Heat transfers Basic equations

It is important to emphasize that, especially in process measurements, radiation can have an essential influence on the wet bulb temperature, and therefore generally the wet bulb temperature is dependent on the mea,surement device and the method of measurement. If the airflow is very low, the radiation can have a remarkable contribution in addition to the convective heat transfer. Basically, an equation analogous to Eq. (4.138) can be empirically determined for each wet bulb temperature and method of measurement. 

The book is arranged in two parts Part I deals with basic relationships and phenomena, including particle size and properties, collision mechanics of solids, momentum transfer and charge transfer, heat and mass transfer, basic equations, and intrinsic phenomena in gas-solid flows. Part II discusses the characteristics of selected gas-solid flow systems such as gas-solid separators, hopper and standpipe flows, dense-phase fluidized beds, circulating fluidized beds, pneumatic conveying systems, and heat and mass transfer in fluidization systems. 

From the basic heat-transfer-rate equation q= UA At,... 

Basic Heat-Transfer Equations. Consider a simple, single-pass, parallel-flow heat exchanger in which both hot (heating) and cold (heated) fluids are flowing in the same direction. The temperature profiles of the fluid streams in such a heat exchanger are shown in Figure 2a. 

Assuming that U, and are invariant with respect to temperature and space, one can integrate equation 14 subject to equation 19, and obtain, after rearrangement, a basic heat-transfer equation for a parallel-flow heat exchanger (4). 

For heat exchangers other than the parallel and counterflow types, the basic heat-transfer equations, and particularly the effective fluid-to-fluid temperature differences, become very complex (5). For simplicity, however, the basic heat-transfer equation for general flow arrangement may be written as... 

The expressions for S can be obtained usiag basic governing heat-transfer equations, such as equations 14 and 19 with proper substitutions of equation 36. For simple, siagle-pass, parallel- and counterflow heat exchangers, the foUowiag expressions result ... 

Equation 2 defines the basic mode of operation of the dryer. The heat-transfer coefficient is a key property of the dryer configuration. 

Overall Heat-Transfer Coeffieient The basic design equation for a heat exchanger is... 

Thermal design concerns itself with sizing the equipment to effect the heat transfer necessaiy to cany on the process. The design equation is the familiar one basic to all modes of heat transfer, namely,... 

Consider a vessel containing an agitated liquid. Heat transfer occurs mainly through forced convection in the liquid, conduction through the vessel wall, and forced convection in the jacket media. The heat flow may be based on the basic film theory equation and can be expressed by... 

Chapter 3 of Volume 1 discusses many of the basic properties of gas and methods presented for calculating them. Chapter 6 of Volume 1 contains a brief discussion of heat transfer and an equation to estimate the heat required to change the temperature of a liquid. This chapter discusses heat transfer theory in more detail. The concepts discussed in this chapter can be used to predict more accurately the required heat duty for oil treating, as well as to size heat exchangers for oil and water. 

In the basic heat transfer equation it is necessary to use the log mean temperature difference. In Equation 2-4 it was assumed that the two fluids are flowing counter-current to each other. Depending upon the configuration of the exchanger, this may not be true. That is, the way in which the fluid flows through the exchanger affects LMTD. The correction factor is a function of the number of tube passes and the number of shell passes. 

Convection is heat transfer between portions of a fluid existing under a thermal gradient. The rate of convection heat transfer is often slow for natural or free convection to rapid for forced convection when artificial means are used to mix or agitate the fluid. The basic equation for designing heat exchangers is... 

The air-cooled heat transfer exchanger is like other exchangers in that the basic heat transfer equation must be statisfied ... 

The basic equations for filmwise condensation were derived by Nusselt (1916), and his equations form the basis for practical condenser design. The basic Nusselt equations are derived in Volume 1, Chapter 9. In the Nusselt model of condensation laminar flow is assumed in the film, and heat transfer is assumed to take place entirely by conduction through the film. In practical condensers the Nusselt model will strictly only apply at low liquid and vapour rates, and where the flowing condensate film is undisturbed. Turbulence can be induced in the liquid film at high liquid rates, and by shear at high vapour rates. This will generally increase the rate of heat transfer over that predicted using the Nusselt model. The effect of vapour shear and film turbulence are discussed in Volume 1, Chapter 9, see also Butterworth (1978) and Taborek (1974). 

The fin surface area will not be as effective as the bare tube surface, as the heat has to be conducted along the fin. This is allowed for in design by the use of a fin effectiveness, or fin efficiency, factor. The basic equations describing heat transfer from a fin are derived in Volume 1, Chapter 9 see also Kern (1950). The fin effectiveness is a function of the fin dimensions and the thermal conductivity of the fin material. Fins are therefore usually made from metals with a high thermal conductivity for copper and aluminium the effectiveness will typically be between 0.9 to 0.95. 

Dukler and Taitel, 1991b). The simplest configuration of annular flow is a vertical falling film with concurrent downward flow. Given information on interfacial shear and considering the film to be smooth, the film thickness and heat transfer coefficient between the wall and the liquid film can be predicted from the following basic equations (Dukler, 1960) ... 

Two-phase mass transfer and heat transfer without phase change are analogous, and the results of mass-transfer studies can be used to help clarify the heat-transfer problems. Cichy et al. (C5) have formulated basic design equations for isothermal gas-liquid tubular reactors. The authors arranged the common visually defined flow patterns into five basic flow regimes, each... 

The heat transferred in an agitated vessel can be expressed by the basic standard equation ... 

There is apparently an inherent anomaly in the heat and mass transfer results in that, at low Reynolds numbers, the Nusselt and Sherwood numbers (Figures. 6.30 and 6.27) are very low, and substantially below the theoretical minimum value of 2 for transfer by thermal conduction or molecular diffusion to a spherical particle when the driving force is spread over an infinite distance (Volume 1, Chapter 9). The most probable explanation is that at low Reynolds numbers there is appreciable back-mixing of gas associated with the circulation of the solids. If this is represented as a diffusional type of process with a longitudinal diffusivity of DL, the basic equation for the heat transfer process is ... 

Conduction is the rate of heat transfer through a medium without mass transfer. The basic rate of conduction heat-transfer equation is Fourier s law ... 

Radiation is the rate of heat transfer by electromagnetic waves emitted by matter. Unlike conduction and convection, radiation does not require an intervening medium to propagate. The basic rate of radiation heat-transfer equation between a high temperature (Th) black body and a low temperature Tf) black body is Stefan-Boltzmann s law ... 

The transport equations for laminar motion can be formulated, in general, easily and difficulties may lie only in their solution. On the other hand, for turbulent motion the formulation of the basic equations for the time-averaged local quantities constitutes a major physical difficulty. In recent developments, one considers that turbulence (chaos) is predictable from the time-dependent transport equations. However, this point of view is beyond the scope of the present treatment. For the present, some simple procedures based on physical models and scaling will be employed to obtain useful results concerning turbulent heat or mass transfer. 

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