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A single comprehensive equation is developed for the rate of heat and mass transfer from a circular cylinder in crossflow, covering a complete range of Pr (or Sc) and the entire range of Re for which data are available. This expression is a lower bound (except possibly for RePr < 0.2); free-stream turbulence, end effects, channel blockage, free convection, etc., may increase the rate. In the complete absence of free convection, the theoretical expression of Nakai and Okazaki may be more accurate for RePr < 0.2. The correlating equation is based on theoretical results for the effect of Pr in the laminar boundary layer, and on both theoretical and experimental results for the effect of Re. The process of correlation reveals the need for theoretical results for the effect of Pr in the region of the wake. Additional experimental data for the effect of Pr at small Pe and for the effect of Re during the transition in the point of separation are also needed.

A single correlating equation is constructed for the mean Nusselt (or Sherwood) number for all Reynolds and Prandtl (or Schmidt) numbers, and for either uniform wall temperature or a uniform heat flux density. The applicability of this equation is limited to fully developed flow in smooth tubes. However, developing as well as fully developed convection is considered. A corresponding equation is constructed for the friction factor for all Reynolds numbers. These expressions are based on interpolation between the various limiting cases, using the model of Churchill and Usagi. The correlating equations appear to represent available experimental and theoretical values within their uncertainty and to be at least as accurate as prior expressions for restricted ranges of Re and Pr or Sc. The equations are suitable for hand-held computers as well as for incorporation in algorithms for design and optimization.

Asymptotic solutions for Pr → 0 and Pr → ∞ and numerical solutions for intermediate Pr were obtained for a uniformly heated flat plate. The method of Churchill and Usagi was utilized to construct a simple correlation for these values. The same method was used to develop simple correlations for plug flow and fully developed flow in a uniformly heated tube. These correlations were in turn combined to develop correlations for the available experimental data and computed values for developing flow in a uniformly heated tube. Derivations and test calculations in which convection normal to the wall was neglected reveal that this error is significant but insufficient to explain all of the discrepancies in the computed values.

A correlating equation for assisting convection was developed by combining correlating equations for pure free and pure forced convection. These component equations are based on laminar boundary‐layer theory for an isothermal, vertical plate. Theoretical values for assisting convection indicate that the third root of the sum of the third powers gives the best representation, as contrasted with the choice and rationalization of the second or fourth power by prior investigators. This expression was modified by the addition of a limiting value Nuo to obtain a better representation below the domain of boundary‐layer theory and was generalized for uniform heating and for spheres and horizontal cylinders by the appropriate choice of the characteristic length.

An algorithm was developed for the finite-difference computation of hydrodynamic stability and natural convection in non-Newtonian fluids heated from below. Test calculations were carried out for fluids whose viscosity characteristics are described by the Ostwald-de Waele (power-law) and Ellis models and for roll-cells with both rigid and dragless vertical boundaries. The effects of time-step and grid-size were tested thoroughly. The results were found to be independent of the assumed initial state.The computed values of the Nusselt number and the critical Rayleigh number for Newtonian fluids agree well with prior experimental results. The computations for the Ostwald-de Waele model indicate that the approximate solution of Tien, Tsuei, and Sun may underestimate the critical Rayleigh Number. November, 1972

A study is made of the natural convection of a fluid contained in a long horizontal enclosure of rectangular cross section with one vertical wall heated and the other cooled. Two‐dimensional motion is assumed. The governing vorticity and energy transport equations are solved by an implicit alternating direction finite‐difference method. Transient and steady state isothermals and streamlines are obtained for Grashof numbers up to 100,000 and for height‐to‐width ratios of 1, 2, and 3.