The heat transfer equipment shown in Fig. P9.3 consists of two tanks, one nested inside the other…

The heat transfer equipment shown
in Fig. P9.3 consists of two tanks, one nested inside the other. Heat is transferred
by convection through the wall of the inner tank. The contents of each tank are
well mixed. The following data and information apply:

1. The holdup volume of the inner tank
is 1 ft3. The holdup of the outer tank is 1 ft3.

2. The cross-sectional area for heat
transfer between the tanks is 1 ft2.

3. The overall heat transfer coefficient
for the flow of heat between the tanks is 10 Btu/(hr)(ft*)(F).

4. The heat capacity of fluid in each
tank is 1 Btu/(lb)(F). The density
The heat transfer equipment shown
in Fig. P9.3 consists of two tanks, one nested inside the other. Heat is transferred
by convection through the wall of the inner tank. The contents of each tank are
well mixed. The following data and information apply:

1. The holdup volume of the inner tank
is 1 ft3. The holdup of the outer tank is 1 ft3.

2. The cross-sectional area for heat
transfer between the tanks is 1 ft2.

3. The overall heat transfer coefficient
for the flow of heat between the tanks is 10 Btu/(hr)(ft*)(F).

4. The heat capacity of fluid in each
tank is 1 Btu/(lb)(F). The density of each fluid is 50 lb/ft3.

Initially the temperatures of the feed
stream to the outer tank and the contents of the outer tank are equal to 100%
The contents of the inner tank are initially at lOOoF. At time zero, the flow
of heat to the inner tank (Q) is changed according to a step change from 0 to
500 Btu/hr.

(a) Obtain an expression for the Laplace
transform of the temperature of the inner tank, T(s).

(b) Invert T(s) and obtain T for time =
0, 5 hr, 10 hr, and 00.

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