Heat transfer number

The final dimensionless group to be evaluated is the interfacial heat-transfer number, and therefore the interfacial heat-transfer coefficient and the interfacial area must be determined. The interface is easily described for this regime, and, with a knowledge of the holdup and the tube geometry, the interfacial area can be calculated. The interfacial heat trasfer coefficient is not readily evaluated, since experimental values for U are not available. A conservative estimate for U is found by treating the interface as a stationary wall and calculating U from the relationship... 

The dimensionless heat-transfer number lumps together all the effects related to the heat transfer in relation to the time scale of the chemical reaction. Note that the HTN is proportional to the heat transfer coefficient, U, which depends on the flow conditions, the properties of the fluid, and to the heat-transfer area per unit volume (S/V). The DHR is a characteristic of the chemical reaction, the reference temperature, and the composition of the reference state. 

Below, we describe tbe design formulation of isothermal batch reactors with multiple reactions for various types of chemical reactions (reversible, series, parallel, etc.). In most cases, we solve the equations numerically by applying a numerical technique such as the Runge-Kutta method, but, in some simple cases, analytical solutions are obtained. Note that, for isothermal operations, we do not have to consider the effect of temperature variation, and we use the energy balance equation to determine tbe dimensionless heat-transfer number, HTN, required to maintain the reactor isothermal. 

Specify the dimensionless heat-transfer number, HTN (using Eq. 6.1.26). 

Two approaches have usually been taken based on (1) correlating the mass transfer number Sh with Re and Sc, and the heat transfer number Nu with Re and Pr and (2) defining a composite dimensionless factor for mass and Jh for heat transfer) and correlating it with Re ... 

Note that for zero convection, the mass and heat transfer numbers and are zero and, therefore, the expressions for the Sherwood and Nusselt numbers reduce to... 

One of the important parameters that describe the influence of energy on the mass transfer is the heat transfer number, LeBi. This parameter is a measure of the heat transfer to the surrounding. Its physical meaning can be recognized by rearranging eq. (9.3-18g) as follows ... 

Effects of the heat transfer number, LeBi, are shown in Figure 10.3-3 and 10.3-4. The same set of parameters in the above table is used in the simulation with the following values of LeBi number 1, 5, 10. ... 

As expected a reduction in the heat transfer number would cause an increase in the micro-particle temperature and as a result the fractional uptake exhibits a distinct two stage uptake when the LeBi is low. The slow second stage of the uptake is dictated by the cooling rate of the micro-particle. 

The effect of the heat transfer number, LeBi, is shown in Figure 10.4-4. The fractional uptake exhibits a two stage uptake and the kink in the fractional uptake occurs at the time at which the particle temperature is maximum. 

The Biot number is a dimensionless heat transfer number. When the Biot number is zero, there is no exchange of heat i.e., adiabatic conditions exist. When the Biot number is infinitely large, the wall temperature T equals the melt temperature T, this corresponds to isothermal conditions. Normal values for the Biot number in extrusion dies range from 1 to 100, depending strongly on the presence and amount of insulation. 

W heat-transfer coefficient (heat-transfer number)... 

Here q, is the latent heat of vaporization. The heat transfer number, V/ represents the ratio of the vaporization potential of the ambient environment to the vaporization energy requirement of the liquid fuel. Integrating Equation (6.32) yields... 

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