Heating/cooling fluid, film coefficient

Figure 10-51. Convection inside film coefficient for gases and low viscosity fluids inside tubes—heating and cooling. (Used by permission McAdams, W. H. Heat Transmission, 2"= Ed., 1942. McGraw-Hill, Inc. All rights reserved.)...

For the individual (film) coefficient h for heating or cooling of fluids, without phase change, in turbulent flow through circular tubes, the following dimensionless equation [2] is well established. In the following equations all fluid properties are evaluated at the arithmetic-mean bulk temperature. 

The rates of heat transfer between the fermentation broth and the heat-transfer fluid (such as steam or cooling water flowing through the external jacket or the coil) can be estimated from the data provided in Chapter 5. For example, the film coefficient of heat transfer to or from the broth contained in a jacketed or coiled stirred-tank fermentor can be estimated using Equation 5.13. In the case of non-Newtonian liquids, the apparent viscosity, as defined by Equation 2.6, should be used. 

The practical heat-transfer coefficient is the sum of all the factors that contribute to reduce heat transfer, such as flow rate, cocurrent or countercurrent, type of metal, stagnant fluid film, and any fouling from scale, biofilm, or other deposits. The practical heat-transfer coefficient ((/practical) is, in reality, the thermal conductance of the heat exchanger. The higher the value, the more easily heat is transferred from the process fluid to the cooling water. Thermal conductance is the reciprocal of resistance (/ ), to heat flow ... 

Because of the fouling effects, there may be a limit on the velocity of one of the fluids in a heat exchanger. For example, the velocity of cooling water in tubes of a shell-and-tube exchanger is often specified as 3 ft/s. If the velocity of one fluid is specified, the coefficient for that fluid is set, and the independent variables become At, and the film coefficient of the other fluid. 

Thus, values of h for heating or cooling increase with thermal conductivity k. Also, h values can be increased by decreasing the effective thickness of the laminar film Ayf by increasing fluid velocity along the interface. Various correlations for predicting film coefficients of heat transfer are provided in Chapter 5. 

A vessel fitted with a cooling coil and an agitator is shown schematically in Figure 8.23. In this case the thermal resistances to heat transfer arise from the fluid film on the inside of the cooling coil, the wall of the tube (usually negligible), the fluid film on the outside of the coil, and the scale that may form on either siuface. The overall heat transfer coefficient, U, can thus be expressed as ... 

We note that the model is based on the assumption that cool-down is limited by the rate at which gas is vented through the line end restriction. For purposes of the model, heat transfer coefficients across the fluid film next to the inside pipe wall are considered infinite. 

At the start of line cool-down, high values of film temperature gradient are obtained. Since the line fluid is primarily gaseous at the beginning of cool-down, the data points obtained represent gas film coefficients (at velocities less than 100 ft/sec) and are relatively low. As line cooling continues, the temperature gradient across the film decreases, and a simultaneous increase in the amount of liquid present in the coolingfluid stream causes an increase in the heat transfer coefficient. 

One of the attractive features of the SDR is that its high fluid dynamic intensity favours the rapid transmission of heat, mass and momentum, thereby making it an ideal vehicle for performing fast endothermic reactions which usually also benefit from an intense mixing environment. It must be noted, however, that heat transfer from the process liquid to any cooling/heating fluid behind the disc involves a second film coefficient which may severely limit the overall heat transfer rate (this is discussed later). Some of the more relevant recent experimental studies of spinning disc performance may now be considered. 

Equation (5.40) is good and applicable for film heat-transfer coefficients for gas-phase, vapor-phase, and condensing fluids. The Cp, K, and U isc input values should be accurate for the tube-side fluid being cooled. 

The specific heat for water is 4.2 kJ kg-1 K 1 and that of the process fluid is 3.4 kJ kg-1 K 1. The process fluid side film heat transfer coefficient is 2500 W m 2 K 1 and the cooling water side heat transfer coefficient is 1200 W raT2 K 1. The tube wall thickness is 3 mm and the thermal conductivity is 220 W m 1 K 1. 

Cooling water, for exanple, will be placed on the tube side because of its tendency to form a scale. Water usually contains dissolved salts, like calcium carbonate, which may deposit on the tube wall. A condensing fluid will be placed in the shell side to prevent the liquid film firom growing too large, reducing the heat-transfer coefficient, or in the tube side if subcooling of the liquid is desirable. In the shell side, turbulence occurs at a lower Reynolds ninnber than in the tube side because of the baffles. Thus, the shell side is the best location for very viscous fluids. 

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