By Vedat S. Arpacı
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Extra info for Conduction Heat Transfer
Example text
2-15) according to the foregoing discussion on the power and heat terms, we obtain the explicit form of the first law of thermodynamics for lumped control volumes: where h: = ei + pivi defines the stagnation enthalpy per unit, mass. 26 LUMPED, INTEGRAL,DIFFERENTIAL FORMULATIONS [2-41 Second law of thermodynamics (lumped formulation). Let us first write the second law of thermodynamics for lumped systems, AS 2 VQ/T, in the rate form dS/dt > q/T. Then, from Table 2-1, inserting into the transformation formula, Eq.
2-20), the heat flux across this boundary evaluated from both continua, regardless of the direction of normal, gives * Hereafter figures illustrating the statement of boundary conditions are drawn for one direction of the boundary normal. INITIAL AND BOUNDARY CONDITIONS 41 - 42 = 01 FIG. 2-20 Furthermore, a second condition may be specified along this boundary relating the temperatures of the two continua. If the continua are assumed, for example, to be solid and in intimate contact, mathematical idealization suggests the equality of temperatures (Tdcr = ( T z ) ~ .
Then, from Table 2-1, inserting into the transformation formula, Eq. (2-6), and the result into Eq. (2-18), we obtain the second law of thermodynamics for lumped control volumes: Introducing the rate of entropy generation* S,, we may write Eq. (2-20) as an equality in the form which gives the conservation of entropy for lumped control volumes. Since 8, is related to the degree of irreversibility,t Eq. (2-21) becomes useful for the study of irreversible processes. This point will be elaborated in the differential formulation.