Heat transfer combined convective

Commercial dryers differ fundamentally by the methods of heat transfer employed (see classification of diyers, Fig. 12-45). These industrial-diyer operations may utihze heat transfer by convection, conduction, radiation, or a combination of these. In each case, however, heat must flow to the outer surface and then into the interior of the solid. The single exception is dielectric and microwave diying, in which high-frequency electricity generates heat internally and produces a high temperature within the material and on its surface. 

Example 1 Combined heat transfer by convection and radiation. The OD of an... 

Heat transfer by convection occurs in liquids and gases where there is a velocity field caused by extorted fluid motion or by natural fluid motion caused by a difference in density. The former case involves forced convection, and the latter case free convection. Combined convection occurs when both forced and free convection are present. The convection coefficient of surface heat transfer, a, defining the heat exchange in the contact boundary layer between fluid and soUd, is determined. Coefficient or is often expressed by equations containing criteria numbers, such as those of Nusselt (Nu), Prandtl (Pr), Reynolds (Re) and Grashof(Gr) ... 

Convective heat transfer, or convection, is the transfer of heat from one place to another by the movement of fluids, a process that is essentially the transfer of heat via mass transfer. Bulk motion of fluid enhances heat transfer in many physical situations, such as between a solid surface and the fluid. Convection is usually the dominant form of heat transfer in liquids and gases. Although sometimes discussed as a third method of heat transfer, convection is usually used to describe the combined effects of heat conduction within the fluid (diffusion) and heat transference by bulk fluid flow streaming. 

Famworth [74] presented a model of the combined conductive and radiative heat flow through fibrous material used for clothing insulation. The amount of heat transferred by convective heat transfer is small compared to that of conductive and radiative heat transport and is neglected. In the case where a sample of fibrous material is held between two plates, one cold and one hot, and in the absence of radiative heat, the heat flow is given by ... 

The most widely used and best known resistance furnaces are iadirect-heat resistance furnaces or electric resistor furnaces. They are categorized by a combination of four factors batch or continuous protective atmosphere or air atmosphere method of heat transfer and operating temperature. The primary method of heat transfer ia an electric furnace is usually a function of the operating temperature range. The three methods of heat transfer are radiation, convection, and conduction. Radiation and convection apply to all of the furnaces described. Conductive heat transfer is limited to special types of furnaces. 

From 760 to 960°C, circulating fans, normally without baffles, are used to improve temperature uniformity and overall heat transfer by adding some convection heat transfer. They create a directional movement of the air or atmosphere but not the positive flow past the heating elements to the work as in a convection furnace. Heating elements ate commonly chrome—nickel alloys in the forms described previously. Sheathed elements are limited to the very low end of the temperature range, whereas at the upper end silicon carbide resistors may be used. In this temperature range the selection of heating element materials, based on the combination of temperature and atmosphere, becomes critical (1). 

Simultaneous Loss by Radiation The heat transferred by radiation is often of significant magnitude in the loss of heat from surfaces to the surroundings because of the diathermanous nature of atmospheric gases (air). It is convenient to represent radiant-heat transfer, for this case, as a radiation film coefficient which is added to the film coefficient for convection, giving the combined coefficient for convection and radiation (h + hf In Fig. 5-7 values of the film coefficient for radiation are plotted against the two surface temperatures for emissivity = 1.0. 

In any operation in which a material undergoes a change of phase, provision must be made for the addition or removal of heat to provide For the latent heat of the change of phase plus any other sensible heating or cooling that occurs in the process. Heat may be transferred by any one or a combination of the three modes—conduction, convection, and radiation. The process involving change of phase involves mass transfer simultaneous with heat transfer. 

If heat is transferred solely by convection and in the absence of other heat effects, the surface temperature approaches the wet-bulb temperature. However, when heat is transferred by radiation, convection, or a combination of these and convection, the temperature at the saturated surface is between the wet-bulb temperature and the boiling point of water. Under these conditions, the rate of heat transfer is increased and a higher drying rate results. 

Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differences (buoyancy forces), the heat transfer is termed free convection. Typical examples are the cold down-draft along a cold wall or the thermal plume upward along a warm vertical surface. Forced convection takes place when fluid movement is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe. 

Contact temperature measurement is based on a sensor or a probe, which is in direct contact with the fluid or material. A basic factor to understand is that in using the contact measurement principle, the result of measurement is the temperature of the measurement sensor itself. In unfavorable situations, the sensor temperature is not necessarily close to the fluid or material temperature, which is the point of interest. The reason for this is that the sensor usually has a heat transfer connection with other surrounding temperatures by radiation, conduction, or convection, or a combination of these. As a consequence, heat flow to or from the sensor will influence the sensor temperature. The sensor temperature will stabilize to a level different from the measured medium temperature. The expressions radiation error and conduction error relate to the mode of heat transfer involved. Careful planning of the measurements will assist in avoiding these errors. 

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. 

Many everyday heat flows, such as those through windows and walls, involve all three heat transfer mechanisms—conduction, convection, and radiation. In these situations, engineers often approximate the calculation of these heat flows using the concept of R values, or resistance to heat flow. The R value combines the effects of all three mechanisms into a single coefficient. 

Engineering thermal design of heat transfer equipment is concerned with heat flow mechanisms of the following three types—simply or in combination (1) conduction, (2) convection, and (3) radiation. Shell and tube exchangers are concerned primarily with convection and conduction whereas heaters and furnaces involve convection and radiation. 

Convective heat transfer to fluid inside circular tubes depends on three dimensionless groups the Reynolds number. Re = pdtu/ii, the Prandtl number, Pr = Cpiilk where k is the thermal conductivity, and the length-to-diameter ratio, L/D. These groups can be combined into the Graetz number, Gz = RePr4/L. The most commonly used correlations for the inside heat transfer coefficient are... 

The parameter h which combines several effects, must be at least as large as the convective heat transfer coefficient (hc calculated from the jH factor correlations discussed in Section 12.5. It is given by an expression of the following form... 

Radauer, H. G., Glatzer, A., and Linzer, w., A Model Combining Convective and Radiative Heat Transfer in CFB Boilers, Circ. Fluid. Bed Tech. V, 9 (1996)... 

Next, consider the gradients of temperature. If the reaction is exothermic, the center of the particle tends to be hotter, and conversely for an endothermic reaction. Two sets of gradients are thus indicated in Figure 8.9. Heat transfer through the particle is primarily by conduction, and between exterior particle surface (Ts) and bulk gas (Tg) by combined convection-conduction across a thermal boundary layer, shown for convenience in Figure 8.9 to coincide with the gas film for mass transfer. (The quantities T0, ATp, A7y, and AT, are used in Section 8.5.5.)... 

Usually, the rate of heat transfer is a combination of conduction and convection in a heat exchanger system as illustrated in Fig. 7.1 and only the fluid temperature on either side of the solid surface is known. For steady state, the rate of conduction heat transfer and the rate of convection heat transfer are equal. The total resistance (R) of the combined rate of heat transfer is... 

Combination of Equations 1 and 2 allows calculation of the rate of heat transfer from the growing crystal surface to the bulk solution. Under heat balance conditions, this rate of heat generation must be balanced by the amount of heat removed from the crystallizer by convection and conduction. This will be determined by the overall heat transfer coefficient, U, between the bulk solution and the refrigerant including convective resistances between the fluid and both sides of the crystallizer wall (refrigerant side and product side) as well as the conductive resistance across the crystallizer wall. 

The mathematical difficulty increases from homogeneous reactions, to mass transfer, and to heterogeneous reactions. To quantify the kinetics of homogeneous reactions, ordinary differential equations must be solved. To quantify diffusion, the diffusion equation (a partial differential equation) must be solved. To quantify mass transport including both convection and diffusion, the combined equation of flow and diffusion (a more complicated partial differential equation than the simple diffusion equation) must be solved. To understand kinetics of heterogeneous reactions, the equations for mass or heat transfer must be solved under other constraints (such as interface equilibrium or reaction), often with very complicated boundary conditions because of many particles. 

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