STUDY OF NATURAL CONVECTION FLOWS IN A TILTED TRAPEZOIDAL ENCLOSURE WITH ISOFLUX HEATING FROM BELOW
Keywords:
Natural convection, trapezoidal enclosure, finite element, isofluxAbstract
Laminar steady state natural convection in a two-dimensional symmetrical trapezoidal enclosure hasbeen studied using a finite element method. In this investigation, the top wall is considered adiabatic,both inclined sidewalls are maintained at a constant cold temperature and an isoflux heat source isprovided at the bottom surface. The pressure-velocity form of the Navier-Stokes equations and energyequation are used to represent the mass, momentum and energy conservations of the fluid medium inthe enclosure. Galerkin weighted residual method of finite element formulation with triangularmesh elements is employed. The fluid investigated here is air of Prandtl number fixed at 0.7. TheRayleigh number is varied from 103 to 106 while the sidewall inclination angle is varied from -15° to45°. The results are presented in terms of streamline and isotherm plots as well as the variation ofaverage Nusselt number with Rayleigh number for different base wall tilt angles of 0°, 15°, and 30°.The results show that the average Nusselt number increases with the increase of Rayleigh numberand the effect of the sidewall inclination angle on heat transfer is significantly reduced at higherRayleigh number. Effects of sidewall inclination angle on convection heat transfer characteristicsdecrease with the increase of base wall tilt angle at higher Rayleigh number and Rayleigh numberequal to 105 can be considered as a critical limit for the present.
References
Asaithambi, A. (2003). Numerical solution ofthe Falkner-Skan equation using piecewiselinear functions. Applied MathematicalComputations, 81:607-614.
Baytas, A.C. and Pop, I. (2001). Natural convection in a trapezoidal enclosure filled witha porous medium. Int. J. of EngineeringScience, 39:125-134.
Baïri, A., Laraqi, N., and García de María, J.M.(2007). Numerical and experimental studyof natural convection in tilted parallelepipediccavities for large Rayleigh numbers.Exp. Thermal and Fluid Science, 31:309-324.
Bejan, A. (1984). Convection Heat Transfer.1st ed. John Willey & Sons, Inc., 494p.
Boussaid, M., Mezenner, A., and Bouhadef, M.(1999). Free heat and mass convection in atrapezoidal enclosure. Int. J. Therm. Sci.,38:363-371.
Corvaro, F. and Paroncini, M. (2008). A numericaland experimental analysis on the naturalconvection heat transfer of a smallheating strip located on the floor of a squarecavity. Applied Thermal Engineering,28:25-35.
Flack, R.D., Konopnicki, T.T., and Rooke, J.H.(1980). The measurement of naturalconvective heat transfer in triangularenclosure. J. Heat Transfer, 102:770-772.
Ganzarolli, M.M. and Milanez, L.F. (1995).Natural convection in rectangular enclosuresheated from below and symmetricallycooled from the sides. Int. J. Heat and MassTransfer, 38:1,063-1,073.
Iyican, L. and Bayazitoglu, Y. (1980). An analyticalstudy of natural convective heat transferwithin trapezoidal enclosure. ASMEJ. Heat Transfer, 102:640–647.
Kumar, R.B.V. and Kumar, B. (2004). Parallelcomputation of natural convection in trapezoidalporous enclosures. Mathematicsand Computers in Simulation, 65:221-229.
Kumar, S. (2004). Natural convective heat transferin a trapezoidal enclosure of box-typesolar cooker. Renewable Energy, 29:211-222.
Kuyper, R.A. and Hoogendoorn, C.J. (1995).Laminar natural convection flow in trapezoidalenclosures. Numer. Heat Transfer,Part A, 28: 55-67.
Lo, D.C., Young, D.L., and Lin, Y.C. (2005).Finite-element analysis of 3D viscous flowand mixed-convection problems by theprojection method. Numer. Heat Transfer,Part A, 48:339-358.
McQuain, W.D., Ribbens, C.J., Wang, C.Y., andWatson, L.T. (1994). Steady viscous lowin a trapezoidal cavity. Computers Fluids,23:613-626.
Natarajan, E., Basak, T., and Roy, S. (2008).Natural convection flows in a trapezoidalenclosure with uniform and non-uniformheating of bottom wall. Int. J. of Heat andMass Transfer, 51:747-756.
Nithyadevi, N., Kandaswamy, P., and Lee, J.(2007). Natural convection in rectangularcavity with partially active side walls. Int.J. of Heat and Mass Transfer, 50:4,688-4697.
Papanicolaou, E. and Belessiotis, V. (2005).Double-diffusive natural convection in anasymmetric trapezoidal enclosure:unsteady behavior in the laminar and theturbulent-flow regime. Int. J. of Heat andMass Transfer, 48:191-209.
Reddy, J.N. (1993). An Introduction to the FiniteElement Method. 2nd ed. McGraw-Hill, NY,896p.
Remley, T.J., Abdel-Khalik, S.I., Jeter, S.M.,Ghiaasiaan, S.M., and Dowling, M.F. (2001).Effect of non-uniform heat flux on wallfriction and convection heat transfer coefficientin a trapezoidal channel. Int. J. Heatand Mass Transfer, 44:2,453-2,459.
Reynolds, D.J., Jance, M.J., Behnia, M., andMorrison, G.L. (2004). An experimentaland computational study of the heat losscharacteristics of a trapezoidal cavityabsorber. Solar Energy, 76:229-234.
Roy, S. and Basak, T. (2005). Finite elementanalysis of natural convection flows in asquare cavity with non-uniformly heatedwall(s). Int. J. Engineering Science, 43:668-680.
Vander Eyden, J.T., Van der Meer, TH.H., Hanjalic,K., Biezen, E., and Bruining, J. (1998).Double-diffusive natural convection intrapezoidal enclosures. Int. J. of Heat andMass Transfer, 13:1,885-1,898.
