Previously published methods for the solution of one-dimensional heat-conduction problems with melting or freezing are briefly reviewed and weaknesses of previous analytic and numerical methods are outlined. Two new and more generally applicable numerical methods, applicable to digital and analog computation, are developed in the paper. Sample problems using these new techniques are solved and compared with the results of a widely used conventional method. An evaluation of the various methods and recommendations on areas of application are included.

Velocity distributions, friction losses, and heat-transfer characteristics were studied analytically and experimentally for fully developed turbulent flow in tubes with twisted tape swirl generators. Data were obtained for pitch-to-diameter ratios from 3.62 to 22.0 with both air and water under isothermal and forced convection heating conditions. The following principal conclusions result: (a) The velocity field is helicoidal and corresponds to a forced vortex in the core superposed on an essentially uniform axial flow. (b) Friction losses may be predicted from the combined effects of the axial and tangential boundary-layer flows coupled with an additional “vortex-mixing” effect. (c) Approximate heat-transfer correlations can be predicted from a Colburn-type analysis. These may be improved by considering a boundary layer and vortex mixing model.

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Friction and heat transfer characteristics of turbulent air flowing through tubes with twisted strip swirl promoters were studied experimentally and analytically. Data were obtained for pitch-to-diameter ratios as low as 3.15 and for Reynolds numbers up to 100,000. Both heating and cooling tests were run for tube wall to fluid bulk temperature ratios from 0.6 to 1.9 (degR/degR) to evaluate compressibility and buoyancy effects. Both temperature-varying properties and the centrifugal force field imposed on the compressible fluid by the twisted strips cause considerable deviations from the incompressible heat transfer predictions. Experimental results are presented as deviations to the incompressible predictions and can be correlated by f=fo(Tˆw/Tˆb)−0.1(HeatingandCooling)Nu=Nuo(Tˆw/Tˆb)−0.32(1+0.25Gr/Re)(Heating)Nu=1.07Nuo(Tˆw/Tˆb)−0.1(1−0.25Gr/Re)(Cooling) where the subscript “o” refers to the incompressible analytical solution. The analysis presented is more direct and complete than the previous development by Smithberg and Landis [3]2 by also accounting for curvature effects and the significant tape distortions encountered with tightly twisted strips.

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