Lumped Problems Bi

An illustrative example for these problems is the cooling of a small metal ball (or billet) in a constant-temperature (large) bath. Let the ball, heated to a uniform temperature To, be quenched into the bath at temperature 2, . 

Consider the entire ball to be a lumped system. The first law of thermodynamics, Eq. (1-10), applied to this system yields (Fig. 3.2), 

in terms of the definitions of specific heat at constant volume and at constant pressure, 

That is why we usually refer to the specific heat for solids and liquids without any reference to volume or pressure [a fact already used in the development leading to Eqs. (2.148) and (2.149)]. Thus, 

Finally, Newton s law, inserted into Eq. (3.3), gives the governing equation, 

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When Bi zero dimensional or lumped model [2, 11], On the other hand, if Bi 1, the fluid can be considered isothermal and Ts = Too, which changes the convection boundary condition to a thermal equilibrium condition. 

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