (2016).
  • [19] Zhao, B. and Tian, Z. High-resolution high-order upwind compact scheme-based numerical computation of natural convection flows in a square cavity. International Journal of Heat and Mass Transfer, 98, 313-328, (2016).
  • [20] Aithal, S.M. Turbulent natural convection in a square cavity with a circular cylinder. Journal of Thermo physics and Heat Transfer, 30(4), 843-853, (2016).
  • [21] Adnani, M., Meziani, B., Ourrad, O. and Zitoune, M. Natural convection in a square cavity: numerical study for different values of prandtl number. Fluid Dynamics and Material Processing, 12(1), 1-14, (2016).
  • [22] Benchabi, R. and Lanani, A. Two-Dimensional numerical simulation of natural convection in a square cavity. Mechanics, 23(4), 545-551, (2017).
  • [23] Solomon, A.B., van Rooyen, J., Rencken, M., Sharifpur, M. and Meyer, J.P. Experimental study on the influence of the aspect ratio of square cavity on natural convection heat transfer with Al2O3/Water nanofluids. International Communications in Heat and Mass Transfer, 88, 254-261, (2017).
  • [24] Yang, G., Iacovides, H., Craft, T. and Apsley, D. RANS modelling for temperature variance in conjugate heat transfer. In Proceedings 5th World Congress on Mechanical, Chemical, and Material Engineering, pp. 15-17, Lisbon, Portugal, (2019, August).
  • [25] Razera, A.L., da Fonseca, R.J.C., Isoldi, L.A., Dos Santos, E.D., Rocha, L.A.O. and Biserni, C. A constructal approach applied to the cooling of semi-elliptical blocks assembled into a rectangular channel under forced convection. International Journal of Heat and Mass Transfer, 184, 122293, (2022).
  • [26] Selimefendigil, F. and Öztop, H.F. Optimization of convective heat transfer performance for fluid flow over a facing step by using an elliptic porous object. Case Studies in Thermal Engineering, 27, 101233, (2021).
  • [27] Khatamifar, M., Lin, W. and Dong, L. Transient conjugate natural convection heat transfer in a differentially-heated square cavity with a partition of finite thickness and thermal conductivity. Case Studies in Thermal Engineering, 25, 100952, (2021).
  • [28] Devi, T.S., Lakshmi, C.V., Venkatadri, K. and Reddy, M.S. Influence of external magnetic wire on natural convection of non-Newtonian fluid in a square cavity. Partial Differential Equations in Applied Mathematics, 4, 100041, (2021).
  • [29] Wen, X., Wang, L.P. and Guo, Z. Development of unsteady natural convection in a square cavity under large temperature difference. Physics of Fluids, 33, 084108, (2021).
  • [30] Goswami, N., Randive, P.R. and Pati, S. Natural convection from a pair of heated cylinders in a square cavity with non-uniform temperature on the side walls. Journal of The Institution of Engineers (India): Series C, 102, 389-396, (2021).
  • [31] El, H.M. and Lafdaili, Z. Turbulent natural-convection heat transfer in a square cavity with nanofluids in presence of inclined magnetic field. Thermal Science, 26(4), 3201-3213, (2022).
  • [32] Turkyilmazoglu, M. Exponential nonuniform wall heating of a square cavity and natural convection. Chinese Journal of Physics, 77, 2122-2135, (2022).
  • [33] Bilal, S., Khan, N.Z., Shah, I.A., Awrejcewicz, J., Akgül, A. and Riaz, M.B. Numerical study of natural convection of power law fluid in a square cavity fitted with a uniformly heated T-fin. Mathematics, 10(3), 342, (2022).
  • [34] Sondur, S.R., Meuris, B. and Mescher, A.M. Benchmarked simulations of natural convection airflow in a square cavity. Numerical Heat Transfer, Part A: Applications, 84(4), 297-314, (2023).
  • [35] Asad, M.F.A., Alam, M.N., Tunç, C. and Sarker, M.M.A. Heat transport exploration of free convection flow inside enclosure having vertical wavy walls. Journal of Applied and Computational Mechanics, 7(2), 520-527, (2021).
  • [36] Asad, M.F.A., Alam, M.N., Rashad, A.M. and Sarker, M.M.A. Impact of undulation on magneto-free convective heat transport in an enclosure having vertical wavy sides. International Communications in Heat and Mass Transfer, 127, 105579, (2021).
  • [37] Hossain, M.S., Asad, M.F.A., Mallik, M.S.I., Yavuz, M., Alim, M.A. and Khairul Basher, K.M. Numerical study of the effect of a heated cylinder on natural convection in a square cavity in the presence of a magnetic field. Mathematical and Computational Applications, 27(4), 58, 1-17, (2022).
  • [38] Asad, M.F.A., Alam, M.N., Ahmad, H., Sarker, M.M.A., Alsulami, M.D. and Gepreel, K.A. Impact of a closed space rectangular heat source on natural convective flow through triangular cavity. Results in Physics, 23, 104011, (2021).
  • [39] Hossain, M.S., Sarder, C.K., Hoque, K.E., Bangalee, M.Z.I., Billah, M.M. and Uddin, M.A. Finite element simulation on MHD free convection in a square enclosure with elliptical shaped obstacle. Ganit: Journal of Bangladesh Mathematical Society, 43(1), 63-75, (2023).
  • [40] Hossain, M.S., Alim, M.A. and Andallah, L.S. Numerical simulation of MHD natural convection flow within porous trapezoidal cavity with heated triangular obstacle. International Journal of Applied and Computational Mathematics, 6, 166, (2020).
  • [41] Hossain, M.S. and Alim, M.A. MHD free convection within trapezoidal cavity with nonuniformly heated bottom wall. International Journal of Heat and Mass Transfer, 69, 327–336, (2014).
  • [42] Hossain, M.S., Alim, M.A. and Andallah, L.S. Numerical investigation of natural convection flow in a trapezoidal cavity with non-uniformly heated triangular block embedded inside. Journal of Advances in Mathematics and Computer Science, 28(5), 1-30, (2018).
  • [43] Taylor, C. and Hood, P. A numerical solution of the Navier-Stokes equations using the finite element technique. Computers & Fluids, 1(1), 73-100, (1973).
  • [44] Reddy J.N. An introduction to the finite element method. In Dynamics of Earth’s Fluid System. McGraw-Hill: New York, (1985).
  • [45] Rahman, M.M., Alim, M.A. and Mamun, M.A.H. Finite element analysis of mixed convection in a rectangular cavity with a heat-conducting horizontal circular cylinder. Nonlinear Analysis: Modelling and Control, 14(2), 217-247, (2009).
There are 45 citations in total.

Details

Primary Language English
Subjects Mathematical Physics (Other), Finite Element Analysis
Journal Section Research Articles
Authors

Sayeda Sadia Billah This is me 0009-0002-4600-6304

Muhammad Sajjad Hossain This is me 0000-0002-8060-1214

Md. Fayz-al Asad 0000-0002-1240-4761

Muhammad Saiful Islam Mallik This is me 0000-0001-8558-8680

Sreebash Chandra Paul This is me 0000-0002-8647-5626

Md. Jahirul Haque Munshi 0000-0001-5995-3082

Md. Manirul Alam Sarker This is me 0000-0001-9337-5642

Publication Date March 31, 2024
Submission Date October 28, 2023
Acceptance Date March 28, 2024
Published in Issue Year 2024 Volume: 4 Issue: 1

Cite

APA Billah, S. S., Hossain, M. S., Asad, M. F.-a., Mallik, M. S. I., et al. (2024). Free convection at different locations of adiabatic elliptic blockage in a square enclosure. Mathematical Modelling and Numerical Simulation With Applications, 4(1), 86-109. https://doi.org/10.53391/mmnsa.1382516


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