Heat transfer across interfaces

Instead, we often use a different model for heat transfer, one better suited to approximate calculations of the heat transferred across interfaces. In this model, the separate phases are imagined to be well mixed, and hence isothermal. The only temperature gradients are close to the interface, in some vaguely defined interfacial region. The heat flux in this model is assumed to be... 

Mass Transfer Rates. Mass transfer occurs across the interface. The rate of mass transfer is proportional to the interfacial area and the concentration driving force. Suppose component A is being transferred from the gas to the liquid. The concentration of A in the gas phase is Ug and the concentration of A in the liquid phase is u . Both concentrations have units of moles per cubic meter however they are not directly comparable because they are in different phases. This fact makes mass transfer more difficult than heat transfer since the temperature is the temperature regardless of what phase it is measured in, and the driving force for heat transfer across an interface is just the temperature difference Tg—Ti. For mass transfer, the driving force is not Ug—ai. Instead, one of the concentrations must be converted to its equivalent value in the other phase. 

The radiative heat transfer across the vapor layer is neglected under the condition that the solid temperature is lower than 700 °C (Harvie and Fletcher, 2001 a,b). On the liquid-vapor interface, the energy-balance equation is... 

Ut is unlikely that appreciable molecular resistance to heat transfer across fluid- solid or fluid-fluid interfaces can be caused by surface contamination. 

In the example given by Figure 2.4, there is no heat transfer across the gas-liquid interface (i.e., q = 0), and we can assume that air does not diffuse into the liquid droplet (i.e., Ng= 0). 

In real contacts between two solid surfaces, direct contact occurs between the two solids at a limited number of spots with voids between these spots filled with some fluid, such as the surrounding medium (air). Heat transfer across the interface occurs by conduction through the solid spots of solid-to-solid direct contact and through the fluid filled gap. 

Let s start by recalling the driving force for heat transfer across an interface. Suppose 1 contact a hot gas with a cold liquid. The temperature profile near the interface will look something like that show at right. There are two characteristics of this sketch which are important ... 

Chemical engineers cannot escape dealing with mass and heat transfer across fluid interfaces that are in more or less chaotic motion, chaos that goes under name of turbulence. 

The gas will not dissolve or condense in the liquid and we will assume that the liquid does not evaporate into the gas. The liquid in the vessel is being heated, and there will be a degree of heat transfer across the liquid-gas interface to the gas. 

Figure 13-11 Simultaneous mass and heat transfer across an interface. [C. D. Holland, Fundamentals and Modeling of Separation Processes, Prentice-Hall, Inc. (1975).]...

For steady state conditions (i.e. constant frozen layer thicknesses) it may be assumed that the temeprature of the liquid/frozen layer interface is the freezing temperature 2 - and the only heat removal is the heat transferred across the resistances from the "hot" liquid to the coolant. Referring to Fig. 9.3 the wall temperatures of the hot and cold fluids are T and 7 respectively. Under these conditions of steady state the heat flux. 

The general equation for heat transfer across an interface is... 

The above examples permit us to reach the following conclusion. For the singularly perturbed boundary value problems arising in the numerical analysis of heat transfer for various technologies, we have constructed special e-uniformly convergent finite difference schemes. These schemes allow us to compute heat fluxes and the quantity of heat transferred across the interfaces of bodies in contact during the processes. Numerical experiments show the efficiency of the new schemes in comparison with classical schemes. 

Part II Building on Fundamentals is devoted to skill building, particularly in the area of catalysis and catalytic reactions. It covers chemical thermodynamics, emphasizing the thermodynamics of adsorption and complex reactions the fundamentals of chemical kinetics, with special emphasis on microkinetic analysis and heat and mass transfer effects in catalysis, including transport between phases, transfer across interfaces, and effects of external heat and mass transfer. It also contains a chapter that provides readers with tooisfor making accurate kinetic measurements and analyzing the data obtained. 

This chapter is divided into three parts. In Section 10.2, we discuss the interesting problem of heat transfer in novel materials called nanofluids, which are suspensions of nanoparticles in liquids. Here, the central question is to understand the heat transfer across the interface between a nanoparticle and the surrounding base fluid. We believe that understanding heat transfer across the interface provides crucial insights into the observed enhanced thermal conductivities of nanoparticle suspensions in polar liquids (Choi 2009). We provide an overview of the computation of thermal conductivity for inhomogeneous systems using MD simulations, followed by a discussion on the heat transfer due to radiative heating. 

Differences in performance between the three different screens are due to the effect of the screen thickness and porosity on the overall heat transfer across the LAD screen. Differences in performance between pressurants are due to modified heat and mass transport at the screen pore L/V interface through evaporation (GHe) and/or condensation (GH2 or GN2). Differences in performances between the two liquids are explained through the differences in superheats required to initiate boiling in the liquid. 

The reactor point effectivenesses thus obtained for various cases are summarized in Table 6.4. Take as an example the first entry in Table 6.4, which is for diffusion-free reactions. Since the only transport resistance to consider is in heat transfer across the pellet-bulk fluid interface, the reactor point effectiveness is simply given by ... 

Throughout this book various transport properties and transfer coefficients have been used. These include effective diffusivity and thermial conductivity for mass and heat transport in catalyst pellets, film transfer coefficients for mass and heat transfer across the pellet-bulk fluid interface, transport properties for the degree of dispersion of mass and heat in the reactor, and heat transfer coefficients for heat exchange between the cooling medium and the reactor. In this chapter these transport properties and transfer coefficients are treated in detail, including experimental methods for obtaining these properties. 

Fig. 20.3-1. Heat transfer across an interface. The overall heat transfer coefficient is a harmonic average of the individual heat transfer coefficients for the hot fluid, the wall, and the cold fluid. This averaging, which corresponds to the electrical problem of several resistances in series, is simpler than the corresponding mass transfer problem examined in Section 8.5.

Some common correlations of heat transfer coefficients are reported in Table 20.4-3. These all refer to heat transfer across a solid-fluid interface because other situations either are rare or are described in different terms. Like the mass transfer correlations in Section 8.3, these are best presented in terms of dimensionless groups. The two most... 

The experimental and theoretical work reported in the literature will be reviewed for each of the five major types of ga s-liquid-particle operation under the headings Mass transfer across gas-liquid interface mass transfer across liquid-solid interface holdup and axial dispersion of gas phase holdup and axial dispersion of liquid phase heat transfer reaction kinetics. 

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