2 A wire of diameter D = 2 mm and uniform temperature T has an electrical resistance of 0.01 2/m and a current flow of 20 A. (a) What is the rate at which heat is dissipated per unit length of wire? What is the heat dissipation per unit volume within the wire? (b) If the wire is not insulated and is in ambient air and large surroundings for which T = Tsur = 20°C, what is the temperature T of the wire? The wire has an emissivity of 0.3, and the coefficient associated with heat transfer by natural convection may be approximated by an expression of the form, h = C[(TT)/D]4, where C = 1.25 W/m7/4. K5/4 If the wire is coated with plastic insulation of 2-mm thickness and a thermal conductivity of 0.25 W/m K, what are the inner and outer surface temperatures of the insulation? The insulation has an emissivity of 0.9, and the convection coefficient is given by the expression of part (b). Explore the effect of the insu- lation thickness on the surface temperatures.

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
2
A wire of diameter D = 2 mm and uniform temperature
T has an electrical resistance of 0.01 N/m and a current
flow of 20 A.
(a) What is the rate at which heat is dissipated per unit
length of wire? What is the heat dissipation per
unit volume within the wire?
(b) If the wire is not insulated and is in ambient air
and large surroundings for which T = Tsur = 20°C,
what is the temperature T of the wire? The
wire has an emissivity of 0.3, and the coefficient
associated with heat transfer by natural convection
may be approximated by an expression of the
form, h = C[(T-T)/D]¹/4, where C = 1.25
W/m7/4.K5/4
(c)
If the wire is coated with plastic insulation of 2-mm
thickness and a thermal conductivity of 0.25 W/m.K,
what are the inner and outer surface temperatures of
the insulation? The insulation has an emissivity of
0.9, and the convection coefficient is given by the
expression of part (b). Explore the effect of the insu-
lation thickness on the surface temperatures.
Note:
1. The metal wire itself is assumed to be at a single
temperature.
2. This is in a cylindrical coordinate.
Transcribed Image Text:2 A wire of diameter D = 2 mm and uniform temperature T has an electrical resistance of 0.01 N/m and a current flow of 20 A. (a) What is the rate at which heat is dissipated per unit length of wire? What is the heat dissipation per unit volume within the wire? (b) If the wire is not insulated and is in ambient air and large surroundings for which T = Tsur = 20°C, what is the temperature T of the wire? The wire has an emissivity of 0.3, and the coefficient associated with heat transfer by natural convection may be approximated by an expression of the form, h = C[(T-T)/D]¹/4, where C = 1.25 W/m7/4.K5/4 (c) If the wire is coated with plastic insulation of 2-mm thickness and a thermal conductivity of 0.25 W/m.K, what are the inner and outer surface temperatures of the insulation? The insulation has an emissivity of 0.9, and the convection coefficient is given by the expression of part (b). Explore the effect of the insu- lation thickness on the surface temperatures. Note: 1. The metal wire itself is assumed to be at a single temperature. 2. This is in a cylindrical coordinate.
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