Editing Heat transfer coefficient (section)

==Thermal resistance due to fouling deposits==
Often during their use, heat exchangers collect a layer of fouling on the surface which, in addition to potentially contaminating a stream, reduces the effectiveness of heat exchangers.   In a fouled heat exchanger the buildup on the walls creates an additional layer of materials that heat must flow through.  Due to this new layer, there is additional resistance within the heat exchanger and thus the overall heat transfer coefficient of the exchanger is reduced.   The following relationship is used to solve for the heat transfer resistance with the additional fouling resistance:<ref name="Mills">{{cite book |author1=A.F. Mills |title=Heat Transfer |publisher=Prentice Hall, Inc |year=1999|edition=second }}</ref>

:<math>\frac{1}{U_{f}P}</math> = <math>\frac{1}{UP}+\frac{R_{fH}}{P_{H}}+\frac{R_{fC}}{P_{C}}</math>

where
:<math>U_{f}</math> = overall heat transfer coefficient for a fouled heat exchanger, <math>\textstyle \rm \frac{W}{m^2K}</math>
:<math>P</math>= perimeter of the heat exchanger, may be either the hot or cold side perimeter however, it must be the same perimeter on both sides of the equation, <math>\rm m</math>
:<math>U</math> = overall heat transfer coefficient for an unfouled heat exchanger, <math>\textstyle \rm \frac{W}{m^2K}</math>
:<math>R_{fC}</math> = fouling resistance on the cold side of the heat exchanger, <math>\textstyle \rm \frac{m^2K}{W}</math>
:<math>R_{fH}</math> = fouling resistance on the hot side of the heat exchanger, <math>\textstyle \rm \frac{m^2K}{W}</math>
:<math>P_C</math> = perimeter of the cold side of the heat exchanger, <math>\rm m</math>
:<math>P_H</math> = perimeter of the hot side of the heat exchanger, <math>\rm m</math>

This equation uses the overall heat transfer coefficient of an unfouled heat exchanger and the fouling resistance to calculate the overall heat transfer coefficient of a fouled heat exchanger.  The equation takes into account that the perimeter of the heat exchanger is different on the hot and cold sides.  The perimeter used for the <math>P</math> does not matter as long as it is the same.  The overall heat transfer coefficients will adjust to take into account that a different perimeter was used as the product <math>UP</math> will remain the same.

The fouling resistances can be calculated for a specific heat exchanger if the average thickness and thermal conductivity of the fouling are known. The product of the average thickness and thermal conductivity will result in the fouling resistance on a specific side of the heat exchanger.<ref name="Mills" />

:<math>R_f</math> = <math>\frac{d_f}{k_f}</math>

where:
:<math>d_f</math> = average thickness of the fouling in a heat exchanger, <math>\rm m</math>
:<math>k_f</math> = thermal conductivity of the fouling, <math>\textstyle \rm \frac{W}{mK}</math>.