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Mixed convection of a viscous dissipating fluid about a vertical flat plate. (English) Zbl 1210.76067
Summary: In this study, the effect of the viscous dissipation in steady, laminar mixed convection heat transfer from a heated/cooled vertical flat plate is investigated in both aiding and opposing buoyancy situations. The external flow field is assumed to be uniform. The governing systems of partial differential equations are solved numerically using the finite difference method. A parametric study is performed in order to illustrate the interactive influences of the governing parameters, mainly, the Richardson number, \(Ri\) (also known as the mixed convection parameter) and the Eckert number, \(Ec\) on the velocity and temperature profiles as well as the friction and heat transfer coefficients. Based on the facts the free stream is either in parallel or reverse to the gravity direction and the plate is heated or cooled, different flow situations are identified. The influence of the viscous dissipation on the heat transfer varied according to the situation. For some limiting cases, the obtained results are validated by comparing with those available from the existing literature. An expression correlating \(Nu\) in terms of \(Pr, Ri\) and \(Ec\) is developed.

MSC:
76E06 Convection in hydrodynamic stability
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74F05 Thermal effects in solid mechanics
74K20 Plates
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[1] Jaluria, Y., Natural convection heat and mass transfer, (1980), Pergamon Press Oxford
[2] Gebhart, B.; Jaluria, Y.; Mahajan, R.L.; Sammakia, B., Buoyancy-induced flows and transport, (1988), Hemisphere · Zbl 0699.76001
[3] Aydın, O., Aiding and opposing mechanisms of mixed convection in a shear- and buoyancy-driven cavity, Int. commun. heat mass transfer, 26, 7, 1019-1028, (1999)
[4] Bejan, A., Convection heat transfer, (1995), Wiley New York
[5] Pop, I.; Ingham, D.B., Convective heat transfer, (2001), Pergamon Amsterdam · Zbl 0856.76015
[6] Jaluria, Y., Basic of natural convection, () · Zbl 0593.76088
[7] Chen, T.S.; Armaly, B.F., Mixed convection in external flow, () · Zbl 0978.76504
[8] Kafoussias, N.G.; Rees, D.A.S.; Daskalakis, J.E., Numerical study of the combined free-forced convective laminar boundary layer flow past a vertical isothermal flat plate with temperature-dependent viscosity, Acta mech., 127, 1-4, 39-50, (1998) · Zbl 0920.76057
[9] Hossain, M.A.; Munir, M.S., Mixed convection flow from a vertical flat plate with temperature dependent viscosity, Int. J. therm. sci., 39, 2, 173-183, (2000)
[10] Abu-Mulaweh, H.I., Measurements of laminar mixed convection flow adjacent to an inclined surface with uniform wall heat flux, Int. J. therm. sci., 42, 1, 57-62, (2003)
[11] Merkin, J.H.; Pop, I., Mixed convection along a vertical surface: similarity solutions for uniform flow, Fluid dyn. res., 30, 233-250, (2002) · Zbl 1064.76610
[12] Steinruck, H., About the physical relevance of similarity solutions of the boundary-layer flow equations describing mixed convection flow along a vertical plate, Fluid dyn. res., 32, 1-2, 1-13, (2003) · Zbl 1029.76015
[13] Pantokratoras, A., Laminar assisting and mixed convection heat transfer from a vertical isothermal plate to water with variable physical properties, Heat mass transfer, 40, 581-585, (2004)
[14] Israel-Cookey, C.; Ogulu, A.; Omubo-Pepple, V.B., Influence of viscous dissipation and radiation on unsteady MHD free-convection flow past an infinite heated vertical plate in a porous medium with time-dependent suction, Int. J. heat mass transfer, 46, 2305-2311, (2003) · Zbl 1032.76682
[15] El-Amin, M.F., Combined effect of magnetic field and viscous dissipation on a power-law fluid over plate with variable surface heat flux embedded in a porous medium, J. magn. magn. mater., 261, 1-2, 228-237, (2003)
[16] Oosthuizen, P.H.; Naylor, D., Introduction to convective heat transfer analysis, (1999), McGraw-Hill New York · Zbl 1012.76540
[17] Saeid, N.W., Mixed convection flow along a vertical plate subjected to time-periodic surface temperature oscillations, Int. J. therm. sci., 44, 531-539, (2005)
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