Problem 5.3.3

Calculate clean coefficient, design coefficient and heating surface requirement for a water heat exchanger for the following data:

Inside film coefficient, h_i, 948.9, BTU per hour per square foot per degree Fahrenheit.

Outside film coefficient, h_o, 1217.7 BTU per hour per square foot per degree Fahrenheit.

Fouling factor, inside R_di, 0.001-hour square foot degree Fahrenheit per BTU.

Fouling factor, Outside R_do, 0.001-hour square foot degree Fahrenheit per BTU.

Log-mean temperature difference, 28.85 degrees Fahrenheit

Inside pipe diameter, d_i 0.1112 foot, outside pipe diameter, d_o 0.125 foot.

Heat Load, Q, is equal to 3.992 times 10 raised to the power 5^th BTU per hour.

Solution:

We will first convert film coefficients to be based on outside diameter. Heat transfer surface is pi d L, so h_io, inside film-coefficient based on outside diameter, can be found by multiplying h_i with d_i and dividing it by d_o, thus correcting it for area difference. This gives us a corrected value of 843.92 BTU per hour per square foot per degree Fahrenheit.

Total resistance (1 over U_c) offered by inside film and outside film is 1 over h_io plus 1 over h_o. Inverse of this resistance is called clean heat-transfer coefficient, Uc. Its value is found to be 498.46 BTU per hour per square foot per degree Fahrenheit.

Let’s add the fouling resistance or dirt factors. R_dio, inside fouling resistance based on outside diameter, can be found by multiplying R_di with d_o and dividing it by d_i, thus correcting it for area difference. This gives us a corrected value of 0.00112 hour-square foot degree Fahrenheit per BTU.

Total fouling resistance, Rd, offered by inside dirt and out dirt is 0.00213 hour-square foot degrees Fahrenheit per BTU.

Overall design coefficient, U_D, can be found by taking the reciprocal of overall design resistance. This overall design resistance (1 over U_D) is equal to sum of the film resistances and fouling resistance. U_D is found to be 242.1 BTU per hour per square foot per degree Fahrenheit.

Heat load, Q, is equal to U times A times delta T log mean. Plugging in the values of Q, U_D, and log mean temperature difference, or, LMTD, we get heat transfer surface to be 57.16 square feet. This surface is provided by a pipe with outer diameter, do, thus requiring a pipe length of A over pi d_o or 145.54 feet. In general we would not be able to get a pipe that long, however, we can get pipes in 20 feet length or so.