Transfer coefficient definition

A direct numerical relationship between heat and momentum fluxes, as for the simple Reynolds analogy for a single phase, is not obtained in this case because of a basic and significant difference in heat transfer coefficient definitions. For singlephase flow in pipes, the mixed mean or integrated average temperature is used in... 

The concentration difference can also be re-defined in different ways, thus there exists a variety of modifications of the basic mass transfer coefficient definition as well. Therefore, care should to be taken to ensure that the mass transfer coefficient parameterizations adopted for modeling purposes, correspond to the model formulation used. 

Table 16.3 shows some possible forms of mass transfer coefficient definitions and the relationships between the coefficients based on EMD and UMD. In addition to Ky and Ky coeflScients, we can also define Ky and Kx coefficients based on mole ratio f(T— Tj) and (Xj — X)] driving forces. 

This value is typical of those found in liquids. This type of mass transfer coefficient definition is preferable to that used first, a point explored further in Section 8.2. 

The definition of the heat-transfer coefficient is arbitrary, depending on whether bulk-fluid temperature, centerline temperature, or some other reference temperature is used for ti or t-. Equation (5-24) is an expression of Newtons law of cooling and incorporates all the complexities involved in the solution of Eq. (5-23). The temperature gradients in both the fluid and the adjacent solid at the fluid-solid interface may also be related to the heat-transfer coefficient ... 

Tbe mass-transfer coefficients k c and /cf by definition are equal to tbe ratios of tbe molal mass flux Na to tbe concentration driving forces p — Pi) and (Ci — c) respectively. An alternative expression for tbe rate of transfer in dilute systems is given by... 

It is important to understand that when chemical reactions are involved, this definition of Cl is based ou the driving force defined as the difference between the couceutratiou of un reacted solute gas at the interface and in the bulk of the liquid. A coefficient based ou the total of both uureacted and reached gas could have values. smaller than the physical-absorption mass-transfer coefficient /c . 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

From these unique functions of RCp the numerical value of jh and jd can be calculated. From the definitions of the Colburn factors, the transfer coefficients hg and kg can be evaluated since all other variables are physical properties, independent of flow. For correctness, the physical properties... 

Now R0 (the shear stress in the fluid at the surface) is equal and opposite to R, the shear stress acting on the surface, —q jQs is by definition the heat transfer coefficient at the surface (h), and (—NA)y=o/ CAjl - CAw) is the mass transfer coefficient ho). Then dividing both sides of equation 12.100 by pu, and of equation 12.101 by u, to make them dimensionless ... 

It should be emphasized that under conditions of energy dissipation the definition of the heat transfer coefficient as k dT/dr)/ T — T ), where T is the average fluid temperature and 7 is the wall temperature, does not characterize the acmal heat transfer properly (Kays and Crawford 1993 Schlichfing 2000). 

From this relationship it is clear that the rate of heat transfer is the product of three factors the overall heat transfer coefficient the area of the hot surface and the temperature drop. If instead of Sj either S2 or Sm had been chosen, one would have obtained the heat transfer coefficients based on these areas, namely, U2 or Um. It follows that a definite area must be chosen and that the overall heat transfer coefficient is automatically based on the chosen area. The choice is, in general, arbitrary. 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

Parsons, R., Electrode reaction orders, charge transfer coefficients and rate constants. Extension of definitions and recommendations for publication of parameters. Pure Appl. Chem., 52, 233 (1979). 

Depending on the driving force we choose to employ in our analysis, there are several definitions of mass transfer coefficients that may be considered appropriate for use. If we consider an arbitrary interface between a fluid and the external surface of a catalyst particle, we might choose to define a mass transfer coefficient based on a concentration driving force (kc) as... 

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