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By Vedat S. Arpacı

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Hr). [2-41 INTEGRAL FORMULATION OF GENERAL LAWS 31 For the case in which P, denotes the power drawn to the system from an external electric circuit, we have where u'" is the rate of local internal e n e T y per unit volume, generated electrically in the system. Introducing Eqs. (2-30), (2-3 I), (2-32), (2-33), (2-34), and (2-35) into Eq. (2-29) gives Furthermore, by employing the definition of stagnation enthalpy per unit mass, h0 = e pv, Eq. (2-36) may be rearranged to yield the first law of thermodynamics for integral control volumes: + Second law of thermodynamics (integral formulation).

2-103) applies. (5) Heat transfer to the ambient by radiation. Let us reconsider Fig. 2-13, and find, for example, the boundary condition prescribing heat transfer by radiation from the boundaries of continuum 1. When T1 is uniform but unspecified, to express the heat flux across the surfaces of 1 by conduction and radiation the required boundary condition may be written in the form LUMPED, INTEGRAL, DIFFERENTIAL FORMULATIONS [2-81 FIG. 2-19 where, as before, the plus and minus signs of the conduction term correspond to differentiation in the direction of inward and outward normals, respectively.

A / FIG. 2-22 Consider, for example, the solidification of a liquid. Here our concern is the boundary condition on the moving interface Nz(t) (Fig. 2-22). The thermal properties of the liquid and solid are distinguished by the subscripts 1 and 2, respectively. Since the densities of the two phases are not the same, in the time interval dt the solid of thicltness dN2 is formed from the liquid of thickness dN1. Applying the first law of thermodynamics to the system shown in Fig. 2-23, whose initial state is the liquid of thickness dN1 and whose final state is the solid of thickness dNz, we have where p is the pressure of the continuum.

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