Question

You have a hot gas that enters a pipe at 140c and ethylene entering the same pipe at 30 C to make an ethylene mixture.

I need to figure out equations for U (overall heat transfer coefficient) as a function of mass flowrate M and the exit temp of the ethylene as a function of mass flowrate.

How do you go about designing these equations?

Answer 1

Hot gas enters the pipe at T = 140°C

Ethylene enters at T = 30°C

First we need to find the mixing temperature

Assumption : no heat loss

m_{​​​​​​h}​​​​​C_​ph(T-130)= m_​​​c C_​​pc (30-T)

For hot fluid

Take physical properties from handbook at average temperature of (T+130)/2

Find Nre

A = π(d^{​​​​​​2})/4

Find Npr

Based on Nre we have different equations

If flow is turbulent

K- thermal conductivity

d- diameter of pipe

If flow is laminar then

Using any of these bases on Nre we can get

hot liquid heat transfer coefficient

2)

Similarly for cold liquid we can find physical properties at average temperature and by following same procedure we can find

h_{​​​​​​c}

Formula for overall heat transfer coefficient

When we substitute all values in h according to Nre we get

U as a function of mass flowrate and T

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