Homework Help is Here – Start Your Trial Now!
Engineering
Chemical Engineering
67 Verify the temperature distribution for case 2 in Section 2-9, i.e., that T – T. То — Т cosh m(L-x) + (h/mk) sinh m(L – x) cosh mL+ (h/mk) sinh m L Subsequently show that the heat transfer is sinh mL+ (h/mk) cosh mL cosh m L+ (h/mk) sinh mL q=/h PkA (To – T∞) that of the surrounding fluid. CASE 2 The fin is of finite length and loses heat by convection from its end.

67 Verify the temperature distribution for case 2 in Section 2-9, i.e., that T – T. То — Т cosh m(L-x) + (h/mk) sinh m(L – x) cosh mL+ (h/mk) sinh m L Subsequently show that the heat transfer is sinh mL+ (h/mk) cosh mL cosh m L+ (h/mk) sinh mL q=/h PkA (To – T∞) that of the surrounding fluid. CASE 2 The fin is of finite length and loses heat by convection from its end.

Introduction to Chemical Engineering Thermodynamics
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
See similar textbooks
icon
Related questions
Question
100%
-67 Verify the temperature distribution for case 2 in Section 2-9, i.e., that T – T cosh m(L – x) +(h/mk) sinh m(L – x) То — То cosh mL+ (h/mk) sinh m L Subsequently show that the heat transfer is sinh mL+ (h/mk) cosh m L cosh mL+ (h/mk) sinh mL q=/h PkA (To – T∞) that of the surrounding fluid. CASE 2 The fin is of finite length and loses heat by convection from its end. If we let m-h P/kA, the general solution for Equation (2-306) may be written 6=Cje +C 12-31] For case I the boundary conditions are e = at x=0 at x00 CHAPTER 2 Steady-Sute Conduction One Dimension and the solution becomes e T-Tx 12-32] To -T For case 3 the boundary conditions are e = at x0 de -0 at x=L dx Thus C +C2 0mm(-Cjemt +Czey Solving for the constants C, and C2, we obtain + 12-33a] cosh [m(L-x)1 12-336| cosh ml. The hyperbolic functions are defined as e +e 2 sinh x cosh x sinh x - - cosh x tanh x= e te The solution for case 2 is more involved alecbraically and the result is T-T _cosh m (L -x) + (h/mk) sinh m (L -x) L 12-34 cosh mL. + (h/mk) sinh m All of the heat lost by the fin must be conducted into the base at x=0. Using the equations for the temperature distribution, we can compute the heat loss from =-kA An altemative method of integrating the convection heat loss could be used: hPT - Tx) dx= [*. In most cases, however, the first equation is easier to apply. For case 1, q=-kA (-mee(0)= APRAG 12-35] For case 3, 12-36| - VA PRAA tanh ml. 2-10 Fins The heat flow for case 2 is sinh mL+ (h/mk) cosh m L qVhPRA (To-T) cosh mL+ (h/mk) sinh mL 12-37]
Transcribed Image Text:-67 Verify the temperature distribution for case 2 in Section 2-9, i.e., that T – T cosh m(L – x) +(h/mk) sinh m(L – x) То — То cosh mL+ (h/mk) sinh m L Subsequently show that the heat transfer is sinh mL+ (h/mk) cosh m L cosh mL+ (h/mk) sinh mL q=/h PkA (To – T∞) that of the surrounding fluid. CASE 2 The fin is of finite length and loses heat by convection from its end. If we let m-h P/kA, the general solution for Equation (2-306) may be written 6=Cje +C 12-31] For case I the boundary conditions are e = at x=0 at x00 CHAPTER 2 Steady-Sute Conduction One Dimension and the solution becomes e T-Tx 12-32] To -T For case 3 the boundary conditions are e = at x0 de -0 at x=L dx Thus C +C2 0mm(-Cjemt +Czey Solving for the constants C, and C2, we obtain + 12-33a] cosh [m(L-x)1 12-336| cosh ml. The hyperbolic functions are defined as e +e 2 sinh x cosh x sinh x - - cosh x tanh x= e te The solution for case 2 is more involved alecbraically and the result is T-T _cosh m (L -x) + (h/mk) sinh m (L -x) L 12-34 cosh mL. + (h/mk) sinh m All of the heat lost by the fin must be conducted into the base at x=0. Using the equations for the temperature distribution, we can compute the heat loss from =-kA An altemative method of integrating the convection heat loss could be used: hPT - Tx) dx= [*. In most cases, however, the first equation is easier to apply. For case 1, q=-kA (-mee(0)= APRAG 12-35] For case 3, 12-36| - VA PRAA tanh ml. 2-10 Fins The heat flow for case 2 is sinh mL+ (h/mk) cosh m L qVhPRA (To-T) cosh mL+ (h/mk) sinh mL 12-37]
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Volumetric properties of pure fluids
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami…
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Process Dynamics and Control, 4e
Process Dynamics and Control, 4e
Chemical Engineering
ISBN:
9781119285915
Author:
Seborg
Publisher:
WILEY
Industrial Plastics: Theory and Applications
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
Unit Operations of Chemical Engineering
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The
SEE MORE TEXTBOOKS