STEADY CONDUCTION

In this chapter we shall consider steady conduction in one-dimensional geometry. Although the main objective is conduction, convection described in terms of an assumed heat transfer coefficient will be included whenever it is pertinent. This may be the case when the heat transfer is desired in terms of ambient temperatures (Section 2.2) or when heat loss normal to the direction of conduction is essential, as in the case of extended surfaces (Section 2.4). Here we continue to employ the five-step formulation but somewhat less explicitly than the way we used it in Chapter 1. Each reader should tailor the degree of elaboration of this formulation to his or her particular needs. 

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Consider condensate forming in an insulated container with the lower surface held at constant temperature, Tw, as shown in Ftg. PI 1.1. Since the condensate cannot drain away, the rate of condensation will decrease as the layer thickness increases. Assuming that the heat transfer is by quasi-steady conduction derive an expression for film thickness as a function of time and for the heat transfer rate as a function of time ... 

One-Dimensional Conduction In the absence of energy source terms, Q is constant with distance, as shown in Fig. 5-la. For steady conduction, the integrated form of (5-1) for a planar system with constant k and A is Eq. (5-2) or (5-3). F or the general case of variables k (k is a function of temperature) and A (cylindrical and spherical systems with radial coordinate r, as sketched in Fig. 5-2), the average heat-transfer area and thermal conductivity are defined such that... 

Conduction dirough Several Bodies in Series Figure 5-1 illustrates diagrammatically the temperature gradients accompanying the steady conduction of heat in series throu three solids. 

FIGURE 2-14 The simpUficaiion of the onedimensional heat conduction equation in a plane wall for the case of constant condticliviiy for steady conduction with no hear generation. 

B Solve steady conduction problems that involve multilayer rectangular, cylindrical, or spherical geometries,... 

Two-dime(t,sional steady conduction in rectangular coordinaiet -... 

As a simple, but practically important application, the conduction of heat independent of time, so called steady conduction, in a flat plate, in a hollow cylinder and in a hollow sphere will be considered in this section. The assumption is made that heat flows in only one direction, perpendicular to the plate surface, and radially in the cylinder and sphere, Fig. 1.3. The temperature field is then only dependent on one geometrical coordinate. This is known as one-dimensional heat conduction. 

If we study the heat transfer from the surface of a sphere with r = R, that is immersed in a stagnant fluid we have a process of steady conduction from the surface of the sphere (r = R) through the fluid, radially outward to r = oo. The radial conductive flux is ... 

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