Heat Exchangers basic Equation

[Ángel Martin]

Heat Exchangers basic Equation. [ HEATX ]
From the Author’s Engineering Collection, included in the PSYCHRO module.

This program calculates the transferred heat and exit temperatures of the fluids in a heat exchanger when all the other parameters are known, including the total area of exchange “A”, and the global heat conduction coefficient “U”. Both cases concurrent (parallel) and counter flow configurations are possible – the initial prompt will select the chosen configuration:

The input data parameters include the following:
- Mass flows for each fluid, m1’ and m2’
- Specific heat capacity for both fluids, Cp1 and Cp2
- Input temperature for cold fluid -T1(I)
- Either input or output temperature for hot fluid; T2(I) or T2(O)

Note: If only the product {A.U} is known you can enter U=1 and the value of U.A. at the "A=?" prompt. Each time a new set of results will be obtained.

Let k1 = m'1.Cp1; and k12 = m’1.Cp1/ m’2.Cp2.
The equations used for the Temperatures at a distance “x” from the inlet and the Total transferred heat Q(A) are as follows:

1. Parallel (concurrent) flow
T1(x) = [1/(1+ k12)] {T2(I) + k12.T1(I) + [T1(I)-T2(I)].exp[ - U.A(x).(1+k12) / k1]} .
T2(x) = T2(I) – k12[T1(x) - T1(I)]
Q(A) = k1 [T1(I)-T2(I)] / (1+ k12).{exp[ –U.A(L).(1+k12) / k1] – 1 }

2. Counter Flow
T1(x) = [1/(1– k12)] {T2(O) + k12.T1(I) + [T1(I)-T2(O)].exp[ –U.A(x).(1– k12) / k1]
T2(x) = T2(O) – k12[T1(x) - T1(I)]
Q(A) = k1 [T1(I)-T2(O)] / (1– k12).{exp [–U.A(L).(1–k12) / k1] – 1 }

Example.

Calculate the output temperature of the oil and the total transferred heat in a parallel flow water-oil heat exchanger with AU= 115.8185 kcal/h.deg C, when the mass flows are m’(water) = 5 kg/min and m‘(oil) = 8 kg/min. if the inlet temperatures are Twater(I) = 20 deg C and Toil(I) = 90 deg C. Use the following for the specific heat capacities: Cp(water) = 1 kcal/kg.C; Cp(oil) = 0.9671 kcal/kg.C.

The results are: Q(A)= 5.999,998790 kcal/min
T1(O) = 39,999996 deg C ; and T2(O) = 77.0744 deg C