Heat transfer coefficient variable effect

If a more complex mathematical model is employed to represent the evaporation process, you must shift from analytic to numerical methods. The material and enthalpy balances become complicated functions of temperature (and pressure). Usually all of the system parameters are specified except for the heat transfer areas in each effect (n unknown variables) and the vapor temperatures in each effect excluding the last one (n — 1 unknown variables). The model introduces n independent equations that serve as constraints, many of which are nonlinear, plus nonlinear relations among the temperatures, concentrations, and physical properties such as the enthalpy and the heat transfer coefficient. 

There are 12 equations in all (overall material and energy balances side A and B energy balances coil 1 to 8 energy balances) and 36 variables. However, the heat transfer coefficients are not known with any great accuracy. Further, both the side and coil heat transfer coefficients depend on the fire-box temperature. It is therefore necessary to calculate values for the heat transfer coefficients from the data. This effectively reduces the number of independent equations to 11. 

Therefore, even a moderate error in the mixer scale-up will have only a small effect on the agitator-side heat transfer coefficient. Other factors that include heat transfer area per unit volume are considerably more significant. For instance, in the jacketed tank, the heat transfer area per unit volume decreases upon scale-up. In order to assure the same proportionate heat removal or addition per unit batch size, additional heat transfer area (e.g., coils) may be required. Additionally, other variables such as temperature driving force may have to be adjusted to compensate for decreased heat... 

The effects of the many variables that bear on the magnitudes of individual heat transfer coefficients are represented most logically and compactly in terms of dimensionless groups. The ones most pertinent to heat transfer are listed in Table 8.8. Some groups have ready physical interpretations that may assist in selecting the ones appropriate to particular heat transfer processes. Such interpretations are discussed for example by GrOber et al. (1961, pp. 193-198). A few are given here. 

The mechanism of heat transfer in circulating fluidized beds is described in this section. Effects of the operating variables on the local and overall heat transfer coefficients are discussed. 

The heat transfer coefficient, h, is the variable whose value is being sought. Consider a series of bodies of the same geometrical shape, e.g., a series of elliptical cylinders (see Fig. 1.13), but of different size placed in various fluids. It can be deduced, either by physical argument or by considering available experimental results, that if, in the case of gas flows, the velocity is low enough for compressibility effects to be ignored, h will depend on ... 

For Rep < 100 and 0.05 < rp/r, < 0.2, wall Biot numbers range between 0.8 and 10 [28], so this means that wall effects cannot be neglected a priori [38]. Also this criterion contains procurable parameters. For the wall heat transfer coefficient hw and the effective heat conductivity in the bed Abc(r, the correlations in Table 2, eqs. 44-47 can be used [8, 39]. These variables are assumed to be composed of a static and a dynamic (i.e. dependent on the flow conditions) contribution. Thermal heat conductivities of gases at 1 bar range from 0.01 to 0.5 Js m l K l, depending on the nature of the gas and temperature. 

The above derivation for LMTD involves two important assumptions (1) the fluid specific heats do not vary with temperature, and (2) the convection heat-transfer coefficients are constant throughout the heat exchanger. The second assumption is usually the more serious one because of entrance effects, fluid viscosity, and thermal-conductivity changes, etc. Numerical methods must normally be employed to correct for these effects. Section 10-8 describes one way of performing a variable-properties analysis. 

In Chapter 5, Z. Yu and Y. Jin of THU describe experimental studies of heat transfer between particle suspensions and immersed surfaces, enumerating the effects of variables and of the radial and axial distribution of the heat transfer coefficient. They then present an analysis of the mechanism of heat transfer, particularly in terms of particle convection. 

The effects of the many variables that bear on the magnitudes of individual heat transfer coefficients are represented most logically... 

In this expression the heat-transfer coefficient h is given by Eq. (13-34), Fig. 10-2, and Eqs. (13-37) and (13-38). Equation (13-40) predicts the effect of a number of basic variables on k. Since Pe is relatively insensitive to particle diameter, the second, third, and fourth terms in the equation require that k increase with particle diameter. Since h increases with mass velocity G, the equation predicts that k will increase with G. It is also expected that k will increase with the conductivity of the solid particle, although the increase will be slight because k occurs in both the numerator and the denominator of the last term. 

The pioneering conclusion drawn by Tuckerman and Pease in 1982 [1] that the heat transfer coefficient for laminar flow through microchannels may be greater than that for turbulent flow, accelerated research in this area. Many experimental [2-6], numerical [7-10], and analytical [11-14] studies have been performed, with some focusing on the effects of roughness [15-21] and temperature-variable thermophysical properties of the fluid [22-26]. 

Compare Eqs. (15.22) and (15.23) with respect to the effect of the following variables on the predicted heat-transfer coefficient (a) thermal conductivity, (A) specific heat,... 

Equation 9.9 indicates the effect of the variables on the thickness of the solid layer and confirms some intuitive observations. Increasing the liquid and coolant temperatures T and Z f e heat transfer coefficient will also reduce the frozen layer thickness. Opposite changes in the variables will have the converse effect. 

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