Calculate the heat transfer coefficient for a shell-and-tube
heat exchanger that has one shell pass and one tube pass. Heat exchanger is fitted with 413 tubes in a
shell of 2.082 feet diameter. The
16-feet long tubes are arranged in a square pitch (0.0833 foot). A number of baffles are installed with a
baffle spacing of 0.7917 foot.
The fluid entering the tube is flowing at 500,000 pounds per
hour and has the following bulk properties: specific heat 0.5 BTUs per pound
per degree Fahrenheit, viscosity 1.21 pounds per foot per hour, thermal
conductivity 0.075 BTU per hour per foot per degree Fahrenheit.
The fluid entering the shell is flowing at 200,000 pounds
per hour and has the following bulk properties: specific heat 1.0 BTUs per pound
per degree Fahrenheit, viscosity 2 pounds per foot per hour, thermal
conductivity 0.36 BTU per hour per foot per degree Fahrenheit.
Tube inside diameter is 0.0516 foot, whereas outside
diameter is 0.0625 foot.
Solution:
Tube-side Calculations:
Mass velocity, G, is calculated by dividing mass flow rate by total
cross-sectional area of the tubes.
Please note that there are 413 tubes.
G is found to be 5.774 times 105 pounds per hour per square
feet.
Reynolds number, Re, becomes d G over mu. G is the same as V rho. As, V is equal to volumetric flow rate (Q)
divided by area (A), and Q is mass flow rate (w) over density (rho). Plugging in the values of d, G, and mu (viscosity),
Reynolds number is found to be 2.466 times 104.
Prandtl number, given by terms c times mu over k is 8,067.
Now we can calculate Nusselt number, Nu, by using the
correlation for heat transfer through shell and tube heat exchangers, 0.023 Re0.8
times Pr0.33. Replacing
Nusselt number with h time di over k. Heat transfer coefficient is found to be 218.3 BTU per hour per
square foot per degree Fahrenheit.
Now, let’s move on to calculate heat transfer coefficient
for the Shell side. There are two
variables, diameter (d), and area (a) that need to be calculated for Shell side. Shell-side area is a function of internal
shell diameter (ID), clearance, C, a difference between tube pitch, Pt,
outside diameter (do) of the inner tubes, and baffle spacing,
B. The formula or the calculation of
area is given as ID times C times B over Pt. Plugging in the values of these terms,
shell area is found to be 0.412 square foot.
Mass velocity, W over a, is found to be 4.851 time 105 pound
per hour per square foot.
Now the equivalent diameter for shell depends upon the tubes
arrangement. For a square pitch
arrangement, hydraulic radius, rH, is given by the term: (Pt2
– pi d02/4) over (pi do). The numerator represents the flow area,
whereas the denominator represents the heat transfer perimeter. The equivalent radius is 4 times the hydraulic
radius, thus giving us de of 0.079 foot.
Now Reynolds number is calculated to be 1.915 times 104,
and Prandtl number as 5.556.
Nusselt number for Shell-side fluid is 0.36 Re0.55times
Pr0.333. This gives a value
of ho as 658.2 BTU per hour per square foot per degree Fahrenheit.