Heat transfer coefficient estimation

In Example 10.3.1 we considered the calculation of the mass transfer coefficient in the gas phase of a thin-film sulfonator. A schematic diagram of a sulfonation reactor was provided by Figure 10.5. Now, in the modeling of the reactor, the estimation of the temperature profiles along the reactor tube is very important. An important parameter in the determination of the temperature profiles is the gas-phase heat transfer coefficient. Estimate this heat transfer coefficient at the entrance to the reactor for the same set of operating conditions as specified in Example 10.3.1. 

The heat transfer coefficients estimated from correlations or analogies are the low flux coefficients and, therefore, need to be corrected for the effects of finite transfer rates before use in design calculations. We recommend the film theory correction factor given by Eq. 11.4.12. 

Internal Cooling Channel Heat Transfer Coefficient Estimation... 

The hybrid solution procedure described in the previous section is computationally more demanding than one that does not rely on the CFD package to predict the heat transfer from the exhaust gas. In fact, this simpler approach was adopted in die early stages of the project, the heat transfer process was modelled using a mean heat transfer coefficient estimated from correlations for convective heat transfer in annuli. However, it was soon realized that this method has a high degree of uncertainty when the heat transfer process takes place under unsteady-state conditions and when the thermal entry length spreads over an appreciable extent of the domain. These conditions are always met in the application under study. 

If a heat transfer tube of a 2.9 cm diameter is submerged horizontally within the fluidized medium at the above operating conditions, what would be the surface heat transfer coefficient estimated by various empirical correlations ... 

If the streams in Problem 18 have the following film heat transfer coefficients, estimate the optimum minimum approach temperature for this problem. 

Heat generated by the adsorption of a component in the gas or liquid phase by the porous solid has to be transported not only between solid and fluid in an operating column, but is subsequently dissipated by transport from fluid to vessel wall and thence to the surrounding environment. A correlation due to Leva (1949) may be used to assess the resistance to heat transfer between fluid and vessel wall. A film heat transfer coefficient estimated from a correlation described by McAdams (1954) enables the evaluation of heat transfer resistance from the vessel wall to the surroundings. 

To the extent that radiation contributes to droplet heatup, equation 28 gives a conservative estimate of the time requirements. The parameter ( ) reflects the dependence of the convective heat-transfer coefficient on the Reynolds number ... 

The rate of heat-transfer q through the jacket or cod heat-transfer areaM is estimated from log mean temperature difference AT by = UAAT The overall heat-transfer coefficient U depends on thermal conductivity of metal, fouling factors, and heat-transfer coefficients on service and process sides. The process side heat-transfer coefficient depends on the mixing system design (17) and can be calculated from the correlations for turbines in Figure 35a. 

A prehminaiy estimate of the size of the exchanger is made, using a heat-transfer coefficient appropriate to the fluids, the process, and the equipment. 

It is assumed that process conditions and physical properties are known and the following are known or specified tube outside diameter D, tube geometrical arrangement (unit cell), shell inside diameter D shell outer tube limit baffle cut 4, baffle spacing and number of sealing strips N,. The effective tube length between tube sheets L may be either specified or calculated after the heat-transfer coefficient has been determined. If additional specific information (e.g., tube-baffle clearance) is available, the exact values (instead of estimates) of certain parameters may be used in the calculation with some improvement in accuracy. To complete the rating, it is necessary to know also the tube material and wall thickness or inside diameter. 

For subcooling, a liquid inventory may be maintained in the bottom end of the shell by means of a weir or a hquid-level-controUer. The subcoohng heat-transfer coefficient is given by the correlations for natural convection on a vertical surface [Eqs. (5-33 ), (5-33Z )], with the pool assumed to be well mixed (isothermal) at the subcooled condensate exit temperature. Pressure drop may be estimated by the shell-side procedure. 

Typical overall heat-transfer coefficients are given in Tables 11-3 through 11-8. Values from these tables may be used for preliminaiy estimating purposes. They should not be used in place of the design methods described elsewhere in this section, although they may serve as a useful check on the results obtained by those design methods. 

The small-spiral-large-sbaft type (Fig. ll-60b) is inserted in a solids-product line as pipe banks are in a fluid line, solely as a heat-transfer device. It features a thin burden ring carried at a high rotative speed and subjected to two-sided conductance to yield an estimated heat-transfer coefficient of 285 W/(m °C) [50 Btu/(h fU °F)], thereby ranking thermally next to the sheU-fluidizer type. This device for powdered solids is comparable with the Votator ol the fluid field. 

Estimate temperature distribution in the evaporator, taking into account boiling-point elevations. If all heating surfaces are to be equal, the temperature drop across each effect will be approximately inversely proportional to the heat-transfer coefficient in that effect. 

These calculations should yield liquor concentrations in each effect that make possible a revised estimate of boihng-point rises. They also give the quantity of heat that must be transferred in each effect. From the heat loads, assumed temperature differences, and heat-transfer coefficients, heating-surface requirements can be determined. If the distribution of heating surface is not as desired, the entire calculation may need to be repeated with revised estimates of the temperature in each effect. 

Tests on plant-scale dryers are usually carried out to obtain design data for a specific material, to select a suitable diyer type, or to check present performance of an existing diyer with the objective of determining its capacity potential. In these tests overall performance data are obtained and the results used to make heat and material balances and to estimate overall drying rates or heat-transfer coefficients. 

In order to estimate diying rates from Eq. (12-42) values of the empirical constants are required for the particular geometry under consideration. For flow parallel to plane plates, exponent n has been reported to range from 0.35 to 0.8 [Chu, Lane, and Conklin, Ind. E/ig. Chem., 45, 1856 (1953) Wenzel and White, Ind. Eng. Chem., 51, 275 (1958)]. The differences in exponent have been attributed to differences in flow pattern in the space above the evaporating surface. In the absence of apphcable specific data, the heat-transfer coefficient for the parallel-flow case can be taken, for estimating purposes, as... 

One manner in which size may be computed, for estimating purposes, is by employing a volumetric heat-transfer concept as used for rotary diyers. It it is assumed that contacting efficiency is in the same order as that provided by efficient lifters in a rotaiy dryer and that the velocity difference between gas and solids controls, Eq. (12-52) may be employed to estimate a volumetric heat-transfer coefficient. By assuming a duct diameter of 0.3 m (D) and a gas velocity of 23 m/s, if the solids velocity is taken as 80 percent of this speed, the velocity difference between the two would be 4.6 m/s. If the exit gas has a density of 1 kg/m, the relative mass flow rate of the gas G becomes 4.8 kg/(s m the volumetric heat-transfer coefficient is 2235 J/(m s K). This is not far different from many coefficients found in commercial installations however, it is usually not possible to predict accurately the acdual difference in velocity between gas and soRds. Furthermore, the coefficient is influenced by the sohds-to-gas loading and particle size, which control the total solids surface exposed to the gas. Therefore, the figure given is only an approximation. 

Equations (13-115) to (13-117) contain terms, for rates of heat transfer from the vapor phase to the hquid phase. These rates are estimated from convective and bulk-flow contributions, where the former are based on interfacial area, average-temperature driving forces, and convective heat-transfer coefficients, which are determined from the Chilton-Colburn analogy for the vapor phase and from the penetration theoiy for the liquid phase. 

The percentage error in the temperature difference translates directly to the percentage error in the estimate Q. As temperature-measurement error increases, so does the heat transfer coefficient error. 

The third interaction compromising the parameter estimate is due to bias in the model. If noncondensables blanket a section of the exchanger such that no heat transfer occurs in that section, the estimated heat-transfer coefficient based on a model assuming all of the area is available will be erroneous. 

Yagi and Wakao (1959) used mass transfer measurement results to estimate the heat transfer coefficient at the tube wall. Material was coated on the inner surface of the packed tubes and the dissolution rate was measured. 

Estimation of the heat transfer coefficients for forced convection of a fluid in pipes is usually based on empirical expressions. The most well known expression for this purpose is ... 

The only information available are the inlet temperatures of the hot and cold fluids and estimates for the overall heat transfer coefficient U and the heat transfer surface A. The flows are fixed and the specific heats of the fluids known. 

---