A hot fluid, at 350 degrees Fahrenheit, is used to heat
water, which is entering the system at 70 degrees Fahrenheit. What is the reasonable water outlet
temperature and heat recovery for the following cases?
(1)
Counter-current flow, (2) co-current (parallel) flow, and
(3) 1-2 multi-pass (1 shell, 2 tube passes).
Hot fluid is flowing at 10,000 pounds per hour, whereas
water flow rate is 20,000 pounds per hour.
Specific heat of both fluids is equal to 1.0 BTU per pound per degree
Fahrenheit.
Solution:
Let’s use lower case t for temperature of the cold fluid,
upper case T for temperature of the hot fluid.
Subscripts 1 and 2 identify incoming and outgoing conditions. With these conventions, upper case T1
is 350 degrees Fahrenheit, and lower case t1 is 70. Heat given by hot fluid should be equal to
heat received by cold fluid. Please
note that R is a ratio of (upper case T1 minus upper case T2)
and (lower case t2 minus lower case t1). R is also equal to the ratio of (lower case
w time lower case c) and (upper case W time upper case C). For our situation, this value is calculated
as 2.
Case (1) Counter-current:
A 10-degree approach in the terminal temperatures is considered as
normal industrial practice in the design of heat exchangers. With this guidance, T2 minus t1
is equal to 10 degrees Fahrenheit. We
can find t2 is calculated as 205 degrees Fahrenheit.
Heat received by cold water is w time c time (t2
minus t1) equals 2.7 million BTUs per hour. Please note that if we use Figure 7-14, we
can find the value of P to be 0.5. So,
t2 is determined to be 210 degrees Fahrenheit, whereas T2
is 70 degrees Fahrenheit (same as t1). No driving force at the exit?
That’s why we have chosen to have at least 10 degrees approach at the
cold side.
Case (2) Co-current:
A 5-degree approach in the terminal temperatures is the maximum for
co-current arrangement. T2
minus t2 is equal to 5 degrees Fahrenheit. Utilizing the basic definition of R, one can find that t2
161.67 degrees Fahrenheit.
Heat received by cold water is w time c time (t2
minus t1) equals 1.83 million BTUs per hour.
Case (3) – 1-2 Multiple Pass. We should use Figure 7-15 (Temperature efficiency for heat
exchangers with one shell pass and even number of tube passes) to get the maximum
efficiency information for this case.
For R equals 2, the value of efficiency, P, is read as 0.375. P is defined in the Figure 7-15 as the ratio
of (t2 minus t1) and (T1 minus t1). Water outlet temperature, t2,
can be calculated to be 175 degrees Fahrenheit. Heat recovery can thus be found as 2.1 million BTUs per hour.