What is fouling on surfaces in heat exchangers, and describe how to determine the overall heat transfer coefficient for a heat exchanger?

Fouling on the surfaces in heat exchangers are the formation of deposits on the heat transfer surfaces which cause an additional resistance to heat transfer. This causes the rate of heat transfer in a heat exchanger to decrease.

The overall heat transfer coefficient (U) is determined by knowing the  thermal resistance (R) of the inner (Ri) and outer(Ro) surfaces and wall (R, wall) of tube.

Explanation:

A heat exchanger normal involves a hot and cold fluid. Heat transfer from hot fluid to the wall by convection occurs first followed by conduction through the wall and lastly convection from wall to cold fluid. Thermal resistance associated with this heat transfer is two convection and one conduction resistances:

R, total = R,i + R,wall + R,o

Where R, i and R,o are the convection resistance of the inner and outer surfaces respectively and R, wall the resistance of the wall.

The Resistance of the wall is:

R, wall = ㏑(D,o/D,i)/(2πkL),  Where D,o = outer diameter, D,i=inner diameter, k = thermal conductivity of the wall material, L = length of the tube.

The inner and outer resistance caused by convection can be determined as:

R,i = 1/(h,i×A,i)

R,o = 1/(h,o×A,o)

Where A,i is the area of the inner surfance and A,o is the area of the outer surfance.

To determine the overall heat transfer coefficient we can combine all the thermal resistance(R) and express the rate of heat transfer between the two fluids as:

Q = ΔT/R = U×A,s ×ΔT

Cancel out ΔT:

1/(U×A,s) = 1/(U,i×A,i) = 1/(U, o×A,o) = R

R = ㏑(D,o/D,i)/(2πkL) + 1/(h,i×A,i) + 1/(h,o×A,o)

∴ 1/(U×A,s) = 1/(U,i×A,i) = 1/(U, o×A,o) = ㏑(D,o/D,i)/(2πkL) + 1/(h,i×A,i) + 1/(h,o×A,o)

simplify to obtain U, U,i or U, o

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