Thermodynamics- Heat Exchangers

Question 1

What do heat exchangers involve?

Answer 1

The transport of heat between two fluids separated by a solid.

Question 2

Describe how a parallel flow heat exchanger (HX) works

Answer 2

Hot fluid is sent along a pipe. Surrounding this pipe, cold fluid is sent along in the same direction. At the inlet of the hot fluid flow, the temperature difference is greatest between two fluids but this decreases quickly towards its outlet as the hot fluid cools and the cold fluid heat up. Both exponential curve.

Question 3

Describe how a counterflow heat exchanger (HX) works

Answer 3

Hot fluid is sent along a pipe. Surrounding this pipe, cold fluid is sent along in the opposite direction. At the inlet of the hot fluid flow, the temperature difference between two fluids is similar to that at its outlet as the hot fluid cools and the cold fluid heats up but in towards the inlet of the hot fluid. Both parallel exponential curves.

Question 4

Formula for heat transfer in a HX

Answer 4

q=hAΔT

Question 5

Describe cross-flow HX

Answer 5

Fluid flows perpendicularly over tubes. There can be fins to stop this outer fluid from mixing, or there can be no fins and the outer fluid can do mixed flow.

Question 6

Describe the shell and tube HX

Answer 6

The tube is around the shell. Fluid flows into the tube at one side and can flow through the shell to the other side where the tube outlet is. The shell has lots of pipes and an inlet and outlet. Baffles used to induce cross-flow and turbulent mixing of the fluid inside the shell. Diagram on page 7.

Question 7

What contributes to overall heat transfer coefficient in HXs?

Answer 7

Convection and conduction associated with the two fluids and the intermediate solid, potential use of fins on both sides, effects of time-dependent surface fouling.

Question 8

What can be said for the value of 1/UA for the hot and cold fluids?

Answer 8

They give the same answer

Question 9

Formula for 1/UA for clean surfaces

Answer 9

1/UA=1/(hA)c + Rw + 1/(hA)h
c and h subscript outside brackets mean hot and cold fluid
Rw is wall conduction resistance.

Question 10

How does formula for 1/UA change for fouling?

Answer 10

The denominators are multiplied by η0. A new term of Rf”/η0A is added for cold and hot fluid (2 new terms). Rw stays the same

Question 11

What does Rf” mean?

Answer 11

Fouling factor per unit surface area where f is subscript. In table 11.1 of textbook.

Question 12

What is η0?

Answer 12

Overall surface efficiency of fin array
Equal to 1-(Af/A)(1-ηf) for c or h
Subscript f means for single fin and A is total SA
See table 3.5 of textbook for ηf formulae

Question 13

Formula for heat transfer using U

Answer 13

q=UAΔTlm

ΔTlm is log mean temperature difference

Question 14

Formula for log mean temperature difference

Answer 14

ΔTlm=(ΔT1-ΔT2)/ln(ΔT1/ΔT2)

ΔT1 and ΔT2 depend on HX type

Question 15

What are ΔT1 and ΔT2 for counter-flow HX?

Answer 15

ΔT1 is Th at its inlet - Tc at its outlet

ΔT2 is Th at its outlet - Tc at its inlet

Question 16

What are ΔT1 and ΔT2 for parallel flow HX?

Answer 16

ΔT1 is Th at its inlet - Tc at its inlet

ΔT2 is Th at its outlet - Tc at its outlet

Question 17

What is the maximum heat transfer rate limited by?

Answer 17

The lower heat capacity rate (not specific) of the two fluids.

Question 18

Formula for overall energy balance of HX

Answer 18

q=mcp(Ti-To)=C(Ti-To)

This is the same when you do values for cold or hot fluid.

Question 19

What sort of procedure would be needed using the LMTD method for which both outlet temperatures must be determined from known inlet temperatures?

Answer 19

It is iterative

Question 20

Formula for HX effectiveness, ε

Answer 20

ε=q/qmax
Where ε is actually a C with a line out of the middle
qmax is maximum possible heat transfer
It’s between 0 and 1

Question 21

Formula for qmax

Answer 21

qmax=Cmin(Th,i-Tc,i)
Cmin is lower of the two heat capacity rates of the two fluids
h, i and c are subscript meaning hot, inlet and cold
The bit in brackets is (ΔT)max

Question 22

Formula for NTU

Answer 22

NTU=UA/Cmin

NTU is number of transfer units

Question 23

Alternative formula for heat transfer using effectiveness

Answer 23

q=εCmin(Th,i-Tc,i)

Question 24

How are ε and NTU related?

Answer 24

NTU is function of ε and Cmin/Cmax

ε is function of NTU and Cmin/Cmax

Question 25

How does ε vary with Cmin/Cmax (Cr)?

Answer 25

ε increases with decreasing Cr for all HX

Question 26

What relation can be used for Cr=0?

Answer 26

For all HX
ε=1-e^(-NTU)
NTU=-ln(1-ε)