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Both results agree with the second law of thermodynamics in that the heat diffuses from higher to lower temperatures. * Once we have classified continua according to their conductivity, it becomes clear that the solids used in the experiments which suggest Fourier's law of conduction must necessarily be homogeneous and isotropic. t A surface described instantaneously in a continuum such that at every point upon it the temperature is the same. STATEMENT O F PARTICULAR LAWS Conduction Conduction * +x 0 C+Z 0 (a) (b) FIG.

Assume that at time t a system coincides with this control volume. We wish to evaluate the time rate of change of the property within the system. * See the concept of lost work in Reference 9, Eq. (7-8). t As S , + 0 Eq. (2-21) applies to reversible processes only. INTEGRAL FORMULATION O F GENERAL LAWS FIG. 2-5 Since the continuum cannot cross its boundaries, this system during a time intervaI At moves with the continuum and a t time t At occupies another volume in space as shown in Fig. 2-5. Thus the required rate of change may be written in the form + (2) + + = system + + lim [ B I ( ~ ~ t ) ~ 3 ( t at11 - [ B I ( ~ ) ~ 2 ( t ),1 At (2-22) A~+O or, by rearranging its terms, + At-o system + ~ ( t At) - B l ( t ) + B3(f At) At first term second term ~ 2 ( t ),] (2-23) At third term where B 1 ,B 2 , and B3 are the instantaneous values of B corresponding to three regions of space, denoted by 1, 2, and 3 in Fig.

The plus and minus signs of the left member of Eq. (2-102) correspond to the differentiations along the inward and outward normals, respectively (Fig. 2-17). I t should be kept in mind that q, shown in Fig. 2-17 is a positive quantity, obtained by arbitrarily selecting it in the direction of the normal. Actually, Eq. (2-102) is independent of the temperature distribution and the direction of the heat transfer. The range of values of heat transfer coefficients occurring under various conditions will now be presented, to give the reader a feeling for the order of magnitudes involved.

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