EFFECTS OF THE WAVY GEOMETRY ON NATURAL CONVECTION HEAT TRANSFER, BOUNDARY LAYER FLOW ALONG A VERTICAL PLATE WITH VARIABLE WALL TEMPERATURE.
Keywords:
Free convection, boundary layer, wavy surface, vertical plate, variable wall temperatureAbstract
In this paper, a numerical study of heat transfer by natural convection along a wavy vertical plate with variable wall temperature is presented. The numerical method is applied to obtain the analytic solution. The homotopic transformation is employed to transform the physical domain into a flat plate. The boundary layer equations and the boundary conditions are discretized by the finite difference scheme and solved numerically using the method of Gauss-Seidel algorithm with relaxation coefficient. Effects of the wavy geometry and the constant m (m ≥ 0) on the velocity profiles, temperature profiles, local Nusselt number and skin friction coefficient are presented and discussed in detail.
Results show that increasing of the constant m leads to increase the heat transfer rate, while the high amplitude wavelength rates reduce in general the heat transfer.
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References
Adams, J.A. , Fadden MC. and Aiche P.W. [1966 ], Simultaneous heat and mass transfer in free convection with opposing body forces, Numer. Heat Transfer, J., Vol. 12, pp 642-647.
Gebhart, B. and Pera L. [1971], The natural of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion, Int. J. Heat Mass Transfer, Vol. 14, pp 2025–2050.
Bottemanne, F.A. [1971], Theoretical solution of simultaneous heat and mass transfer by free
convection about a vertical flat plate, Appl. Sci Res., Vol.25, No. 1, pp 137-149.
Pera, L. and Gebhart, B. [1972], Natural convection flows adjacent to horizontal surfaces resulting from the combined buoyancy effects of thermal and mass diffusion", Int. j. of Heat and Mass Transfer, Vol. 15, pp 269-278.
Callahan,G.D. and Marner W.J. [1976], Transient free convection with mass transfer on a isothermal vertical flat plat, Int. J. Heat Mass Transfer, Vol. 19, pp 165–174.
Chen, T.S. and Yuh, C.F. [1979], combined heat and mass transfer in natural convection on inclined surfaces, Num. Heat Transfer, Vol. 2, pp 233–250.
Chen, T.S and Yuh, C.F. [1980], combined heat and mass transfer in natural convection along a vertical cylinder, Int. J. Heat Mass Transfer, Vol. 23, pp 451-461.
Yao, L.S [1983], Natural convection along a wavy surface, ASME, J. Heat Transfer, Vol. pp 105, 465-468.
Raju, M.S., Liu, X.Q. and Law C.K. [1984], A formulation of combined forced and free convection
past horizontal and vertical surfaces, Int. J. Heat Mass Transfer, Vol. 27, pp 2215-2224.
Lin, H.-T., Yu, W.-S. and Yang, S.-L. [1989], Free convection on an arbitrarily inclined plate with
uniform surface heat flux, Wärme- und Stoffübertr, Vol. 24, pp 183-190.
Marcoux, M., Charrier-Mojtabi M.C. and Azaiez M. [1999], Double-diffusive convection in an annular vertical porous layer, Int. J. of Heat and Mass Transfer, Vol. 42 . pp 2313-2325.
Ching-Yang ,C. [2000], Natural convection heat and mass transfer near a vertical wavy surface with constant wall temperature and concentration in a porous medium, Int. Comm. Heat and Mass Transfer, Vol. 27, No. 8, pp 1143-1154.
Anwar, H. Md., Sazzad M. M. and Ioan, P. [2001], Natural convection flow of a viscous fluid with viscosity inversely proportional to linear function of temperature from a vertical wavy cone, Int. J. Therm. Sci. Vol. 40, pp 366–371.
Mamou, M. [2003], Stability analysis of the perturbed rest state and of the finite amplitude steady double-diffusion convection in a shallow porous enclosures, Int. Journal of Heat and Mass Transfer, Vol. 46, No.12 , pp 2263–2277.
Jer-Huan, J., Wei-Mon and Yan Hui-Chung, L. [2003], Natural convection heat and mass transfer along a vertical wavy surface, Int. Journal of Heat and Mass Transfer Vol. 46, pp 1075–1083.
Si-Abdallah, M., Zeghmati B., Michel D. [2005], Numerical study of a thermal laminar natural convection in the boundary layer of a wavy cone trunk, J. of Energy Heat and Mass Transfer, Vol. 27 , pp 139-152.
Kefeng, S. and Wen-Qiang L. [2006], Time evolution of double-diffusive convection in a vertical cylinder with radial temperature and axial solutal gradients, Int. J. Heat mass transfer, Vol. 49, pp 995–1003.
Si-Abdallah, M., Zeghmati, B. and Daguenet, M. (2006), Numerical study of laminar natural convection heat and mass transfer in the boundary layer of a wavy cylinder. The third Int. conference on advances in mechanical engineering and mechanics, December 17-19, Hammamet Tunisia.
Deswita, L. , Nazar, R., Ahmad A. and Ioan, P. [2009], Similarity solutions of free convection boundary layer flow on a horizontal plate with variable wall temperature, European Journal of Scientific Research, Vol. 27, No.2, pp.188-198.
