11.50 In a supercomputer, signal propagation delays are reduced by resorting to high-density circuit arrange- ments which are cooled by immersing them in a special dielectric liquid. The fluid is pumped in a closed loop through the computer and an adjoining shell-and-tube heat exchanger having one shell and two tube passes. Coolant loop Heat exchanger Computer Twe Pump During normal operation, heat generated within the com- puter is transferred to the dielectric fluid passing through the computer at a flow rate of m, = 4.81 kg/s. In turn, the fluid passes through the tubes of the heat exchanger and the heat is transferred to water passing over the tubes. The dielectric fluid may be assumed to have constant proper- ties of c,= 1040 J/kg · K, µ = 7.65 × 10~4 kg/s•m,

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11.50 In a supercomputer, signal propagation delays are
reduced by resorting to high-density circuit arrange-
ments which are cooled by immersing them in a special
dielectric liquid. The fluid is pumped in a closed loop
through the computer and an adjoining shell-and-tube
heat exchanger having one shell and two tube passes.
Coolant
loop
Heat
exchanger
Computer
Two
Pump
During normal operation, heat generated within the com-
puter is transferred to the dielectric fluid passing through
the computer at a flow rate of rm, = 4.81 kg/s. In turn, the
fluid passes through the tubes of the heat exchanger and
the heat is transferred to water passing over the tubes. The
dielectric fluid may be assumed to have constant proper-
ties of c, = 1040 J/kg • K, µ= 7.65 × 10-4 kg/s•m,
k = 0.058 W/m K, and Pr= 14. During normal opera-
tion, chilled water at a flow rate of ri, = 2.5 kg/s and an
inlet temperature of Twj = 5°C passes over the tubes. The
water has a specific heat of 4200 J/kg ·K and provides an
average convection coefficient of 10,000 W/m² · K over
the outer surface of the tubes.
(a) If the heat exchanger consists of 72 thin-walled
tubes, each of 10-mm diameter, and fully devel-
oped flow is assumed to exist within the tubes,
what is the convection coefficient associated with
flow through the tubes?
(b) If the dielectric fluid enters the heat exchanger at
T = 25°C and is to leave at T, = 15°C, what is
the required tube length per pass?
Transcribed Image Text:11.50 In a supercomputer, signal propagation delays are reduced by resorting to high-density circuit arrange- ments which are cooled by immersing them in a special dielectric liquid. The fluid is pumped in a closed loop through the computer and an adjoining shell-and-tube heat exchanger having one shell and two tube passes. Coolant loop Heat exchanger Computer Two Pump During normal operation, heat generated within the com- puter is transferred to the dielectric fluid passing through the computer at a flow rate of rm, = 4.81 kg/s. In turn, the fluid passes through the tubes of the heat exchanger and the heat is transferred to water passing over the tubes. The dielectric fluid may be assumed to have constant proper- ties of c, = 1040 J/kg • K, µ= 7.65 × 10-4 kg/s•m, k = 0.058 W/m K, and Pr= 14. During normal opera- tion, chilled water at a flow rate of ri, = 2.5 kg/s and an inlet temperature of Twj = 5°C passes over the tubes. The water has a specific heat of 4200 J/kg ·K and provides an average convection coefficient of 10,000 W/m² · K over the outer surface of the tubes. (a) If the heat exchanger consists of 72 thin-walled tubes, each of 10-mm diameter, and fully devel- oped flow is assumed to exist within the tubes, what is the convection coefficient associated with flow through the tubes? (b) If the dielectric fluid enters the heat exchanger at T = 25°C and is to leave at T, = 15°C, what is the required tube length per pass?
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