• Received : 2015.02.25
  • Accepted : 2015.10.01
  • Published : 2015.12.25


Two-dimensional steady laminar natural convection around a heat conducting and generating solid body inside a square enclosure with different thermal boundaries is performed. The mathematical model is governed by the coupled equation of mass, momentum and energy. These equations are discretized by finite volume method with power-law scheme and solved numerically by SIMPLE algorithm with under-relaxation technique. Effect of Rayleigh number, temperature difference ratio of solid-fluid, aspect ratio of solid-enclosure and the thermal conductivity ratio of solid-fluid are investigated numerically for Pr = 0.7. The flow and heat transfer aspects are demonstrated in the form of streamlines and isotherms respectively.


  1. A. Bejan, Convection Heat Transfer, John Wiley, New York, 1984.
  2. G. De Vahl Davis, Natural convection of air in a square cavity: A benchmark numerical solutions, International Journal for Numerical Methods in Fluids, 3 (1983), 249-264.
  3. J.M House, C. Beckermann and T.F. Smith, Effect of centered conducting body on natural convection heat transfer in an enclosure, Numerical Heat Transfer Part A: Applications, 18 (1990), 213-225.
  4. J.Y. Oh, M.Y. Ha and K.C. Kim, Numerical study of heat transfer and flow of natural convection in an enclosure with a heat-generating conducting body, Numerical Heat Transfer Part A: Applications, 31 (1997), 289-303.
  5. D.G. Roychowdhury, S.K. Das and T.S. Sundararajan, Numerical simulation of natural convection heat transfer and fluid flow around a heated body inside an enclosure, Heat and Mass Transfer, 38 (2002), 565-576.
  6. M.K. Das and 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 (2004), 4987-5000.
  7. S.H. Tasnim and M.R. Collins, Numerical analysis of heat transfer in a square cavity with a baffle on the hot wall, International Communication in Heat and Mass Transfer, 31 (2004), 639-650.
  8. J.R. Lee and M.Y. Ha, Study of natural convection in a horizontal enclosure with a conducting body, International Journal of Heat and Mass Transfer, 48 (2005), 3308-3318.
  9. H. Khozeymehnezhad and S.A Mirbozorigi, Comparison of natural convection around a circular cylinder with a square cylinder inside a square enclosure, Journal of Mechanical Engineering and Automation, 2 (2012), 176-183.
  10. E. Fontana, A. Silva and V.C. Mariani, Natural convection in a partially open square cavity with internal heat source: an analysis of the opening mass flow, International Journal of Heat and Mass Transfer, 54 (2011), 1369-1386.
  11. M.U. Ahammad, M.M. Rahman and M.L. Rahman, Effect of inlet and outlet position in a ventilated cavity with a heat generating square block, Engineering e-transactions, 7 (2012), 107-115.
  12. R. Nasrin and S. Parvin, Flow behavior for combined convection in a vertical channel controlled by a heatgenerating tube, International Journal of Energy and Technology, 4 (2012), 1-7.
  13. A. Raji, M. Hasnaoui, M. Naimi, K. Slimari and M.T. Ouazzani, Effect of the subdivision of an obstacle on the natural convection heat transfer in a square cavity, Computers and Fluids, 68 (2012), 1-15.
  14. M.U. Ahammad, M.M. Rahman and M.L. Rahman, Mixed convection flow and heat transfer behavior inside a vented enclosure in the presence of heat generating obstacle, International Journal of Innovation and Applied Studies, 3 (2013), 967-978.
  15. R.K. Singh, K.B Sahu and T.D Mishra , Analysis of heat transfer and flow due to natural convection in air around heated square cylinder of different sizes insides an enclosure, International Journal of Engineering Research and Applications, 3 (2013), 766-771.
  16. M.A. Taghikhani and H.R chovoshi, Two dimensional MHD free convection with internal heating in a square cavity, Thermal Energy and Power Engineering, 2 (2013), 22-88.
  17. A.H Bhuiyan, M.A. Alim and M.N Uddin, Effect of Hartmann number on free convective flow in a square cavity with different positions of heated square block, International Journal of Mathematical, computational, Physical and Quantum Engineering, 8 (2014), 385-390.
  18. M. Sathiyamoorthy, T. Basak, S. Roy and I. Pop, Steady natural convection flows in a square cavity with linearly heated side wall(s), International Journal of Heat and Mass Transfer, 50 (2007), 766-775.
  19. T. Basak, S. Roy and A.R. Balakrishnan, Effect of thermal boundary conditions on natural convection flows with a square cavity, International Journal of Heat and Mass Transfer, 49 (2009), 4525-4535.
  20. S. Hussion, A. Hussein, Numerical investigation of natural convection phenomena in a uniformly heated circular immersed in square enclosure filled with air at different vertical locations, International Communications in Heat and Mass Transfer, 37 (2010), 1115-1126.
  21. Aswatha, C.J.G Gowda, S.N. Sridhara and K.N. Seetharamu, Effect of different thermal boundary conditions at bottom wall on natural convection in cavities, Engineering Science and Technology, 6 (2011), 109-130.
  22. S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere McGraw-Hill Washington DC, 1980.