In a shell-and-tube heat exchanger with h i= h o= 5600 W/(m2 K) and negligible wall resistance, by what per cent would the overall heat transfer coefficient (based on the outside area) change if the number of tubes was doubled? The tubes have an outside diameter of 2.5 cm and a tube wall thickness of 2 mm. Assume that the flow rates of the fluids are constant, the effect of temperature on fluid properties is negligible, and the total cross sectional area of the tubes is small compared to the flow area of the shell.
GIVEN
• Shell and tube heat exchanger
• Heat transfer coefficients: h i= h o= 5600 W/(m2 K)
• Negligible wall resistance
• Tube outside diameter (Do) = 2.5 cm = 0.025 m
• Tube wall thickness (t) = 2 mm = 0.002 m
FIND
• The per cent change in the overall heat transfer coefficient if the number of tubes is doubled
ASSUMPTIONS
• Flow rates of the fluids are constant
• The effect of temperature of fluid properties is negligible
• The fluid flow is turbulent in the tubes (this is consistent with the high heat transfer coefficients)
SKETCH
The inside diameter (Di) = Do – 2t = 2.5 cm – 2(0.2cm) = 2.1 cm = 0.021 m
The original overall heat transfer coefficient is. Neglecting wall resistance
Since the total cross sectional area of the tubes is small compared tot the flow area of the shell, doubling the number of tubes will have little effect on the shell-side fluid velocity. Therefore, the shell side heat transfer coefficient will not change. Doubling the number of tubes with the same mass flow rate cuts the fluid velocity in the tubes in half. For turbulent flow in tube
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