Chemical Engineering Question:

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Answer #1
The overall heat transfer coefficient is generally weakly dependent on temperature. As the temperatures of the fluids change, the degree to which the overall heat transfer coefficient will be affected depends on the sensitivity of the fluid's viscosity to temperature. If both fluids are water, for example, the overall heat transfer coefficient will not vary much with temperature because water's viscosity does not change dramatically with temperature. If, however, one of the fluids is oil which may have a viscosity of 1000 cP at 50 °F and 5 cP at 400 °F, then indeed the overall heat transfer coefficient would be much better at higher temperatures since the oil side would be limiting. Realize that the overall heat transfer coefficient is dictated by the local heat transfer coefficients and the wall resistances of the heat exchanger. The local heat transfer coefficients are dictated by the fluid's physical properties and the velocity of the fluid through the exchanger. So, for a given heat exchanger, fluid flow rates, and characteristics of each fluid....the area of the exchanger and the overall heat transfer coefficients are fixed (theoretically anyway....as the overall heat transfer coefficient does vary slightly along the length of the exchanger with temperature as I've noted and the U-value will decrease over time with fouling).

Answer #2
However, if the inlet temperatures of the fluids change, the heat duty (Q) is where variable that will change with it for the most part. For example, for an installed heat exchanger, if the LMTD or log mean temperature difference increases or decreases based on temperature variations of the fluids, then a given, fixed exchanger will simply transfer more heat (for a larger LMTD) or less heat (for a small LMTD). In short, temperature difference is the "driving force" which determines how much heat is transferred. If the LMTD decreases, but you want to keep Q the same, then you have two choices: increase the heat transfer area or find a way to increase the overall heat transfer coefficient (U-value) via heat transfer enhancement or a different heat exchanger technology. Again, with an increased temperature, the viscosity of the fluids will decrease (to what degree depends on the fluids), so there would technically be an increase in the U-value, but often times, it will not be substantial.