A shell-and-tube heat exchanger having one shell pass and four tube passes is shown schematically in the following sketch. The fluid in the tubes enters at 200°C and leaves at 100°C. The temperature of the fluid is 20°C entering the shell and is 90°C leaving the shell. The overall heat transfer coefficient based on the surface area of 12 m2 is 300 W/(m2 K). Calculate the heat transfer rate between the fluids.

Question

GIVEN

• A shell-and-tube heat exchanger with one shell pass and four tube passes

• Temperature of fluid in tube

? Tt,in = 200°C

? Tt,out = 100°C

• Temperature of fluid in shell

? Ts,in = 20°C

? Ts,out = 90°C

• Overall heat transfer coefficient (U) = 300 W/(m2 K)

• Surface area (A) = 12 m2

FIND

• The heat transfer rate (q)

ASSUMPTIONS

• Steady state

• Exchanger geometry is countnerflow

SKETCH

Answer 1

A log-mean temperature difference for this counterflow arrangement is





This value must be modified to account for the shell-and-the geometry





F = 0.85



The heat transfer rate is given by



COMMENTS

Since ?Ta is less than 50% greater than ?Tb, the mean temperature difference may be used in place of the LMTD without introducing significant error. Use of the mean temperature difference in this case leads to a heat transfer rate of 2.907 × 105 W (1% higher)