3. A long hollow cylinder has inner and outer radii R, and R2, respectively. The temperature of the inner surface at radius R, is held at a constant value, T1, while that of the outer surface at radius R₂ is held constant at a value of T2. Heat is generated in the wall of the cylinder at a rate per unit volume given by q = I'r; where r is radial position and I' is a constant. Assuming constant thermal conductivity and heat flow only in the radial direction, derive expressions for: (a) The steady-state temperature profile, T(r), in the cylinder wall. (b) The heat flux at the outer surface of the cylinder.
3. A long hollow cylinder has inner and outer radii R, and R2, respectively. The temperature of the inner surface at radius R, is held at a constant value, T1, while that of the outer surface at radius R₂ is held constant at a value of T2. Heat is generated in the wall of the cylinder at a rate per unit volume given by q = I'r; where r is radial position and I' is a constant. Assuming constant thermal conductivity and heat flow only in the radial direction, derive expressions for: (a) The steady-state temperature profile, T(r), in the cylinder wall. (b) The heat flux at the outer surface of the cylinder.
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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Transcribed Image Text:3. A long hollow cylinder has inner and outer radii R, and R2, respectively. The temperature of
the inner surface at radius R, is held at a constant value, T₁, while that of the outer surface at
radius R₂ is held constant at a value of T₂. Heat is generated in the wall of the cylinder at a rate
per unit volume given by q = ['r; where r is radial position and I' is a constant. Assuming
constant thermal conductivity and heat flow only in the radial direction, derive expressions for:
(a) The steady-state temperature profile, T(r), in the cylinder wall.
(b) The heat flux at the outer surface of the cylinder.
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