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Assignment 1 3221

(1) The document is a homework assignment for a convective heat and mass transfer class. It contains two problems: (2) The first problem asks students to rederive the energy equation taking into account kinetic energy changes, and show the result is identical. (3) The second problem involves analyzing heat transfer in a semi-infinite fin using scale analysis. Students are asked to: (a) show the longitudinal conduction term becomes negligible for large x, (b) determine the far-field fin temperature T∞ using a convection-generation balance, and (c) determine the length δ near the wall where conduction and generation balance.

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Prikshit Hooda
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94 views2 pages

Assignment 1 3221

(1) The document is a homework assignment for a convective heat and mass transfer class. It contains two problems: (2) The first problem asks students to rederive the energy equation taking into account kinetic energy changes, and show the result is identical. (3) The second problem involves analyzing heat transfer in a semi-infinite fin using scale analysis. Students are asked to: (a) show the longitudinal conduction term becomes negligible for large x, (b) determine the far-field fin temperature T∞ using a convection-generation balance, and (c) determine the length δ near the wall where conduction and generation balance.

Uploaded by

Prikshit Hooda
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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ME 642

Convective Heat and Mass Transfer


Home Assignment 1
9th January 2019
Marks: 20 Due Date: 15th January 2019

(1) During the derivation of the energy equation in class, we have assumed that changes
in kinetic energy V2/2 are negligible relative to changes in internal energy e, where e
should, in general, be replaced by e + V2/2 . Retrace the path leading to the energy
equation by taking into account changes in kinetic energy and show that the result of
this more rigorous analysis is identical.

[10]

(2) According to the one-dimensional (longitudinal) conduction model of a fin as shown


in the figure below, the temperature distribution along the fin, T(x), obeys the energy
equation:

Where, A, h, P, and q’’’’ are the fin cross-sectional area, fin-fluid heat transfer coefficient,
perimeter of the fin cross section (called the wetted perimeter), and volumetric rate of heat
generation. Consider the semi-infinite fin that, as shown below, is bathed by a fluid of
temperature T0 and is attached to a solid wall of temperature T0. The heat generated by the
fin is
absorbed by either the fluid or the solid wall.

Using scale analysis, answer the following questions.


(a) As a system for scale analysis, select the fin section of length x, where x is measured away
from the wall. Let T∞ be the fin temperature sufficiently far from the wall. Show that if x is
large enough, the longitudinal conduction term becomes negligible in the energy equation.
(b) Invoking the balance between lateral convection and internal heat generation, determine
the fin temperature, T∞ sufficiently far from the wall.
c) Determine the fin section of length δ near the wall where the heat transfer is ruled by the
balance between longitudinal conduction and internal heat generation.
[10]
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