Heat transfer dimensionless group correlation

The dimensionless group hD/k is called the Nusselt number, /VNu, and the group Cp i/k is the Prandtl number, NPl. The group DVp/p is the familiar Reynolds number, NEe, encountered in fluid-friction problems. These three dimensionless groups are frequently used in heat-transfer-film-coefficient correlations. Functionally, their relation may be expressed as... 

Empirical dimensionless group correlations have been used in the scale-up process. In particular, the correlation for the inside film heat transfer coefficient for agitated, jacketed vessels has been employed for the scale-up to a larger vessel. Reaction calorimeters are often used to give some indication of heat transfer coefficients compared to water in the same unit. Correlation for plant heat transfer is of the general form... 

The functional dependence expressed in Equations 4.29 and 4.31 governs the behavior of convective heat transfer. In some cases the functionality can be determined analytically, but in most cases it can be determined only as a statistical correlation of experimental data. Dimensionless groups are used to generalize empirical correlations for convective heat transfer. These groups can be determined from the parameters in Equations 4.29 and 4.31. They are the Reynolds, Nusselt, Grashof, and Prandtl numbers, respectively, defined as ... 

Example Buckingham Pi Method—Heat-Transfer Film Coefficient It is desired to determine a complete set of dimensionless groups with which to correlate experimental data on the film coefficient of heat transfer between the walls of a straight conduit with circular cross section and a fluid flowing in that conduit. The variables and the dimensional constant believed to be involved and their dimensions in the engineering system are given below ... 

The dimensionless relations are usually indicated in either of two forms, each yielding identical resiilts. The preferred form is that suggested by Colburn ran.s. Am. In.st. Chem. Eng., 29, 174—210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cQ, the Prandtl number c Jk, and the Reynolds number DG/[L. For more accurate correlation of data (at Reynolds number <10,000), two additional dimensionless groups are used ratio of length to diameter L/D and ratio of viscosity at wall (or surface) temperature to viscosity at bulk temperature. Colburn showed that the product of the Stanton number and the two-thirds power of the Prandtl number (and, in addition, power functions of L/D and for Reynolds number <10,000) is approximately equal to half of the Fanning friction fac tor//2. This produc t is called the Colburn j factor. Since the Colburn type of equation relates heat transfer and fluid friction, it has greater utility than other expressions for the heat-transfer coefficient. 

Not only is the type of flow related to the impeller Reynolds number, but also such process performance characteristics as mixing time, impeller pumping rate, impeller power consumption, and heat- and mass-transfer coefficients can be correlated with this dimensionless group. 

Heat Transfer In general, the fluid mechanics of the film on the mixer side of the heat transfer surface is a function of what happens at that surface rather than the fluid mechanics going on around the impeller zone. The impeller largely provides flow across and adjacent to the heat-transfer surface and that is the major consideration of the heat-transfer result obtained. Many of the correlations are in terms of traditional dimensionless groups in heat transfer, while the impeller performance is often expressed as the impeller Reynolds number. 

Forced convection heat transfer has been measured under widely differing conditions, and using the dimensionless groups makes correlation of the experimental... 

Convective heat transfer to fluid inside circular tubes depends on three dimensionless groups the Reynolds number. Re = pdtu/ii, the Prandtl number, Pr = Cpiilk where k is the thermal conductivity, and the length-to-diameter ratio, L/D. These groups can be combined into the Graetz number, Gz = RePr4/L. The most commonly used correlations for the inside heat transfer coefficient are... 

Many of the results and correlations in heat and mass transfer are expressed in terms of dimensionless groups such as the Nusselt, Reynolds and Prandtl numbers. The definitions of those dimensionless groups referred to in this chapter are given in Appendix 2. 

In addition to correlations of the above type, that is, where the ratio of a two-phase heat-transfer coefficient is compared to a fictitious singlephase coefficient, relationships in terms of dimensionless groups have also been presented. In general, these are of the form. 

Conventional dimensional analysis employs single length and time scales. Correlations are thus obtained for the mass or heat transfer coefficients in terms of the minimum number of independent dimensionless groups these can generally be represented by power functions such as... 

As a result, many correlations are available for heat and mass transfer at moderate pressures that have been developed over time. Perry and Green [6] give a fairly complete amount of data with regards to correlations for different arrangements [7], On the other hand, very few data and correlations are available in the field of high pressure heat and mass transfer, as will be reviewed later. Correlations are in terms of the individual coefficients, ki and h, included in dimensionless groups such as those given before in Eqns. (3.4-10). 

Maintenance of proper temperature is a major aspect of reactor operation. The illustrations of several reactors in this chapter depict a number of provisions for heat transfer. The magnitude of required heat transfer is determined by heat and material balances as described in Section 17.3. The data needed are thermal conductivities and coefficients of heat transfer. Some of the factors influencing these quantities are associated in the usual groups for heat transfer namely, the Nusselt, Stanton, Prandtl, and Reynolds dimensionless groups. Other characteristics of particular kinds of reactors also are brought into correlations. A selection of practical results from the abundant literature will be assembled here. Some modes of heat transfer to stirred and fixed bed reactors are represented in Figures 17.33 and 17.18, and temperature profiles in... 

A mechanistic account of suspension-to-surface heat transfer is necessary to quantify the heat transfer behavior accurately and to assess the form of dependency of dimensionless groups in the correlations. In the following, the modes and regimes of suspension-to-surface heat transfer along with the three mechanistic models accounting for this heat transfer behavior are described. 

Fluid flow is often turbulent, and so heat transfer by convection is often complex and normally we have to resort to correlations of experimental data. Dimensional analysis will give us insight into the pertinent dimensionless groups see Chapter 6, Scale-Up in Chemical Engineering, Section 6.7.4. 

Transfer properties, the heat and mass transfer coefficient and friction factor, depend not only on transport and thermodynamic properties but also on the hydro-dynamic behavior of a fluid. The geometry of the system will influence the hydro-dynamic behavior. By reducing the parameters by arranging them into dimensionless groups, we can reduce the number of parameters that have to be varied to correlate any of the transfer properties. For example, the ffiction factor equation. 

There are many well-known dimensionless groups that are used in transport phenomena. Earlier, the Reynolds number was used to correlate data on pressure drop in pipe flow. For correlating data on heat transfer, often the dimensionless groups Nus-selt (Nu), Reynolds (Re), Prandtl (Pr), and Grashof (Gr) are used. They are defined as ... 

For forced convection, the heat transfer coefficient is normally correlated in terms of tliree dimensionless groups the Nusselt number, Nu, the Reynolds number, Re, and the Prandtl number, Pr. For the single spherical pellets discussed here, Nu and Re take the following forms ... 

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