Empirical equations for heat transfer

Some empirical equations for heat transfer in free flow... 

The derivation of specific values for the inside and outside film coefficients, / , and h, is a rather involved procedure requiring a great deal of applied experience and the use of complex mathematical equations and correlations these computations are best left to the staff heat transfer specialist, equipment vendor, or a consultant. Listed are four references that deal specifically with evaporation and the exposition and use of semi-empirical equations for heat transfer coefficients. 

There are more data for heat transfer in laminar flow than for mass transfer, and the correlations should be similar, with Pr and Nu replacing Sc and Sh. An empirical equation for heat transfer at Graetz numbers greater than 20 is [15]... 

Turbulent flow in tubes. For turbulent flow of power-law fluids through tubes, Clapp (C4) presents the following empirical equation for heat transfer ... 

In the macroscopic heat-transfer term of equation 9, the first group in brackets represents the usual Dittus-Boelter equation for heat-transfer coefficients. The second bracket is the ratio of frictional pressure drop per unit length for two-phase flow to that for Hquid phase alone. The Prandd-number function is an empirical correction term. The final bracket is the ratio of the binary macroscopic heat-transfer coefficient to the heat-transfer coefficient that would be calculated for a pure fluid with properties identical to those of the fluid mixture. This term is built on the postulate that mass transfer does not affect the boiling mechanism itself but does affect the driving force. 

Equation (21.50) has been used to predict the internal mass-transfer resistance for separation processes using hollow-fiber membranes. The recommended equation for heat transfer, Eq. (12,23), has an empirical coefficient of 2.0, and this higher... 

Another approach to estimating the temperature difference involves the solution of equation (12.5.4) for the temperature difference using measured reaction rates and empirical correlations for heat transfer coefficients. Hence,... 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

The similarities between the governing equations for heat, mass, and momentum transfer suggest that empirical correlations for the mass-transfer coefficient would be similar to those for the heat-transfer coefficient. This turns out to be the case, and some of the empirical relations for mass-transfer coefficients are presented below. Gilliland 14] presented the equation... 

An empirical equation for calculating the inside heat transfer coefficient, hj, for the turbulent flow of liquids in a pipe is given by ... 

Example 1.2. Check the dimensional consistency of the following empirical equation for a heat-transfer coefficient (see Chap. 12) ... 

The eddy diffusivity depends on the fluid properties but also on the velocity and position in the flowing stream. Therefore Eq, (21.30) cannot be directly integrated to determine the flux for a given concentration difference. This equation is used with theoretical or empirical relationships for e f in fundamental studies of mass transfer, and similar equations are used for heat or momentum transfer in developing analogies between the transfer processes. Such studies are beyond the scope of this text, but Eq. (21.30) is useful in helping to understand the form of some empirical correlations for mass transfer. 

A simple correlation has been given by Yoo [13], who compared his results for Carbopol and Attagel solutions with those of previous investigators. Yoo s empirical equation for predicting turbulent heat transfer for purely viscous fluids is given by... 

For practical spray heat transfer calculations, a summary of empirical and interpolation correlations for each regime of spray boiling curve, ranging from single-phase to film boiling, and of transition conditions between these regimes has been provided [139,140]. As an illustration of how the hydrodynamic and other parameters affect heat transfer to sprays, the empirical equation for the critical heat flux q"cw is provided as an example [139] ... 

Determining the values of h and from experiments is a challenging task, and a great many empirical correlations have been presented. Most of the data are for heat transfer without reaction, such as for heating air in a steam-jacketed pipe packed with spheres. For these tests, Q is measured from the change in sensible heat of the air, and U is calculated from the usual equation, Q = VAAT. The small steam-film and metal-wall resistances can be subtracted from the overall resistance to obtain an overall bed coefficient, ho. ... 

Both heat and mass transfer coefficients are influenced by thermal and flow properties of the air and, of course, by the geometry of the system. Empirical equations for various geometries have been proposed in the literature. Table 4.9 summarizes the most popular equations used for drying. 

In this approach, the smaller scale models are used to determine the closure equations to be used in larger scale models. The final aim is to obtain better and more general closure equations for heat, momentum and mass transfer that can be applied in phenomenological models and account for the presence of and permeation of gas through membranes in membrane assisted fluidized bed reactors instead of the previous described (empirical) closure equations obtained for reactors without membranes. 

The heat transfer coefficient a. ex the side of the cooling medium can be calculated based on empirical equations, for example, those given in Section 3.2.1.2 for cylinders in cross flow or by more sophisticated correlations given in the literature (VDI, 2002 Cengel, 2002). 

Pumparound sections usually contain from 4 ft to 9 ft of packed depth. The traditional method for calculating bed depth is by use of Equation 6-20. This equation is a simplified representation of a complex group of heat and mass transfer processes. A considerable amount of industrial experience has led to the development of satisfactory empirical equations for the calculation of overall heat transfer coefficients. 

Colburn j factor (Symbol j ) A semi-empirical equation used for heat transfer in mr-bulent flow with Reynolds numbers tanging from 5,000 to 200,000 inside long mbes and defined as ... 

The convective heat-transfer coefficient and friction factor for laminar flow in noncircular ducts can be calculated from empirically or analytically determined Nusselt numbers, as given in Table 5. For turbulent flow, the circular duct data with the use of the hydrauhc diameter, defined in equation 10, may be used. 

Laminar Flow Normally, laminar flow occurs in closed ducts when Nrc < 2100 (based on equivalent diameter = 4 X free area -i-perimeter). Laminar-flow heat transfer has been subjected to extensive theoretical study. The energy equation has been solved for a variety of boundaiy conditions and geometrical configurations. However, true laminar-flow heat transfer veiy rarely occurs. Natural-convecdion effects are almost always present, so that the assumption that molecular conduction alone occurs is not vahd. Therefore, empirically derived equations are most rehable. 

Circular Tubes Numerous relationships have been proposed for predicting turbulent flow in tubes. For high-Prandtl-number fluids, relationships derived from the equations of motion and energy through the momentum-heat-transfer analogy are more complicated and no more accurate than many of the empirical relationships that have been developed. 

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