- #1

TFM

- 1,026

- 0

## Homework Statement

A heat exchanger consists of two straight co-axial tubes, each of square cross-section. Liquid 1 enters at a rate m1 kg.s-1 at one end (x = 0) of the exchanger at temperature T10, and flows through the inner tube. Liquid 2 emerges at a rate m2 kg.s-1 at x = 0 at temperature T20, having flowed through the space between the two tubes. The outer tube is heavily lagged. The tube separating the two liquid streams has wall thickness, s, square cross-section of side, a, and its material has thermal conductivity, . By considering an element of length x to x = x of the exchanger operating in the steady state, calculate the heat which must flow transversely through the metal between the liquids. Hence show that the temperature difference, T(x) = T1(x) - T2(x), between the two liquid streams at distance x along the exchanger is

T(x) = (T10 - T20).exp(-x)

where = (4a/s)[(m1C1)-1 – (m2C2)-1] and C1 and C2 are the specific heats of the two liquids.

You may make the two simplifying assumptions: (i) that due to efficient turbulent mixing, there are no transverse temperature gradients within the two liquids and (ii) that longitudinal heat conduction within the liquid and the solid along the direction of flow may be neglected, due to the smallness of the temperature gradients in the x direction.

## Homework Equations

N/A

## The Attempt at a Solution

I am trying to do this problem, but I am having trouble visualising what is happening. I have attached the diagram given.

I have included what I think is happening, the T10 fluid is lowing through the inner tube, and T20 out the outer tube. The insulation is around the outside. Does this look right?

TFM