Heat transfer coefficient function

Heat transfer in static mixers is intensified by turbulence causing inserts. For the Kenics mixer, the heat-transfer coefficient b is two to three times greater, whereas for Sulzer mixers it is five times greater, and for polymer appHcations it is 15 times greater than the coefficient for low viscosity flow in an open pipe. The heat-transfer coefficient is expressed in the form of Nusselt number Nu = hD /k as a function of system properties and flow conditions. 

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. 

Likewise, the microscopic heat-transfer term takes accepted empirical correlations for pure-component pool boiling and adds corrections for mass-transfer and convection effects on the driving forces present in pool boiling. In addition to dependence on the usual physical properties, the extent of superheat, the saturation pressure change related to the superheat, and a suppression factor relating mixture behavior to equivalent pure-component heat-transfer coefficients are correlating functions. 

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. 

For annuli containing externally Hnned tubes the heat-transfer coefficients are a function of the fin configurations. Knudsen and Katz (Fluid Dynamics and Heat Transfer, McGraw-Hill, New York, 1958) present relationships for transverse finned tubes, spined tubes, and longitudinal finned tubes in annuli. 

Results of diying tests can be correlated empirically in terms of overall heat-transfer coefficient or length of a transfer unit as a function of operating variables. The former is generally apphcable to all types of dryers, while the latter applies only in the case of continuous diyers. The relationship between these quantities is as follows. 

Both reactors used 38.1 mm 0 tubes. The commercial reactor was 12 m long while the length of the laboratory reactor was 1.2 m. Except for the 10 1 difference in the lengths, everything else was the same. Both reactors were simulated at 100 atm operation and at GHSV of 10,000 h-1. This means that residence times were identical, and linear gas velocities were 10 times less in the lab than at the production unit. Consequently the Re number, and all that is a function of it, were different. Heat transfer coefficients were 631 and 206 in wattsWK units for the large and small reactors. 

Figure 10-44. Keep track of fouling by monitoring the overall heat transfer coefficient as a function of flow rate. (Used by permission Ganapa-thy, V., Chemical Engineering, Aug. 6,1984, p. 94. McGraw-Hill, Inc. All rights reserved.)...

The thesis of Steward indicates that the overall liquid film and mass transfer coefficients were functions of the gas flow rate and the column pressure and are independent of the liquid flow rate and inlet air temperature. The gas film heat transfer coefficient was found to be a function only of the air flow rate. 

From both of these equations, it will be noted that the heat transfer coefficient is noi a function of the temperature difference. Here Re" — (d N pj x-) and Re = (udvp/n), where dv is the tube diameter and u is the average velocity of the liquid in the film in the axial direction. 

Obtain by dimensional analysis a functional relationship for the wall heat transfer coefficient for a fluid flowing through a straight pipe of circular cross-section. Assume that the effects of natural convection can be neglected in comparison with those of forced convection. 

Outline a method for calculating the temperature of the oil as a function of distance from the inlet for a given value of the heat transfer coefficient between the pipeline and the surroundings. 

A 50% glycerol-water mixture is flowing at a Reynolds numher of 1500 through a 25 mm diameter pipe. Plot the mean value of the heat transfer coefficient as a function of pipe length assuming that ... 

By dimensional analysis, derive a relationship for the heat transfer coefficient h for natural convection between a surface and a fluid on the assumption that the coefficient is a function of the following variables ... 

Fig. 5.46 A plot of the experimentally determined heat transfer coefficient as a function of the superficial gas velocity and the gas Reynolds number. The liquid mass fluxes are 78.6 and 290 kg/m s, the heat fluxes are 20 and 33 kW/m and the pressure ranges from 140 to 200 kPa. Reprinted from Bao et al. (2000) with permission...

The detail experimental study of flow boiling heat transfer in two-phase heat sinks was performed by Qu and Mudawar (2003b). It was shown that the saturated flow boiling heat transfer coefficient in a micro-channel heat sink is a strong function of mass velocity and depends only weakly on the heat flux. This result, as well as the results by Lee and Lee (2001b), indicates that the dominant mechanism for water micro-channel heat sinks is forced convective boiling but not nucleate boiling. 

There are two causes for oscillations of the heat flux, with 7 = const. (1) fluctuations of the heat transfer coefficient due to velocity fluctuations, and (2) fluctuations of the fluid temperature. At small enough Reynolds numbers the heat transfer coefficient is constant (Bejan 1993), whereas at moderate Re (Re 10 ) it is a weak function of velocity (Peng and Peterson 1995 Incropera 1999 Sobhan and Garimella 2001). Bearing this in mind, it is possible to neglect the influence of velocity fluctuations on the heat transfer coefficient and assume that heat flux flucmations are expressed as follows ... 

Heat transfer can, of course, be increased by increasing the agitator speed. An increase in speed by 10 will increase the relative heat transfer by 10. The relative power input, however, will increase by 10In viscous systems, therefore, one rapidly reaches the speed of maximum net heat removal beyond which the power input into the batch increases faster than the rate of heat removal out of the batch. In polymerization systems, the practical optimum will be significantly below this speed. The relative decrease in heat transfer coefficient for anchor and turbine agitated systems is shown in Fig. 9 as a function of conversion in polystyrene this was calculated from the previous viscosity relationships. Note that the relative heat transfer coefficient falls off less rapidly with the anchor than with the turbine. The relative heat transfer coefficient falls off very little for the anchor at low Reynolds numbers however, this means a relatively small decrease in ah already low heat transfer coefficient in the laminar region. In the regions where a turbine is effective,... 

As is common in most polymer reactor design problems, heat transfer is one of the major process concerns. For example, if the heat transfer is primarily through the wall of a jacketed reactor, the overall heat transfer coefficient is a function of both the agitator configuration and the degree of swelling of the particles. 

The mass transfer coefficients, Kg and Ky, are overall coefficients analogous to an overall heat transfer coefficient, but the analogy between heat and mass transfer breaks down for mass transfer across a phase boundary. Temperature has a common measure, so that thermal equilibrium is reached when the two phases have the same temperature. Compositional equilibrium is achieved at different values for the phase compositions. The equilibrium concentrations are related, not by equality, as for temperature, but by proportionality through an equilibrium relationship. This proportionality constant can be the Henry s law constant Kh, but there is no guarantee that Henry s law will apply over the necessary concentration range. More generally, Kyy is a function of composition and temperature that serves as a (local) proportionality constant between the gas- and liquid-phase concentrations. 

The differential equation describing the temperature distribution as a function of time and space is subject to several constraints that control the final temperature function. Heat loss from the exterior of the barrel was by natural convection, so a heat transfer coefficient correlation (2) was used for convection from horizontal cylinders. The ends of the cylinder were assumed to be insulated. The equations describing these conditions are ... 

Note that the outlet approximations must be consistent with a final steady-state heat balance. Note also that is easy to allow in the simulation for variations in the heat transfer coefficient, density and specific heats as a function of temperature. The modelling methods demonstrated in this section are applied in the simulation example HEATEX. 

Estimate the optimum thickness of insulation for the roof of a house, given the following information. The insulation will be installed flat on the attic floor. Overall heat transfer coefficient for the insulation as a function of thickness, U values (see Chapter 12) ... 

Overall heat transfer coefficient for the insulation as a function of thickness, U values (see Chapter 12) ... 

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