analyzed fully developed laminar flow through a heated tube
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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Please try your best to show all steps
![analyzed fully developed laminar flow through a heated tube and
considered the case of a constant wall heat flux, qo. Do the following: Show that
the limiting Nusselt number (fully developed heat transfer) is 4.364.
a. Find T(r) by integrating the energy balance
d dT
2(v₂)
dTm
1 (d) = ²) [₁- ()],
r dr
α
dz
(Remember that the temperature profile is linear so dTm/dz is a constant.)
b. Now derive an expression for Tm according to the definition
(v₂T)
(v₂)
Tm =
c. Substitute the expression forTm into the "Newton's Law" expression
qoh (Tom)
find that
and simplify.
d. Finally, knowing from the energy balance that
p(v₂)CpR dTm
2
dz
% =
Nu =
hD
k
= 4.364](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F403d5df5-c9a3-47af-a06d-d9770154fd48%2F11b285e3-b5db-42cf-a36f-b02e70a509de%2Fa1xztmh_processed.png&w=3840&q=75)
Transcribed Image Text:analyzed fully developed laminar flow through a heated tube and
considered the case of a constant wall heat flux, qo. Do the following: Show that
the limiting Nusselt number (fully developed heat transfer) is 4.364.
a. Find T(r) by integrating the energy balance
d dT
2(v₂)
dTm
1 (d) = ²) [₁- ()],
r dr
α
dz
(Remember that the temperature profile is linear so dTm/dz is a constant.)
b. Now derive an expression for Tm according to the definition
(v₂T)
(v₂)
Tm =
c. Substitute the expression forTm into the "Newton's Law" expression
qoh (Tom)
find that
and simplify.
d. Finally, knowing from the energy balance that
p(v₂)CpR dTm
2
dz
% =
Nu =
hD
k
= 4.364
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