W.M. Kays

Heat transfer in annular passages—hydrodynamically developed turbulent flow with arbitrarily prescribed heat flux

Abstract The problem of turbulent flow heat transfer in a concentric circular tube annulus with fully developed velocity profile and constant heat rate per unit of length is considered. Experimentally obtained solutions are presented for the thermal entry length for a fluid with Pr = 0·7. Asymptotic solutions (fully developed velocity and temperature profiles) are developed for a wide range of radius ratio, Reynolds number, and Prandtl number. The solutions are based on empirical velocity and eddy diffusivity profiles, and the validity of the solutions is demonstrated experimentally for Pr = 0·7. A superposition method is demonstrated for solving the problem of asymmetric heating from the two surfaces of an annulus, and experimental data on asymmetric heating are presented which are in excellent agreement with the analysis. This paper is the third in a series (1, 2) culminating a four year study of heat transfer in annular passages.

HEAT TRANSFER IN ANNULAR PASSAGES. SIMULTANEOUS DEVELOPMENT OF VELOCITY AND TEMPERATURE FIELDS IN LAMINAR FLOW

Abstract An analysis is made of the problem of laminar flow heat transfer in an annulus with simultaneously developing velocity and temperature distributions and constant wall heat flux. A solution is obtained first for the hydrodynamic problem and then for the combined hydrodynamic and thermal problem by an integral method. Results are tabulated for several inner to outer tube radius ratios and Prandtl numbers. Experimental measurements made for Prandtl number = 0.7 showed excellent agreement with the analysis. This paper is the fourth in a series culminating a four year study of heat transfer in annular passages. ∥

Heat transfer to a turbulent boundary layer with varying free-stream velocity and varying surface temperature—an experimental study

Abstract Experimental data are presented for heat transfer to an essentially constant property turbulent boundary layer for various rates of free-stream acceleration. A limited amount of data for free-stream deceleration is also presented. The experimental apparatus was so constructed that surface temperature could be varied in an arbitrary manner, although the bulk of the data presented are for simple steps in surface temperature. It is found that acceleration causes a depression in the heat transfer rate below what would be predicted assuming a boundary-layer structure such as obtains for constant free-stream velocity. An empirical correlation of the results is presented. When used in conjunction with superposition theory, the results can be used to calculate heat-transfer rates for any arbitrary free-stream velocity variation, and any arbitrary surface temperature variation.

The turbulent boundary layer on a porous plate: Experimental heat transfer with uniform blowing and suction

Abstract There exists a need for additional experimental work in the field of heat transfer through a turbulent boundary layer with blowing and suction. An apparatus has been constructed which allows the determination of Stanton number to within 0·0001 units over most of the range between the asymptotic suction layer and the apparent “blow off” of the boundary layer. Data are presented for the case of uniform blowing and suction, constant free stream velocity, and essentially constant properties. Stanton numbers ranged from 0·0080 (asymptotic suction layer behavior; blowing fraction of −0·00765) to a value of 0·0001 (near “blow off”; blowing fraction of + 0·00955). The Reynolds number range is 1·3 × 105−2·3 × 106. Tabular and graphical results are presented.

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).

Heat transfer to the transpired turbulent boundary layer

Abstract This paper contains a summarization of five years work on an investigation on heat transfer to the transpired turbulent boundary layer. Experimental results are presented for friction coefficient and Stanton number over a wide range of blowing and suction for the case of constant free-stream velocity, holding certain blowing parameters constant. The problem of the accelerated turbulent boundary layer with transpiration is considered, experimental data are presented and discussed, and theoretical models for solution of the momentum equation under these conditions are presented. Data on turbulent Prandtl number are presented so that solutions to the energy equation may be obtained. Some examples of boundary layer heat transfer and friction coefficient predictions are presented using one of the models discussed, employing a finite difference solution method.

Experimental results for the transpired turbulent boundary layer in an adverse pressure gradient

The fluid mechanics of transpired incompressible turbulent boundary layers under zero and adverse pressure gradient conditions is investigated using an open-ended wind tunnel with a porous floor in the test section and a secondary air system for supply and metering of the transpiration air. All velocity profiles and turbulence profiles are obtained by linearized constant-temperature hot-wire anemometry. The wall shear stress is determined by measuring the shear stress away from the wall and extrapolating to the wall by integrating the boundary layer equations for the shear-stress profile. Equilibrium boundary layers are obtained when the transpiration velocity is varied such that the blowing parameter and the Clauser pressure gradient parameter are held constant. The experimental results obtained are presented in tabular and graphical forms.

The accelerated fully rough turbulent boundary layer

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity. An appropriate acceleration parameter K r for fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fraction F greater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state when K r is held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant. Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (for F equal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

Free convection over a vertical porous plate with transpiration

The problem of free convection over an isothermal vertical porous plate with transpiration is studied in this paper both numerically and experimentally. The effects of uniform transpiration on heat transfer and temperature and velocity profiles are predicted. Experimental data on non-dimensional temperature profiles for values of streamwise variable ξ⧋ υexv4Grx14 in the range −2 ⩽ ξ ⩽ 2, obtained interferometrically, show close agreement with numerical predictions. An accuracy of ± 1°F in temperature profile measurement is estimated for (Tw−T∞) = 50°F.

Heat transfer to a strongly accelerated turbulent boundary layer: Some experimental results, including transpiration

Abstract Heat transfer experiments have been carried out in air on a turbulent boundary layer subjected to a strongly accelerated free-stream flow, with and without surface transpiration. Stanton number, mean temperature and mean velocity profiles, and turbulence intensity profiles were measured along the accelerated region. The tests were conducted with favorable pressure gradients denoted by values of the acceleration parameter K(= ν U 2 ∞ dU ∞ dx of 2.0 × 10 −6 and 2.5 × 10 −6 . The blowing fraction, F (= ρ 0 V 0 ρ ∞ U ∞ ), ranged from 0.0 to 0.004. The flow was incompressible ( U ∞, max = 86 fps ) with a moderate temperature difference, 25°F, across the boundary layer. The primary objective of the program was to obtain detailed heat transfer data in strong accelerations and to provide a base for future prediction procedures. A secondary objective was to determine whether relaminarization of the boundary layer occurs at K = 2.5 × 10 −6 . The experimental results demonstrate that the Stanton number, as a function of enthalpy thickness Reynolds number, falls increasing below the behavior observed in unaccelerated flow as K is increased, with or without blowing. The profile traverses show that, at the end of acceleration, the boundary layer is still fully turbulent. Further heat transfer results are presented which illustrate the effects of various conditions at the start of acceleration (notably the thickness of the thermal and hydrodynamic layers) and step-changes in blowing within the acceleration region.