Thermal transport turbulent

The foregoing discussion relates to the transport of momentum under steady, uniform conditions in turbulently flowing streams. Such matters are of direct interest to the chemical engineer but usually only as they influence the power requirements for the movement of fluids. A deeper interest exists in prediction of the thermal transport and temperature... 

The present approach to the prediction of thermal transport in turbulent flow neglects the effect of thermal flux and temperature distribution upon the relationship of thermal to momentum transport. The influence of the temperature variation upon the important molecular properties of the fluid in both momentum and thermal transport may be taken into account without difficulty if such refinement is necessary. 

Reynolds (Rl) suggested that the natures of turbulent momentum and thermal transport were similar. K rm n (K2) extended this analysis and defined eddy conductivity in the following way for steady, uniform, two-dimensional flow ... 

In the consideration of thermal transport the molecular Prandtl number of the fluid is important (Ml). However, in turbulent flow it is necessary to consider additional Prandtl numbers. The conventional molecular Prandtl number is defined by... 

In predicting convective thermal transport to turbulent streams it has usually been sufficient to determine the corresponding thermal flux at the boundary for a specified area. Such methods have been refined by many workers and ably summarized by McAdams (Ml) and Jakob (Jl). 

During recent years experimental work continued actively upon the macroscopic aspects of thermal transfer. Much work has been done with fluidized beds. Jakob (D5, J2) made some progress in an attempt to correlate the thermal transport to fluidized beds with transfer to plane surfaces. This contribution supplements work by Bartholomew (B3) and Wamsley (Wl) upon fluidized beds and by Schuler (S10) upon transport in fixed-bed reactors. The influence of thermal convection upon laminar boundary layers and their transition to turbulent boundary layers was considered by Merk and Prins (M5). Monaghan (M7) made available a useful approach to the estimation of thermal transport associated with the supersonic flow of a compressible fluid. Monaghan s approximation of Crocco s more general solution (C9) of the momentum and thermal transport in laminar compressible boundary flow permits a rather satisfactory evaluation of the transport from supersonic compressible flow without the need for a detailed iterative solution of the boundary transport for each specific situation. None of these references bears directly on the problem of turbulence in thermal transport and for that reason they have not been treated in detail. 

Fallis (FI) considered thermal transport in transitional and turbulent boundary flows and supplied a reasonable analysis of this difficult problem which is in agreement with the work of Eber (El) and the theory of Eckert and Drewitz (E2). Callaghan (Cl) contributed to the analogies between thermal and material transport in turbulent flow with particular emphasis upon the behavior near and in the boundary layer. The effect... 

In the case of turbulent flow it is possible to employ the same eddy concepts as were used in connection with the consideration of thermal transport. In the case of steady, uniform flow between parallel plates the eddy diffusivity may be defined by... 

Material transport is usually associated with thermal transport except in situations involving homogeneous phases which can be treated as ideal solutions (L4). For this reason it is necessary to consider the behavior of combined thermal and material transport in turbulent flow. The evaporation of liquids under macroscopic adiabatic conditions is a typical example of such a phenomenon. Under such circumstances the behavior in the boundary layer is similar to that found in the field of aerodynamics in a blowing boundary layer (S4). However, it is not... 

Satterfield (S2, S3) carried out a number of interesting macroscopic studies of simultaneous thermal and material transfer. This work was done in connection with the thermal decomposition of hydrogen peroxide and yielded results indicating that for the relatively low level of turbulence experienced the thermal transport did not markedly influence the material transport. However, the results obtained deviated by 10 to 20 from the commonly accepted macroscopic methods of correlating heat and material transfer data. The final expression proposed by Satterfield (S3), neglecting the thermal diffusion effect (S19) in the boundary layer, was written as... 

Constantinescu et al [69] for isothermal turbulent lubrication. In these approaches it is implicitely assumed that the thermal transport phenomena are basically the same in laminar and in turbulent... 

The problems that arise when experiments are carried out in a greatly reduced scale can be overcome if the Reynolds number is high and the flow pattern is governed mainly by fully developed turbulence. It is possible to ignore the Reynolds number, the Schmidt number, and the Prandtl number because the structure of the turbulence and the flow pattern at a sufficiently high level of velocity will be similar at different supply velocities and therefore independent of the Reynolds number. The transport of thermal energy and mass by turbulent eddies will likewise dominate the molecular diffusion and will therefore also be independent of the Prandtl number and the Schmidt number. 

J. B. Opfell and B. H. Sage, Turbulence in Thermal and Material Transport Robert E. Treybal, Mechanically Aided Liquid Extraction... 

In this equation S includes heat of chemical reaction, any interphase exchange of heat, and any other user-defined volumetric heat sources. At is defined as the thermal conductivity due to turbulent transport, and is obtained from the turbulent Prandtl number... 

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