Heat transfer flux

Isbin, H. S., Vanderwater, R., Fauske, H., and Singh, S., A model for correlating two phase, steam water, burnout heat transfer fluxes, J. Heat Transfer 83, 149 (1961). 

Two-phase flows in micro-channels with an evaporating meniscus, which separates the liquid and vapor regions, have been considered by Khrustalev and Faghri (1996) and Peles et al. (1998, 2000). In the latter a quasi-one-dimensional model was used to analyze the thermohydrodynamic characteristics of the flow in a heated capillary, with a distinct interface. This model takes into account the multi-stage character of the process, as well as the effect of capillary, friction and gravity forces on the flow development. The theoretical and experimental studies of the steady forced flow in a micro-channel with evaporating meniscus were carried out by Peles et al. (2001). These studies revealed the effect of a number of dimensionless parameters such as the Peclet and Jacob numbers, dimensionless heat transfer flux, etc., on the velocity, temperature and pressure distributions in the liquid and vapor regions. The structure of flow in heated micro-channels is determined by a number of factors the physical properties of fluid, its velocity, heat flux on... 

This means that the heat transfer flux is proportional to the negative temperature gradient. If the positive L direction is chosen as the direction of heat flow, then temperature decreases along this direction and dT/dl is negative. One can write... 

Isbin, H. S., R. Vanderwater, H. K. Fauske, and S. Singher, 1961, A Model for Correlating Two-Phase, Steam-Water, Burnout Heat Transfer Fluxes, Trans. ASME, J. Heat Transfer 83 149-157. (5) Ishii, M., 1975, Thermo Fluid Dynamic Theory of Two-Phase Flav, chaps. IX and X, Eyralles Press, Paris (Sci. and Medical Pub. of France, New York). (3)... 

DISCUSSION AND CONCLUSIONS In this study a general applicable model has been developed which can predict mass and heat transfer fluxes through a vapour/gas-liquid interface in case a chemical reaction occurs in the liquid phase. In this model the Maxwell-Stefan theory has been used to describe the transport of mass and heat. A film model has been adopted which postulates the existence of a well-mixed bulk and stagnant zones where the principal mass and heat transfer resistances are situated. Due to the mathematical complexity the equations have been solved numerically by a finite-difference technique. In this paper (Part I) the Maxwell-Stefan theory has been compared with the classical theory due to Pick for isothermal absorption of a pure gas A in a solvent containing component B. Component A is allowed to react by a unimolecular chemical reaction or by a bimolecular chemical reaction with... 

A high heat transfer flux per unit reactor volume is needed. 

When the gas emissivity is sufficiently small, the calculation is quite simple. The procedure can be presented by introducing an equivalent electric network, as shown in many textbooks (see for example Incropera and DeWitt, 2002). To calculate the heat transfer fluxes it is necessary to calculate the equivalent resistances due to the non-black surfaces (R, ) and those associated with the view factors (RfY-... 

As with the shrinking core model, boundary layer mass and heat transfer fluxes are applicable as well as the surface reaction flux. The fluxes are combined in a way similar to that of the shrinking core model to give the results in Table 5.3 for a. shrinking sphere model. When this model is applicable, the partide morphology dianges drastically during reaction from particles to flakes of partides. 

The mass flux, Ji, is related to the heat transfer flux, required to evaporate those molecules... 

For a plate geometry, the overall heat transfer flux, q (energy/area/ time), resulting from the total temperature profile over the boundary layer and across the pores is given by... 

At steady state, both the mass transfer flux and the heat transfer flux are balanced according to... 

This section will present one of the possible physical interpretations of these important dimensionless numbers. First, to show the meaning of Nusselt number, we consider the heat transfer flux in the x direction in the case of a pure molecular mechanism compared with the heat transfer characterizing the process when convection is important. The corresponding fluxes are then written as ... 

As for the Prandtl number, we consider the heat transfer flux which can be written with the use of the fluid enthalpy (Eq. (6.164)) and the molecular momentum flux given by Eq. (6.165) ... 

For solid walls, no-penetration and no-slip are typically applied to the momentum equation. Boundary conditions such as velocity, pressure and temperature at the inlet are usually known and specified, whereas their counterparts at the outlet are derived from assumptions of no-stress or fully developed and simulated flow. The thermal wall boundary conditions influence the flow significantly. Simple assumptions of constant wall temperature, insulated side walls and constant wall heat transfer flux have been used extensively for simple applications. More specifically, the following assumptions are normally made for a retort as shown in Figure 6.29 (the directions of the velocity in the following description refer to a cylindrical coordinate system in this figure). 

Alternatively, the wall heat transfer flux can be expressed in terms of an overall heat transfer coefficient. For reactors with constant cross-sectional area A the geometric factor reduces to It is... 

The interfacial heat transfer flux involves the interfacial heat which can be related to the heat of vaporization or condensation and the heat flux of the phase on the k side of the interface [112]. 

The corresponding surface average convective heat transfer flux qk n k)A is generally approximated by ... 

To be consistent with the mass transfer model, the interfacial heat transfer flux through each of the films consists of both conductive (3.167) and convective (3.175) contributions. The heat transfer terms are approximated by... 

When we have obtained steady state, the rate of heat transfer (flux times area) through the surrounding fluid is constant with respect to the radial position ... 

Fig. 7.11. A Sketch of the heat transfer flux model, determining the flux from the bulk of the tank to the heat transfer medium.

A review of the heat transfer characteristics of fluidized beds has been given by Yates [143]. It is generally accepted that the heat transfer between gas and particles is very efficient in fluidized beds as a result of the high surface area of the particle phase. The heat transfer fluxes between an immersed surface and the gas-fluidized bed material are more important from a practical design... 

Q Total flow rate (m3 s-1) q Heat transfer flux (W m-2 or kcal h-1 m-2) qp Adsorbed amount (kmol kg-1)... 

Use the film theory approach to predict the effect of a simultaneous mass transfer flax on the heat transfer flux as in the coedensation of a binary vapor on a cold surface. The bulk gas condition are temperature T2 and mole fraction yAa2, while the coedilions at ihe liquid surface are T, and yAil. 

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