6. Consider the steady-state operation of a counterflow heat exchanger. The en- ergy balance for an elemental control volume in the cold stream is shown below. Write a similar energy balance for an elemental control volume in the hot stream. Then for each stream, derive the differential equation for temperature as function of the exchanger length. [Ans.: dTJdx (UP/C,)(T, – T)]. (UP/C)(T, - T) and dT;ldx = %3D %3D - T. c,in i CT. C-(T. +- -dx) dx dT i I nin dx UPdx(T,- T) h
6. Consider the steady-state operation of a counterflow heat exchanger. The en- ergy balance for an elemental control volume in the cold stream is shown below. Write a similar energy balance for an elemental control volume in the hot stream. Then for each stream, derive the differential equation for temperature as function of the exchanger length. [Ans.: dTJdx (UP/C,)(T, – T)]. (UP/C)(T, - T) and dT;ldx = %3D %3D - T. c,in i CT. C-(T. +- -dx) dx dT i I nin dx UPdx(T,- T) h
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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THE PROBLEM IS FROM THE BOOK: ENGINEERING THERMOFLUIDS, M. MASSOUD.
![6. Consider the steady-state operation of a counterflow heat exchanger. The en-
ergy balance for an elemental control volume in the cold stream is shown below.
Write a similar energy balance for an elemental control volume in the hot stream.
Then for each stream, derive the differential equation for temperature as function
of the exchanger length. [Ans.: dTJdx
(UP/C)(T, — Т.)].
(UP/C)(T, - T) and dT,ldx
%3D
dT.
T
с, in
CT.
C-(T. +
dx)
dx
T
h,in
dx
UPdx(T, - T)
7. Solve the differential equations obtained in Problem Vla.6 using the following
boundary conditions, T,(x = 0) = Tho and T,(x = L) = Ti for the hot and T.(x = 0)
Tei and T.(x = L) = = Cmin, Th = {Tho
Teo for the cold stream. [Ans: if C.
C,Tci – C,(Th,o– Tei)exp[-(1/C. – 1/Ch)UPx]}/(1 – C,) similar relation for T].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8427a694-a84f-42d0-ba3b-da8cbefd1a1a%2F70713be3-6adf-4e89-b4b9-31a4fb4f2b70%2Fqjkcxlc_processed.png&w=3840&q=75)
Transcribed Image Text:6. Consider the steady-state operation of a counterflow heat exchanger. The en-
ergy balance for an elemental control volume in the cold stream is shown below.
Write a similar energy balance for an elemental control volume in the hot stream.
Then for each stream, derive the differential equation for temperature as function
of the exchanger length. [Ans.: dTJdx
(UP/C)(T, — Т.)].
(UP/C)(T, - T) and dT,ldx
%3D
dT.
T
с, in
CT.
C-(T. +
dx)
dx
T
h,in
dx
UPdx(T, - T)
7. Solve the differential equations obtained in Problem Vla.6 using the following
boundary conditions, T,(x = 0) = Tho and T,(x = L) = Ti for the hot and T.(x = 0)
Tei and T.(x = L) = = Cmin, Th = {Tho
Teo for the cold stream. [Ans: if C.
C,Tci – C,(Th,o– Tei)exp[-(1/C. – 1/Ch)UPx]}/(1 – C,) similar relation for T].
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