Conduction-Convection Systems

We shall defer part of our analysis of conduction-convection systems to Chap. 10 on heat exchangers. For the present we wish to examine some simple extended-surface problems. Consider the one-dimensional fin exposed to a surrounding fluid at a temperature T as shown in Fig. 2-9. The temperature of the base of the fin is T0. We approach the problem by making an energy balance on an element of the fin of thickness dx as shown in the figure. Thus 

Energy in left face = energy out right face + energy lost by convection 

The defining equation for the convection heat-transfer coefficient is recalled as 

Here it is noted that the differential surface area for convection is the product of the perimeter of the fln and the differential length dx. When we combine the quantities, the energy balance yields 

The other boundary condition depends on the physical situation. Several cases may be considered  

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Radiation heat-transfer phenomena can be exceedingly complex, and the calculations are seldom as simple as implied by Eq. (1-11). For now, we wish to emphasize the difference in physical mechanism between radiation heat-transfer and conduction-convection systems. In Chap. 8 we examine radiation in detail. 

Figure 8-1 depicts a combined conduction-convection system. Basically, the inner cylinder could be a pipe and the outer cylinder a layer of insulation. One fluid flows inside the pipe and another is outside the insulation. The temperature profiles in the solid objects and between the fluids and solid surfaces are shown,... 

In order to develop a combined conduction-convection system, we make use of the approach developed earlier—namely, that of the electrical analog. For such a system, the energy or heat transferred is analogous to electrical current. Furthermore, we know the heat transferred is directly related to the temperature driving force (AT). Finally, we also know that the heat transferred will also be directly related to the available surface area (A). On this basis, we can write an empirical equation of the form... 

Because the evaporation of the solvent is an endothermic process, heat must be suppHed to the system, either through conduction, convection, radiation, or a combination of these methods. The total energy flux into a unit area of coating, is the sum of the fluxes resulting from conduction, convection, and radiation (see Heat exchange technology, HEAT thansfer). 

Heat will be lost from the system by conduction, convection and radiation. If the temperature difference between the reactants and their surroundings is not too great, the rate of heat loss, Ql, is given by... 

Heat flow, whether by radiation, conduction, convection, or the bulk transfer of matter, introduces temperature as another variable. Thus, for systems in motion, thermal similarity requires kinematic similarity. Thermal similarity is described by... 

Heat can be defined as a portion of the total energy flow across a system boundary and is caused by a temperature difference between the system and the surroundings. Heat can be exchanged by conduction, convection and/or radiation. We can evaluate heat transfer by use of the energy balance, which will be discussed later. 

The influential parameters in a thermal convection system may be represented by the characteristic length l, velocity U, density p, viscosity fi, specific heat at constant pressure cp, and thermal conductivity K. Thus, we have... 

The governing heat transfer modes in gas-solid flow systems include gas-particle heat transfer, particle-particle heat transfer, and suspension-surface heat transfer by conduction, convection, and/or radiation. The basic heat and mass transfer modes of a single particle in a gas medium are introduced in Chapter 4. This chapter deals with the modeling approaches in describing the heat and mass transfer processes in gas-solid flows. In multiparticle systems, as in the fluidization systems with spherical or nearly spherical particles, the conductive heat transfer due to particle collisions is usually negligible. Hence, this chapter is mainly concerned with the heat and mass transfer from suspension to the wall, from suspension to an immersed surface, and from gas to solids for multiparticle systems. The heat and mass transfer mechanisms due to particle convection and gas convection are illustrated. In addition, heat transfer due to radiation is discussed. 

In separation processes and chemical reactors, flow through cylindrical ducts filled with granular materials is important. In such systems conduction, convection, and radiation all contribute to the heat flow, and thermal conduction in axial ke x and radial ke r directions may be quite different, leading to highly anisotropic thermal conductivity. For a bed of uniform spheres, the axial and radial elements are approximated by... 

Liquid storage requires highly sophisticated tank systems. Heat transfer into the tank through conduction, convection and radiation has to be minimized. Therefore, the specially insulated vessels consist of an inner tank and an outer container with an... 

Rate of heating this is very important if you intend to repeat the experiment on a subsequent occasion. Obviously the rate of heating of the sample in the crucible is not instantaneous but depends upon conduction, convection and radiation within the system. Thermal lag is therefore likely to be observed. 

On Earth, heat travels by conduction, convection, and radiation. However, conduction and natural convection are almost entirely nonexistent in the vacuum of space. Radiation is the primary method of heat transport in space. Space-based electronics that need to be kept cold are attached to radiators that face deep space and radiate excess heat into space. These electronics (i.e., space based phased-array-radar and laser systems) and radiators are thermally insulated from the rest of the spacecraft. Cooling is achieved through surface thermal radiation to deep space. Space-based electronics thermal management encompasses not only the removal of waste heat, but also the conservation of heat to provide a benign environment for the instruments and on-board electronic equipment. 

However, thermodynamics does not state how the heat transferred depends on this temperature driving force, or how fast or intensive this irreversible process is. It is the task of the science of heat transfer to clarify the laws of this process. Three modes of heat transfer can be distinguished conduction, convection, and radiation. The following sections deal with their basic laws, more in depth information is given in chapter 2 for conduction, 3 and 4 for convection and 5 for radiation. We limit ourselves to a phenomenological description of heat transfer processes, using the thermodynamic concepts of temperature, heat, heat flow and heat flux, fn contrast to thermodynamics, which mainly deals with homogeneous systems, the so-called phases, heat transfer is a continuum theory which deals with fields extended in space and also dependent on time. 

In contrast to heat conduction, in mass diffusion the average velocity of the particles of the individual materials in a volume element can be different from each other, so that a relative movement of the individual particles to each other is macroscopically perceptible. In general this results in a macroscopic movement of all particles in a volume element and therefore convection. As these considerations show, in contrast to heat conduction quiescent systems cannot always be assumed for mass diffusion. This can only be assumed under certain conditions, which we will now discuss. 

Heat transfer or thermal energy exchange occurs if and only if there is a temperature difference. Moreover, thermal energy can only be transferred from a system or substance with a higher temperature to a system or substance with a lower temperature. The phenomenological laws will be discussed here to provide a quantitative relation of a heat flux, as a measure of energy transfer, with a system temperature gradient. Such a relation will be discussed for conductive, convective, and radiative heat transfer mechanisms. 

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