Prandtl number heat exchangers

Heat Exchangers Since most cryogens, with the exception of helium 11 behave as classical fluids, weU-estabhshed principles of mechanics and thermodynamics at ambient temperature also apply for ctyogens. Thus, similar conventional heat transfer correlations have been formulated for simple low-temperature heat exchangers. These correlations are described in terms of well-known dimensionless quantities such as the Nusselt, Reynolds, Prandtl, and Grashof numbers. 

From Tolmin s theory and experimental data (e.g., Reichardtthe relationship between velocity profile and temperature profile in the jet cross-section can be expressed using an overall turbulent Prandtl number Pr = v /a, where Vf is a turbulent momentum exchange coefficient and a, is a turbulent heat exchange coefficient ... 

The first type is of interest only when considering fluids of low Prandtl number, and this does not usually exist with normal plate heat exchanger applications. The third is relevant only for fluids such as gases which have a Prandtl number of about one. Therefore, let us consider type two. 

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... 

Heat exchange in stirred reactors is described in [207]. By using dimensional analysis of heat flow and energy balance equations, the Nusselt number, containing hT, can be expressed as a function of the Reynolds number and the Prandtl number ... 

In heat-exchanger applications, it is frequently important to match heat-transfer requirements with pressure-drop limitations. Assuming a fixed total heat-transfer requirement and a fixed temperature difference between wall and bulk conditions as well as a fixed pressure drop through the tube, derive expressions for the length and diameter of the tube, assuming turbulent flow of a gas with the Prandtl number near unity. 

Under mechanical equilibrium on a molecular scale, the exchange of momentum proceeds faster than the exchange of mass and heat for liquids. On the other hand, the molecular exchange of momentum, matter, and heat is on the same order as gases. The rate of exchange of transport processes is measured by the Schmidt number Sc and the Prandtl number Pr. Usually, the assumption of mechanical equilibrium in gases for heat and mass transfer is not reliable. 

Note that the Prandtl number has no effect on the initial region. The regularities of mass exchange are similar to those of heat exchange, except for that the criterion number is the Schmidt number Sc. 

The heat-transfer coefficient, k, for laminar flow in tubes can be enhanced by a factor of two- to sixfold using static mixer elements in the heat-exchanger tubes. The heat-transfer coefficient is correlated using the Nusselt, Prandtl, and Reynolds numbers. Table 9.21 gives constants for Koch SMX and SMXL mixers for... 

In double-pipe and shell-and-tube heat exchangers, fluids flow through straight, smooth pipes and tubes of circular cross section. Many correlations have been published for the prediction of the inside-wall, convective heat transfer coefficient, /i when no phase change occurs. For turbulent flow, with Reynolds numbers, = D,G/ ji, greater than 10,000, three empirical correlations have been widely quoted and applied. The first is the Dittus-Boelter equation (Dittus and Boelter, 1930) for liquids and gases in fully developed flow (Z>,/L < 60), and with Prandtl numbers, = Cp[iJk, between 0.7 and 100 ... 

Heat transfer by convection occurs in liquids and gases where there is a velocity field caused by extorted fluid motion or by natural fluid motion caused by a difference in density. The former case involves forced convection, and the latter case free convection. Combined convection occurs when both forced and free convection are present. The convection coefficient of surface heat transfer, a, defining the heat exchange in the contact boundary layer between fluid and soUd, is determined. Coefficient or is often expressed by equations containing criteria numbers, such as those of Nusselt (Nu), Prandtl (Pr), Reynolds (Re) and Grashof(Gr) ... 

Both the recuperator and gas cooler are laminar flow heat exchangers with a low Prandtl number working fluid (HeXe) on at least one side. The NRPCT was unable to locate a well documented convection coefficient correlation that was applicable to both laminar flow and low Prandtl number gases. The Kays... 

Pr the gas Prandtl number, dimensionless q heat exchange rate per unit of area, W/m ... 

The model of the recuperator uses the default volume control flags except for the following 1) the vertical stratification model is not used (since not relevant to single phase flow), 2) the ORNL ANS narrow channel model heat transfer correlation Is applied, and 3) wail friction is not computed along the direction of flow. The ORNL ANS model provides the best approximation of experimental data for the low Prandtl number gas being used and the laminar flow regime. The Nusselt number from the ORNL ANS model is adjusted for both compact heat exchanger effects and Reynolds number... 

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