Investigation of transient conduction–radiation heat transfer in a square cavity using combination of LBM and FVM
Tóm tắt
In this paper, the effect of surface radiation in a square cavity containing an absorbing, emitting and scattering medium with four heated boundaries is investigated, numerically. Lattice Boltzmann method (LBM) is used to solve the energy equation of a transient conduction–radiation heat transfer problem and the radiative heat transfer equation is solved using finite-volume method (FVM).
In this work, two different heat flux boundary conditions are considered for the east wall: a uniform and a sinusoidally varying heat flux profile. The results show that as the value of conduction–radiation decreases, the dimensionless temperature in the medium increases. Also, it is clarified that, for an arbitrary value of the conduction–radiation parameter, the temperature decreases with decreasing scattering albedo. It is observed that when the boundaries reflect more, a higher temperature is achieved in the medium and on boundaries.
Tài liệu tham khảo
Chen S and Doolen G D 1998 Latice Boltzmann method for fluid flows. Ann. Rev. Fluid Mech. 30(1): 329–364
Succi S 2001 The lattice Boltzmann equation: for fluid dynamics and beyond. UK: Clarendon Press
Yi H L, Yao F J and Tan H P 2016 Lattice Boltzmann model for a steady radiative transfer equation. Phys. Rev. E 90(2): 023312
Keshtkar M M and Amiri B 2018 Numerical simulation of radiative–conductive heat transfer in an enclosure with an isotherm obstacle. Heat Transf. Eng. 39(1): 72–83
Mondal B and Chatterjee D 2012 Lattice Boltzmann simulation of heat conduction problems in non-isothermally heated enclosures. Heat Transf. Asian Res. 31(2): 127–144
Mondal B and Mishra S C 2009 The lattice Boltzmann method and the finite volume method applied to conduction–radiation problems with heat flux boundary conditions. Int. J. Numer. Methods Eng. 78(2): 172–195
Sajjadi H and Kefayati G R MHD turbulent and laminar natural convection in a square cavity utilizing Lattice Boltzmann Method. Heat Transf. Asian Res. 45(8): 795–814
Baghban M, Mansouri S H and Shams Z 2014 Inverse radiation–conduction estimation of temperature-dependent emissivity using a combined method of genetic algorithm and conjugate gradient. J. Mech. Sci. Technol. 28(2): 739–745
Siegel R 2001 Thermal radiation heat transfer, 4th edtion. USA: Taylor & Francis
Ho J R, Kuo C P, Jiaung W S and Twu C J 2002 Lattice Boltzmann scheme for hyperbolic heat conduction equation. Numer. Heat Transf. Part B Fundam. 41(6): 591–607
Jiaung W S, Ho J R and Kuo C P 2001 Lattice Boltzmann method for the heat conduction problem with phase change. Numer. Heat Transf. Part B Fundam. 39(2): 167–187
Fiveland W 1984 Discrete-ordinates solutions of the radiative transport equation for rectangular enclosures. J. Heat Transf. 106(4): 699–706
Truelove J 1988 Three-dimensional radiation in absorbing–emitting-scattering media using the discrete-ordinates approximation. J. Quant. Spectrosc. Radiat. Transf. 39(1): 27–31
Fiveland W 1988 Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method. J. Thermophys. Heat Transf. 2(4): 309–316
Keshtkar M M, Gandjalikhan Nassab S A and Nasr M R J 2009 Heat transfer characteristics of a cylindrical porous radiant air heater under the influence of a two-dimensional axisymmetric radiative field. Proc. Inst. Mech. Eng. Part A J. Power Energy 223(8): 913–923
Keshtkar M M and Gandjalikhan Nassab S A 2009 Theoretical analysis of porous radiant burners under 2D radiation field using discrete ordinates method. J. Quant. Spectrosc. Radiat. Transf. 110(17): 1894–1907
Ansari A and Gandjalikhan Nassab S A 2013 Forced convection of radiating gas over an inclined backward facing step using the blocked-off method. Therm. Sci. 17(3): 773–786
Murakami S and Asako Y 2013 A finite volume method on distorted quadrilateral meshes for discretization of the energy equation’s conduction term. Heat Transf. Asian Res. 42(2): 163–184
Sun Y, Zhang, X and Howell J R 2016 Evaluation of three different radiative transfer equation solvers for combined conduction and radiation heat transfer. J. Quant. Spectrosc. Radiat. Transf. 184: 262–273
Hunter B and Guo Z 2016 Improved treatment of anisotropic scattering in radiation transfer analysis using the finite volume method. Heat Transf. Eng. 37(4): 341–350
Chai J C, Lee H S and Patankar S V 1994 Finite volume method for radiation heat transfer. J. Thermophys. Heat Transf. 8(3): 419–425
Asghari A, Gandjalikhan Nassab S A and Ansari A 2015 Numerical study of combined radiation and turbulent mixed convection heat transfer in a compartment containing participating media. J. Mech. 31(4): 467–480
Mishra S C and Sahai H 2014 Analysis of non-Fourier conduction and volumetric radiation in a concentric spherical shell using lattice Boltzmann method and finite volume method. Int. J. Heat Mass Transf. 68: 51–66
Sun Y and Zhang X 2016 Analysis of transient conduction and radiation problems using lattice Boltzmann and finite volume methods. Int. J. Heat Mass Transf. 97: 611–617
Mishra S C and Lankadasu A 2005 Transient conduction-radiation heat transfer in participating media using the lattice Boltzmann method and the discrete transfer method. Numer. Heat Transf. Part A Appl. 47(9): 935–954
Mondal B and Mishra S C 2008 Lattice Boltzmann method applied to the solution of the energy equations of the transient conduction and radiation problems on non-uniform lattices. Int. J. Heat Mass Transf. 51(1): 68–82
Mondal B and Mishra S C 2009 Analysis of 3-D conduction-radiation heat transfer using the Lattice Boltzmann method. J. Thermophys. Heat Transf. 23(1): 210–216
Mishra S C, Poonia H, Vernekar R R and Das A K 2014 Lattice Boltzmann method applied to radiative transport analysis in a planar participating medium. Heat Transf. Eng. 35(15): 1267–1278
Mondal B and Chatterjee D 2012 Lattice Boltzmann simulation of heat conduction problems in non-isothermally heated enclosures. Heat Transf. Asian Res. 41(2):127–144
Sun Y and Zhang X 2015 Analysis of transient conduction and radiation problems using the lattice Boltzmann and discrete ordinates methods. Numer. Heat Transf. Part A Appl. 68(6): 619–637
Sasmal A and Mishra S C 2016 Analysis of conduction and radiation heat transfer in a differentially heated 2‐D square enclosure. Heat Transf. Asian Res. 46(4): 384–408
Mishra S C and Roy H K 2007 Solving transient conduction and radiation heat transfer problems using the lattice Boltzmann method and the finite volume method. J. Comput. Phys. 223(1): 89–107