Heat Exchanger Modeling, Sizing, and Design

1 Lectures 19 Applied heat Transfer CM3110 12/3/2019. CM3110. Transport I. Part II: heat Transfer Applied heat Transfer: heat Exchanger Modeling, Sizing, and Design Professor Faith Morrison Department of Chemical Engineering Michigan Technological University 1. Faith A. Morrison, Michigan Tech U. Applied heat Transfer Before turning to radiation (last topic) we will discuss a few practical applications How can we use Fundamental heat Transfer to understand real devices like heat exchangers? heat transfer hot fluid process stream process stream heat Exchanger cold less cold heat transfer fluid less hot 2. Faith A. Morrison, Michigan Tech U. 1. Lectures 19 Applied heat Transfer CM3110 12/3/2019.

2 Applied heat Transfer The Simplest heat Exchanger : Double Pipe heat Exchanger counter current T1 less hot T1 T2. cold less cold The heat transfer from the T2 . outside to the inside is just hot heat flux in an annular shell 3. Faith A. Morrison, Michigan Tech U. Applied heat Transfer Example 4: heat flux in a cylindrical shell Maybe we can use heat transfer Assumptions: coefficient to understand forced- long pipe convection heat exchangers.. steady state BUT .. k = thermal conductivity of wall h1, h2 = heat transfer coefficients at and . Cooler fluid at Tb2. R1. r . R2. Hot fluid at Tb1. 4. Faith A. Morrison, Michigan Tech U. 2. Lectures 19 Applied heat Transfer CM3110 12/3/2019.

3 Applied heat Transfer BUT: The temperature difference between the fluid and the wall varies along the length of the heat Exchanger . The Simplest heat Exchanger : Double Pipe heat Exchanger counter current T1 less hot T , outer bulk temperature T , inner bulk temperature T1 T2. cold less cold x Newton's law of L. T2 cooling hot assumes a How can we develop a model so that constant h. we can use the concept of to characterize heat exchangers? 5. Faith A. Morrison, Michigan Tech U. Applied heat Transfer Let's look at the solution for radial conduction in an annulus Example 4: heat flux in a solid cylindrical shell Solution: qr c1 Flux is not constant A r c T 1 ln r c2. k Boundary conditions?

4 6. Faith A. Morrison, Michigan Tech U. 3. Lectures 19 Applied heat Transfer CM3110 12/3/2019. Applied heat Transfer Example 4: heat flux in a cylindrical shell, Newton's law of cooling boundary Conditions Results: Radial heat Flux in a Solid Cylindrical Shell 1 1. ln .. 1 1 1. ln . 1. 1 1 1 . ln . 7. Faith A. Morrison, Michigan Tech U. Applied heat Transfer Cooler fluid at Tb2. R1. r Example 4: heat flux in a solid cylindrical shell . R2. Solution for Hot fluid at Tb1. heat Flux: 1. 1 1 1 . ln . Calculate Total heat flow through any chosen : (including and ). 2 . 2 . 1 1 1. ln . Note that total heat flow is proportional to bulk and (almost) area of heat transfer 8. Faith A.

5 Morrison, Michigan Tech U. 4. Lectures 19 Applied heat Transfer CM3110 12/3/2019. Applied heat Transfer Cooler fluid at Tb2. R1. r . R2. Total heat flow through any chosen : Hot fluid at Tb1. (including and ).. 2 . 2 . 1 1 1. ln . Note that total heat flow is proportional to bulk and (almost). area of heat transfer 9. Faith A. Morrison, Michigan Tech U. Applied heat Transfer Define Overall heat -Transfer Coefficient, U. T = driving temperature difference Do we use inner or outer area? 10. Faith A. Morrison, Michigan Tech U. 5. Lectures 19 Applied heat Transfer CM3110 12/3/2019. Applied heat Transfer Overall heat transfer coefficients in pipe Area must be specified when Q U1 A1 T is reported 1.

6 2 . 1 1 1. ln . Q U 2 A2 T. 1.. 2 . 1 1 1. ln . 11. Faith A. Morrison, Michigan Tech U. Applied heat Transfer heat flux in a cylindrical shell: . But, in an actual heat Exchanger , and vary along the length of the heat Exchanger heat transfer hot fluid process stream process stream heat Exchanger cold less cold heat transfer fluid What kind of average less hot do we use? 12. Faith A. Morrison, Michigan Tech U. 6. Lectures 19 Applied heat Transfer CM3110 12/3/2019. Applied heat Transfer The Simplest heat Exchanger : Double Pipe heat Exchanger counter current T1 less hot T , outer bulk temperature T , inner bulk temperature T1 T2. cold less cold x L. T2 . hot We will do an open system energy balance on a differential section to determine the correct average temperature difference to use.

7 13. Faith A. Morrison, Michigan Tech U. Applied heat Transfer T1 less hot The Simplest heat Exchanger : T1 T2. Double Pipe heat Exchanger counter current cold less cold Another way of looking at it: T2 . hot . Inside System .. Outside System .. 14. Faith A. Morrison, Michigan Tech U. 7. Lectures 19 Applied heat Transfer CM3110 12/3/2019. The Simplest heat Exchanger : T1 less hot Double Pipe heat Exchanger counter current T1 T2. Another way of looking at it: cold less cold T2 . Can do three balances: hot . 1. Balance on Inside the inside System system .. Outside System .. 15. Faith A. Morrison, Michigan Tech U. The Simplest heat Exchanger : T1 less hot Double Pipe heat Exchanger counter current T1 T2.

8 Another way of looking at it: cold less cold T2 . Can do three balances: hot . 1. Balance on Inside the inside System system . 2. Balance on the outside . system . Outside System .. 16. Faith A. Morrison, Michigan Tech U. 8. Lectures 19 Applied heat Transfer CM3110 12/3/2019. The Simplest heat Exchanger : T1 less hot Double Pipe heat Exchanger counter current T1 T2. Another way of looking at it: cold less cold T2 . Can do three balances: hot . 1. Balance on Inside the inside System system . 2. Balance on the outside . system 3. Overall . Outside balance System .. 17. Faith A. Morrison, Michigan Tech U. The Simplest heat Exchanger : T1 less hot Double Pipe heat Exchanger counter current T1 T2.

9 Another way of looking at it: cold less cold T2 . hot . Inside System . We can do: a macroscopic balances over the entire heat Exchanger , or Outside a pseudo microscopic System balance over a slice of the heat Exchanger . 18. Faith A. Morrison, Michigan Tech U. 9. Lectures 19 Applied heat Transfer CM3110 12/3/2019. The Simplest heat Exchanger : T1 less hot Double Pipe heat Exchanger counter current T1 T2. Another way of looking at it: cold less cold T2 . hot . Inside System . We can do: a macroscopic balances over the entire heat Exchanger , or Outside a pseudo microscopic System balance over a slice of the heat Exchanger All the details of the algebra are here: . ~fmorriso/cm310 19.

10 Faith A. Morrison, Michigan Tech U. Applied heat Transfer Pseudo Microscopic Energy Balance on a slice of the heat Exchanger Open system energy balance on a differential volume: , . , INSIDE. BALANCE. recall: is out-in 20. Faith A. Morrison, Michigan Tech U. 10. Lectures 19 Applied heat Transfer CM3110 12/3/2019. Applied heat Transfer Pseudo Microscopic Energy Balance on a slice of the heat Exchanger . INSIDE. BALANCE. , recall: is out-in 21. Faith A. Morrison, Michigan Tech U. Applied heat Transfer Pseudo Microscopic Energy Balance on a slice of the heat Exchanger Adiabatic heat OVERALL. Exchanger > Qin= 0 BALANCE. , 0. 22. Faith A. Morrison, Michigan Tech U. 11. Lectures 19 Applied heat Transfer CM3110 12/3/2019.