Numerical Solutions of 2-D Laminar Free Convection in an Isoceles Triangular Cavity Filled with a Darcy-Brinkman Porous Medium: Effect of Heat Source Size
In this work, a numerical study of free convection in an isoceles porous triangular cavity with a partially heated horizontal base and cooled upper walls is analysed. The uniform heat source is located centrally at the base wall. Darcy-Brinkman model is used; it is also assumed that the fluid used is incompressible and obeys the Boussinesq approximation. The non-dimensionless governing equations, stream function-vorticity, momentum and energy are discretized by finite difference method and solved using the successive over-relaxation (SOR) method. Streamline and isotherm patterns were presented at different lengths of heater (
), Darcy number (
), Prandtl number (
) and for different Rayleigh number (
). On the basis of the results, it is observed that the presence of a localized heat source may slightly accelerate the flow, but does not change the fundamental mode of convection. Beyond the critical value of Rayleigh number, the average Nusselt number characterizing overall heat transfer increases rapidly with decreasing source size.
References
[1]
Alves, T.A. and Altemani, C.A.C. (2012) An Invariant Descriptor for Heaters Temperature Prediction in Conjugate Cooling. International Journal of Thermal Sciences, 58, 92-101. https://doi.org/10.1016/j.ijthermalsci.2012.03.007
[2]
Kuznetsov, G.V. and Sheremet, M.A. (2008) New Approach to the Mathematical Modeling of Thermal Regimes for Electronic Equipment. Russian Microelectronics, 37, 131-138. https://doi.org/10.1134/s1063739708020078
[3]
Sheremet, M.A. and Pop, I. (2014) Natural Convection in a Square Porous Cavity with Sinusoidal Temperature Distributions on Both Side Walls Filled with a Nanofluid: Buongiorno’s Mathematical Model. Transport in Porous Media, 105, 411-429. https://doi.org/10.1007/s11242-014-0375-7
[4]
Bagchi, A. and Kulacki, F.A. (2013) Natural Convection in Superposed Fluid-Porous Layers, Springer Briefs in Applied Sciences and Technology. Springer.
[5]
Nield, D.A. and Bejan, A. (2017) Convection in Porous Media, Volume 3. Springer.
[6]
Pop, I. and Ingham, D.B. (2001) Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media. Pergamon.
[7]
Kambiz, V. (2015) Handbook of Porous Media. CRC Press.
[8]
Ingham, D.B. and Pop, I. (2005) Transport Phenomena in Porous Media III. Elsevier Science.
[9]
Asan, H. and Namli, L. (2000) Laminar Natural Convection in a Pitched Roof of Triangular Cross-Section: Summer Day Boundary Conditions. EnergyandBuildings, 33, 69-73. https://doi.org/10.1016/s0378-7788(00)00066-9
[10]
Holtzman, G.A., Hill, R.W. and Ball, K.S. (2000) Laminar Natural Convection in Isosceles Triangular Enclosures Heated from Below and Symmetrically Cooled from Above. Journal of Heat Transfer, 122, 485-491. https://doi.org/10.1115/1.1288707
[11]
Asan, H. and Namli, L. (2001) Numerical Simulation of Buoyant Flow in a Roof of Triangular Cross-Section under Winter Day Boundary Conditions. Energy and Buildings, 33, 753-757. https://doi.org/10.1016/s0378-7788(01)00063-9
[12]
Akinsete, V.A. and Coleman, T.A. (1982) Heat Transfer by Steady Laminar Free Convection in Triangular Enclosures. International Journal of Heat and Mass Transfer, 25, 991-998. https://doi.org/10.1016/0017-9310(82)90074-6
[13]
Ridouane, E.H., Campo, A. and Hasnaoui, M. (2006) Benefits Derivable from Connecting the Bottom and Top Walls of Attic Enclosures with Insulated Vertical Side Walls. Numerical Heat Transfer, Part A: Applications, 49, 175-193. https://doi.org/10.1080/10407780500302257
[14]
Kpode, K., Sow, M.L. and Mbow, C. (2016) Unsteady Natural Convection with Summer Boundary Conditions in a Habitat at High Rayleigh Number and at High Time. Energy and Buildings, 121, 72-77. https://doi.org/10.1016/j.enbuild.2016.03.068
[15]
Poulikakos, D. and Bejan, A. (1983) Numerical Study of Transient High Rayleigh Number Convection in an Attic-Shaped Porous Layer. Journal of Heat Transfer, 105, 476-484. https://doi.org/10.1115/1.3245610
[16]
Varol, Y., Oztop, H.F. and Varol, A. (2007) Natural Convection in Porous Triangular Enclosures with a Solid Adiabatic Fin Attached to the Horizontal Wall. International Communications in Heat and Mass Transfer, 34, 19-27. https://doi.org/10.1016/j.icheatmasstransfer.2006.09.004
[17]
Varol, Y., Oztop, H.F. and Varol, A. (2007) Free Convection in a Triangular Porous Media Filled Enclosure Heated or Cooled Horizontal and Vertical Walls. The 3rd International Energy, Exergy and Environment Symposium, Évora, 1-5 July 2007.
[18]
Varol, Y., Oztop, H.F. and Varol, A. (2006) Free Convection in Porous Media Filled Right-Angle Triangular Enclosures. International Communications in Heat and Mass Transfer, 33, 1190-1197. https://doi.org/10.1016/j.icheatmasstransfer.2006.08.008
[19]
Basak, T., Roy, S. and Krishna Babu, S. (2008) Natural Convection and Flow Simulation in Differentially Heated Isosceles Triangular Enclosures Filled with Porous Medium. Chemical Engineering Science, 63, 3328-3340. https://doi.org/10.1016/j.ces.2008.03.038
[20]
Basak, T., Roy, S., Babu, S.K. and Pop, I. (2008) Finite Element Simulations of Natural Convection Flow in an Isosceles Triangular Enclosure Filled with a Porous Medium: Effects of Various Thermal Boundary Conditions. International Journal of Heat and Mass Transfer, 51, 2733-2741. https://doi.org/10.1016/j.ijheatmasstransfer.2007.10.009
[21]
Varol, Y., Oztop, H.F. and Varol, A. (2008) Free Convection Heat Transfer and Flow Field in Triangular Enclosures Filled with Porous Media. Journal of Porous Media, 11, 103-115. https://doi.org/10.1615/jpormedia.v11.i1.70
[22]
Varol, Y., Oztop, H.F. and Koca, A. (2008) Entropy Production Due to Free Convection in Partially Heated Isosceles Triangular Enclosures. Applied Thermal Engineering, 28, 1502-1513. https://doi.org/10.1016/j.applthermaleng.2007.08.013
[23]
Weinan, E. and Liu, J.G. (1996) Vorticity Boundary Condition and Related Issues for Finite Difference Schemes. Journal of Computational Physics, 124, 368-382.
[24]
Poulikakos, D., Bejan, A., Selimos, B. and Blake, K.R. (1986) High Rayleigh Number Convection in a Fluid Overlaying a Porous Bed. InternationalJournalofHeatandFluidFlow, 7, 109-116. https://doi.org/10.1016/0142-727x(86)90056-1
