Natural convection flows with variable viscosity, heat and mass diffusion along a vertical plate

• Autorzy: Dimian M. F. , Hadhoda M. K.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is a numerical study of laminar double diffusive free convection viscous flows adjacent to a vertical plate, taking into account the variation of the viscosity and double-diffusive heat and mass transfer with temperature. The governing conservation equations of mass, momentum, energy and chemical species are non-dimensionalized by using appropriate transformations. The resulting equations are solved numerically by using the fourth order Runge-Kutta integration scheme along with the Nachtsheim-Swiger shooting technique. It is noticed that both the velocity and concentration of air are increasing as the parameter Β 2, (the species diffusion parameter) increases, but an opposite effect for the velocity is observed at a certain distance far from the plate. It is also observed that the temperature decreases as the parameter Β 2 increases. The shearing stress at the plate, the local Nusselt number and the local Sherwood number are obtained. The friction coefficient at the plate, of heat and mass transfer at the plate, the momentum, thermal and concentration boundary layers thickness (δ, δ T, δ C) have been estimated for different values of α, Sc and N.

Słowa kluczowe

EN

convection flow; mass diffusion; viscoelascic fluid

PL

przepływ konwekcyjny; dyfuzja masy; ciecz lepkosprężysta

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2004
• Tom: Vol. 7, nr 2
• Strony: 61--76
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Dimian M. F.

autor

Hadhoda M. K.

• Department of Mathematics, Faculty of Science, Ain Sham University, Cairo, Egypt,

Bibliografia

• [1] Adams, JA, Rogers, DF: Computer Aided Heat Transfer Analysis, (1973), McGraw-Hill, Tokyo.
• [2] Allain, C, Cloitre, M, Mongruel, A: Scaling in flows driven by heat and mass convection in a porous medium, Europhys. Lett., (1992), 20, 313-318.
• [3] Angirasa, D and Srinivasan, J: Natural convection flows due to the combined buoyancy of heat and mass diffusion in a thermally stratified mediums, J. Heat Transfer, 111, (1989), 657-633.
• [4] Elbashbeshy, EMA and Ibrahim, FN: Steady free convection flow with variable viscosity and thermal diffusivity along a vertical plate, J. Phys. D: Appl. Phys., (1993), 26, 2137-2143.
• [5] Eltayeb, IA and Loper, DE: On the stability of vertical double-diffusive interfaces. Part1. A single plane interface, J. Fluid Mech., (1991), 228, 149-181.
• [6] Gebhart B: Heat Transfer, (1971), 2nd ed., McGraw-Hill, New York.
• [7] Gebhart, B, Jaluria, Y, Mahajan, RL and Sammakia B: Buoyancy induced flow and transport, Chap. 6, Hemisphere, Washington/ Springer-Verlag, (1971).
• [8] Gebhart, B and Pera, L: The Nature of Vertical Natural Convection Flows Resulting Prom the Combined Buoyancy Effects of Thermal and Mass diffusion, Int. J. Heat Mass Transfer, (1971), 14, 2025-2035.
• [9] Hyun, MT, Kuo, DC, Bergman, TL and Ball, KS: Direct simulation of double diffusion in low Prandtl number liquids, Int. J. of Computation, Part A. Applications, (1995), 27(6), 639-650.
• [10] Ibrahim, FN and Ibrahim, EI: Variable Viscosity Flow of Dilute Suspension Between Two Parallel Plates, Proc. Math. Phys. Soc., Egypt, (1984), 57, 145-157.
• [11] Ibrahim FN: Steady free convection flow wit h variable viscosity and thermal diffusivity along a vertical plate, J. Phys. D: Appl. Phys.: (1993), 26, 2137-2143.
• [12] Jaluria, Y: Natural Convection Heat and Mass Transfer, Pergamon, Oxford, (1980).
• [13] Jaluria, Y and Gebhart, B: Stability and Transition of Buoyancy Induced Flows in a Stratified Medium, J. Fluid Mech., (1974), 66, 3, 593-612.
• [14] Lee, KT: Natural convection heat and mass transfer in partially heated vertical parallel plates, Int. J. Heat and Mass Transfer, (1999), 42, 4417-4425.
• [15] Mongruel, A, Cloitre, M and Allain, C: Scaling as boundary layer flows driven by double diffusive convection, Int. J. Heat Mass Transfer, (1996), 39, 3899-3916.
• [16] Nachtsheim, PR and Swigert, P: Satisfaction of Asymptotic Boundary Conditions in Numerical Solution of Systems of Nonlinear Equations of the Boundary Layer Type, NAGA TN D-3004, (1965).
• [17] Ostrach, S: Natural Convection with Combined Driving Forces, J. Physico-Chemical Hydrodynamics, (1980), 1, 233-247.
• [18] Pera, L and Gebhart, B: Natural convection flows adjacent to horizontal surfaces resulting from the combined buoyancy effects of thermal and mass diffusion, Int. J. Heat Mass Transfer, (1972), 15, 269-278.
• [19] Pop, I, Gorla, RS and Rashidi, M: The effect of variable viscosity on flow and heat transfer to a continuous moving fiat plate, Int. J. Eng. Sci., (1992), 30, 1-6.
• [20] Saddeek, MA: The effect of variable viscosity on hydromagnetic flow and heat transfer past a continuously moving porous boundary with radiation, Int. Comm. Heat Mass Transfer, (2000), 27, 7, 1037-1046.
• [21] Schlichting, H: Boundary layer theory, McGraw-Hill, New York, (1968).
• [22] Vedhanayagam, M, Altenkirch, RA and Eichhorn, R: A Transformation of the Boundary Layer Equations for Free Convection Past a Vertical Flat Plate With Arbitrary Blowing and Wall Temperature Variation, Int. J. Heat Mass Transfer, (1980), 23, 1286-1288.
• [23] Williams, C, Mulligan, JC, and Rhyne, TB: Semi-similar Solutions for Unsteady Free-Convection Boundary Layer Flow on a Vertical Flat Plate, J. Fluid Mech., (1987), 75, 309-332.