Numerical and experimental investigations into the upstream transpiration problem in free convection

Influence of step discontinuity in porous plate temperature in free convection with transpiration

Abstract: A simple finite difference scheme is used to solve the second order, simultaneous, non-linear partial differential equations with a nonhomogeneous boundary condition, to study the influence of a step discontinuity in the surface temperature on heat transfer from a vertical porous plate in free convection with uniform transpiration The numerical procedure is described in detail and results are presented forPr =072 in the blowing parameter range, - 15 < ©1< 15, for non-dimensional temperature range of 025 to 20

An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force

Abstract: The free-convection flow and heat transfer (generated by a body force) about a flat plate parallel to the direction of the body force are formally analyzed and the type of flow is found to be dependent on the Grashof number alone. For large Grashof numbers (which are of interest in aeronautics), the flow is of the boundary-layer type and the problem is reduced in a formal manner, which is analogous to Prandtl's forced-flow boundary-layer theory, to the simultaneous solution of two ordinary differential equations subject to the proper boundary conditions. Velocity and temperature distributions for Prandtl numbers of 0.01, 0.72, 0.733, 1, 1, 10, 100, and 1000 are computed, and it is shown that velocities and Nusselt numbers of the order of magnitude of those encountered in forced-convection flows may be obtained in free-convection flows. The theoretical and experimental velocity and temperature distributions are in good agreement. A flow and a heat-transfer parameter, from which the important physical quantities such as shear stress and heat-transfer rate can be computed, are derived as functions of Prandtl number alone.

The turbulent boundary layer on a porous plate: Experimental skin friction with variable injection and suction

Abstract: Experimental skin friction results from constant free-stream velocity boundary layers are reported for a variety of constant and slowly varying injection and suction wall conditions. A description is given of the flow characteristics of these air experiments. The uniform injection results are in good agreement with the results of Kendall and the Stevenson, Rotta, and Kinney results from the Mickley-Davis data. For all turbulent flows examined, C f 2 is found to be a a function of local Reθ and B. The friction factor ratio C f C fo |Reθ is found to be a function of B alone, and is given as an empirical function of B. Of seven theories examined, the theories of Rubesin and of Torii et al. are in best agreement with all of the results when considered on a local Ree and B basis. A simple calculation method of C f 2 vs. Rex is suggested for slowly varying Vw(X).

The Effect of Mass Transfer on Free Convection

Abstract: Consideration is given to the constant property laminar boundary layer equations with free convection and mass transfer. Similar solutions are possible for blowing rate distributions varying as the distance from the leading edge raised to the power (n -- 1)/4 where n is the exponent in a power law surface temperature distribution. Solutions to the equations in the form of skin fi- iction and heat-transfer parameters, and velocity and temperature profiles are presented for the constant wall temperature case for a fluid with Pr = 0.73. The cases considered range from strong suction to strong blowing. Mass transfer has a pronounced effect on the heat transfer but only a slight effect on the skin friction. In light of the solutions presented, these effects are shown to be physically rational. (auth)

Transpiration and natural convection: the vertical-flat-plate problem

Abstract: A study is made of the natural convective flow which is induced in an infinite expanse of gas by the presence of a vertical hot flat plate from which hot gas of the same chemical type is being blown. The transpiration rate is assumed to be such that a self-similar boundary-layer type of solution is available. It differs from previous analyses in the following respects. Most important, the density is not assumed to be constant a t any stage in the description of the flow field. Also the form of the induced flow in the outer domain is calculated and proves to be substantially independent of the blowing rate in this case; the induced outer flow is found to be of large lateral extent. Finally, the variable-gas-property problem is carried to second order and solutions are obtained by using an ‘exact’ form of Howarth-Dorodnitsyn variable. The opportunity is taken t o make some comments about the comparison between theory and experiment for finite flat plates without transpiration.