Heat-Transfer Process

Were we can give these equations for the heat transfer process along radius R. The other processes of heat transfer can be simulated analogously by changing formula for heat transfer area and distances between centers of cells. For Dirichlet cells, bordering a gas medium, an equation of heat balance can be written in the form ... 

Heat transfer and mass transfer occur simultaneously whenever a transfer operation involves a change in phase or a chemical reaction. Of these two situations, only the first is considered herein because in reacting systems the complications of chemical reaction mechanisms and pathways are usually primary (see HeaT-EXCHANGETECHNOLOGy). Even in processes involving phase changes, design is frequendy based on the heat-transfer process alone mass transfer is presumed to add no compHcations. But in fact mass transfer effects do influence and can even limit the process rate. 

The maximum velocity at the axis is twice the average, whereas the velocity at the wall is zero. The effect of the burner wall is to cool the flame locally and decrease the burning velocity of the mixture. This results in flame stabilization. However, if the heat-transfer processes (conduction, convection, and radiation) involved in cooling the flame are somehow impeded, the rate of heat loss is decreased and the local reduction in burning velocity may no longer take place. This could result in upstream propagation of the flame. 

The heat-transfer process involves (1) latent heat transfer owing to vaporization of a small portion of the water and (2) sensible heat transfer owing to the difference in temperature of water and air. Approximately 80 percent of this heat transfer is due to latent heat and 20 percent to sensible heat. 

The most generally accepted theory of the coohng-tower heat-transfer process is that developed by Merkel (op. cit.). This analysis is based upon enthalpy potential difference as the driving force. 

NO Emission Control It is preferable to minimize NO formation through control of the mixing, combustion, and heat-transfer processes rather than through postcombustion techniques such as selective catalytic reduction. Four techniques for doing so, illustrated in Fig. 27-15, are air staging, fuel staging, flue-gas recirculation, and lean premixing. 

A common process task involves heating a slurry by pumping it through a well-stirred tank. It is useful to know the temperature profile of the slurry in the agitated vessel. This information can be used to optimize the heat transfer process by performing simple sensitivity studies with the formulas presented below. Defining the inlet temperature of the slurry as T, and the temperature of the outer surface of the steam coil as U then by a macroscopic mass and energy balance for the system, a simplified calculation method is developed. 

Chemical reactions obey the rules of chemical kinetics (see Chapter 2) and chemical thermodynamics, if they occur slowly and do not exhibit a significant heat of reaction in the homogeneous system (microkinetics). Thermodynamics, as reviewed in Chapter 3, has an essential role in the scale-up of reactors. It shows the form that rate equations must take in the limiting case where a reaction has attained equilibrium. Consistency is required thermodynamically before a rate equation achieves success over tlie entire range of conversion. Generally, chemical reactions do not depend on the theory of similarity rules. However, most industrial reactions occur under heterogeneous systems (e.g., liquid/solid, gas/solid, liquid/gas, and liquid/liquid), thereby generating enormous heat of reaction. Therefore, mass and heat transfer processes (macrokinetics) that are scale-dependent often accompany the chemical reaction. The path of such chemical reactions will be... 

It is discovered that in the cooling tower the water moving downward from the jets changes its direction to upward after drop formation. There is an effective heat transfer process when the drops move upward heat transfers from the outlet air to the drops through convection and condensation. 

Drops collide with the drop separator and drain down to the lower part of the tower. These drops are large, so their total surface area is small and insignificant. The effective heat transfer process takes place when the drops move with the air flow, so this arrangement has to be treated as a parallel flow heat transfer. 

Most heat transfer processes used in production facilities involve combinations of conduction and convection ti ansfer processes. For example, in heat exchangers the transfer of heat energy from the hot fluid to the coLl fluid involves tliree steps. First, the heat energy is transferred from the luH fluid to the exchanger tube, then through the exchanger tube wall, ctud finally from the tube wall to the cold fluid. The first and third steps are convection transfer processes, while the second step is conduction process. 

Wliile heat transfer processes are very useful in the energy field, there are many other industries that rely heavily on heat transfer. The production of chemicals, the cooling of electronic equipment, and food preparation (both freezing and cooking) rely heavily on a thorough knowledge of heat transfer. 

Often, a reasonable and convenient way to understand the heat transfer process in a heat exchanger unit is to break down the types of heat transfer that must occur such as, vapor subcooling to dew point, condensation, and liquid subcooling. Each of these demands heat transfer of a different type, using different AT values, film coefficients, and fouling factors. This is illustrated in Figure 10-36. It is possible to properly determine a weighted overall temperature... 

The removal of heat within an enclosed space must be considered as a multi-step heat transfer process. Heat passes from the occupants or equipment to the air within the space, and from there to the refrigerant or chilled water. It follows that the temperature differences at each step are a reciprocal function of the air mass flow. Where there is a high latent heat load within the space, the relative humidity will also vary with the air flow - the variation being higher with low air flow. 

Because most thermoset composites cure by a thermally activated reaction, a complicated heat transfer process occurs during solidification, the result of an exothermic cross linking reaction in the resin. The complications of thermoset resin curing are compounded by the competing mechanisms of... 

A mechanism of heat transfer in which heat energy is transmitted by convection current motion through gases and liquids. Part of the heat-transfer process in a boiler is by convection whereby the circulation of water carries heat from the tube near the fire to the drum and surrounding areas. 

More recently, Zucrow et al. (Zl) have run experiments which show that in the region of low flow rates the burning rates of certain propellants actually decrease with increasing gas flow. As the gas flow rate increases, the burning rate is observed to go through a minimum and then increase with further increases in gas flow rate. The decrease in burning rate was attributed to undefined mass-transfer processes. Eventually, the convective heat-transfer processes overcome this effect to give results similar to those obtained by others. 

Now that the overall coefficient U has been broken down into its component parts, each of the individual coefficients /q, hi, and hi must be evaluated. This can be done from a knowledge of the nature of the heat transfer process in each of the media. A study will therefore be made of how these individual coefficients can be calculated for conduction, convection, and radiation. 

Analytical solutions of equation 9.44 in the form of infinite series are available for some simple regular shapes of particles, such as rectangular slabs, long cylinders and spheres, for conditions where there is heat transfer by conduction or convection to or from the surrounding fluid. These solutions tend to be quite complex, even for simple shapes. The heat transfer process may be characterised by the value of the Biot number Bi where ... 

Heat transfer by convection occurs as a result of the movement of fluid on a macroscopic scale in the form of eddies or circulating currents. If the currents arise from the heat transfer process itself, natural convection occurs, such as in the heating of a vessel containing liquid by means of a heat source situated beneath it. The liquid at the bottom of the vessel becomes heated and expands and rises because its density has become less than that of the remaining liquid. Cold liquid of higher density takes its place and a circulating current is thus set up. 

In these equations all of the physical properties ate taken at the mean bulk temperature of the fluid (T, + T0)/2, where 7) and T0 are the inlet and outlet temperatures. The difference in the value of the index for heating and cooling occurs because in the former case the film temperature will be greater than the bulk temperature and in the latter case less. Conditions in the film, particularly the viscosity of the fluid, exert an important effect on the heat transfer process. 

Thus, a velocity boundary layer and a thermal boundary layer may develop simultaneously. If the physical properties of the fluid do not change significantly over the temperature range to which the fluid is subjected, the velocity boundary layer will not be affected by die heat transfer process. If physical properties are altered, there will be an interactive effect between the momentum and heat transfer processes, leading to a comparatively complex situation in which numerical methods of solution will be necessary. 

Heat transfer processes besides pure radiative transfer are involved in control of the temperature of the air, especially below the effective emission height of 6 km. Referring back to Chapter 7, we see that vertical motions of air in the troposphere are a main factor dictating that temperature decreases as altitude increases - air loses internal energy... 

One of the common problems associated with underwater pelletizers is the tendency of the die holes to freeze off. This results in nonuniform polymer melt flow, increased pressure drop, and irregular extrudate shape. A detailed engineering analysis of pelletizers is performed which accounts for the complex interaction between the fluid mechanics and heat transfer processes in a single die hole. The pelletizer model is solved numerically to obtain velocity, temperature, and pressure profiles. Effect of operating conditions, and polymer rheology on die performance is evaluated and discussed. 

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