Exercise: Calculating F for a 2-4 heat exchanger

F for a 2-4 Heat Exchanger

Exercise Problem:

You are asked to size a heat exchanger to heat 8 kg/s of milk for pasturization from 20 degrees C to 72 degrees C using hot water. The hot water at the inlet is 90 degrees C, and is flowing at a rate of 10 kg/s.

Answer:

Part 1: Find water outlet temperature

Step 1: Set the energies of the two substances equal to each other

Using the following equation, set it so the energy lost by the water is the energy gained by the milk. Cp used for water and milk are found from the site Engineering Toolbox.

$Q = \dot{m} (C p) (Δ T)$

So, with 1 being water and 2 being milk,

$- \dot{m_{1}} (C p_{1}) (Δ T_{1}) = \dot{m_{2}} (C p_{2}) (Δ T_{2})$

$- 10 k g / s * (4.18 k J / k g * C) * (90 - T 2) = 8 k g / s * (4 k J / k g * C) * (20 - 72)$

So T2 ≈ 50 degrees C

Part 2: Find F

Step 1: Find S and R values

F graphs typically use R and S. For the graph I am using, Figure 11-4 from Perry's Chemical Engineers Handbook, they are defined as the following

$S = \frac{(t 2 - t 1)}{(T 1 - t 1)}$

$R = \frac{(T 1 - T 2)}{(t 2 - t 1)}$

In this case, T1 and T2 correspond to the shell while t1 and t2 correspond to the tubes.

For this example I used the milk as the tube side and the water as the shell side.

$S = \frac{(50 - 90)}{(20 - 90)}$

$R = \frac{(20 - 72)}{(50 - 90)}$

As such, R=1.3, and S=0.57

Step 2: Look up F on a log mean temperature difference (LMTD) chart

Using the following example style graph, find where S (The x-axis) and R (The lines on the graph) intersect and then find F on the y-axis. This doesn't have actual values, this is just an example for how to read this type of graph.

Figure 11-4, Graph b, from Perry's Engineers Handbook is the graph I used to find an actual value.

From Perrys, F=0.83