E. M. Sparrow

Combined Forced and Free Convection in a Boundary Layer Flow

Consideration is given to the combined forced and free convection flow and heat transfer about a nonisothermal body subjected to a nonuniform free stream velocity. Similar solutions for the laminar boundary layer equations are found to exist when the free stream velocity and surface temperature vary respectively as xm and x2m−1. The parameter controlling the relative importance of the free and forced convection is Gr/Re2. A flow separation phenomenon may occur when the forced and free convection act in opposite directions. Extensive numerical solutions of the transformed boundary layer equations have been carried out for the cases of uniform wall temperature and uniform wall heat flux for a Prandtl number of 0.7 (gases) over a wide range of values of Gr/Re2. Results are reported for the heat transfer, shear stress, and velocity and temperature fields. Criteria are given for cataloging flows as purely forced, purely free, and mixed.

Heat Transfer to Longitudinal Laminar Flow Between Cylinders

Consideration is given to the fully developed heattransfer characteristics for longitudinal laminar flow betweem cylinders arranged in an equilateral triangular array. The analysis is carried out for the condition of uniform heat transfer per unit length. Solutions are obtained for the temperature distributiom, and from these, Nusselt numbers are derived for a wide range of spacingto-diameter ratios. it is found that as the spacing ratio increases, so also does the wall-to-bulk temperature difference for a fixed heat transfer per unit length. Corresponding to a uniform surface temperature around the circumference of a cylinder, the circumferential variation of the local heat flux is computed. For spacing ratios of 1.5 to 2.0 amd greater, uniform peripheral wall temperature and uniform peripheral heat flux are simultaneously achieved. A simplified analysis which neglects circumferential variations is also carried out, and the results are compared with those from the more exact formulation. (auth)

Thermal radiation between parallel plates separated by an absorbing-emitting nonisothermal gas

Abstract A complete formulation, including the local details of gas absorption-emission processes, has been made for thermal radiation in a parallel plate enclosure. The temperature is permitted to vary continuously between the plates, and the emissive power of the gas may have an arbitrary dependence on temperature. Thermal conductivity effects have been omitted. Solutions of the governing integral equations have been carried out for values of the single governing parameter kL (k = absorption coefficient, L = spacing) in the range 0.1 to 2.0. Temperature distributions and heat transfer results are given. For moderate values of kL, the temperature is quite uniform across the gas.

Unsteady Turbulent Heat Transfer in Tubes

An analysis is made of the unsteady turbulent heat transfer in a circular tube whose wall temperature varies arbitrarily with time. The flow is steady and fully developed. The formulation permits the heat-transfer coefficient to vary with time and position in accordance with the energy conservation principle. This is in contrast to previous transient analyses where it was standard to use steady-state, fully developed coefficients. The first step in the analysis yields the heat-transfer response to a step jump in wall temperaiure, and this is then generalized by a superposition technique to apply to arbitrary time variations. Use of the generalized results is illustrated by application to the case where the wall temperature varies linearly with time. Comparison is made between the unsteady heat-transfer results of the present theory and those computed using steady-state heat-transfer coefficients.

Application of Variational Methods to Radiation Heat-Transfer Calculations

A variational method is presented for solving a class of integral equations which arise in radiation heat-transfer problems. First, to demonstrate the formulation of radiation problems in terms of integral equations, consideration is given to a system consisting of two nonblack, finite, parallel plates. After a general description of the variational method, its use is illustrated by application to the parallelplate system. Comparisons are made which show very good agreement with exact solutions. (auth)

Comparison of Turbulent Heat-Transfer Results for Uniform Wall Heat Flux and Uniform Wall Temperature

The purpose of this note is to examine in a more precise way how the Nusselt numbers for turbulent heat transfer in both the fully developed and thermal entrance regions of a circular tube are affected by two different wall boundary conditions. The comparisons are made for: (a) Uniform wall temperature (UWT); and (b) uniform wall heat flux (UHF). Several papers which have been concerned with the turbulent thermal entrance region problem are given. 1 Although these analyses have all utilized an eigenvalue formulation for the thermal entrance region there were differences in the choices of eddy diffusivity expressions, velocity distributions, and methods for carrying out the numerical solutions. These differences were also found in the fully developed analyses. Hence when making a comparison of the analytical results for uniform wall temperature and uniform wall heat flux, it was not known if differences in the Nusselt numbers could be wholly attributed to the difference in wall boundary conditions, since all the analytical results were not obtained in a consistent way. To have results which could be directly compared, computations were carried out for the uniform wall temperature case, using the same eddy diffusivity, velocity distribution, and digital computer program employed for uniform wall heat flux. In addition, the previous work was extended to a lower Reynolds number range so that comparisons could be made over a wide range of both Reynolds and Prandtl numbers.

Application of variational methods to the thermal entrance region of ducts

Abstract A variational method is presented for solving eigenvalue problems which arise in connection with the analysis of convective heat transfer in the thermal entrance region of ducts. Consideration is given to both situations where the temperature profile depends upon one cross-sectional co-ordinate (e.g. Circular tube) or upon two cross-sectional co-ordinates (e.g. Rectangular duct). The variational method is illustrated and verified by application to laminar heat transfer in a circular tube and a parallel-plate channel, and good agreement with existing numerical solutions is attained. Then, application is made to laminar heat transfer in a square duct as a check, an alternate computation for the square duct is made using a method indicated by Millsaps and Pohlhausen. The variational method can, in principle, also be applied to problems in turbulent heat transfer.