(n) Write the simplified form of the equation that describes the system. (b) Write the boundary conditions required to solve the problem. (c) Solve the energy equation for the radial temperature profile T(r). The solution must be in terms of r, ro, k, To, and ġ̟.
(n) Write the simplified form of the equation that describes the system. (b) Write the boundary conditions required to solve the problem. (c) Solve the energy equation for the radial temperature profile T(r). The solution must be in terms of r, ro, k, To, and ġ̟.
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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Question
Transcribed Image Text:4)
Heat is generated internally in a long solid cylindrical rod according to the following
equation:
4 = 4.
where à is the local rate of heat generation per unit volume and ġ̟ is a constant. The rod
has a radius ro, thermal conductivity k, and surface temperature To. Assume steady-state.
(a) Write the simplified form of the equation that describes the system.
(b) Write the boundary conditions required to solve the problem.
(c) Solve the energy equation for the radial temperature profile T(r). The solution must be in
terms of r, r, k, To, and ġ̟.
For the following parts of the problem, assume ġ, = 1.8x107 W/m³. The rod has a diameter
of 2.0 cm, thermal conductivity of k = 40 w/m•K and surface temperature of T. = 700 K.
(d) Calculate the maximum temperature in the rod.
(e) Calculate the rate of heat transfer per unit length from the rod surface.
(f) If a coolant at T =25°C flows past the outside surfacc of the rod, calculate the value of
the required convection heat transfer coefficient.
Basic the energy equation:
DT
V. kVT + ġ +0 = pcv
Dt
in solids mostly cv = cp,
1 ƏT
+
r dr
in cylindrical coordinates 27
dr
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