4. A 100 mm diameter cylindrical rod has a uniform internal heat generation of q, = 7*107 W/m³. With steady-state conditions, the equation for the temperature distribution is T(r) = a + br², where T is in Celsius, r is in meters, a = 900°C, and b = -5.40*105 °C/m². The rod properties are k=25 W/(m K), density= 1100 kg/m³, and cp = 750 J/(kg K). (a) What is the heat transferred (in Watts) at r=0 (centerline) and r=r. (outer surface) if the rod is 3 m long? (b) The heat generation is increased to ġ2 =1*10° W/m³. At t=0, what is the time rate of %3D temperature change evaluated at r=0 and r=r,?
4. A 100 mm diameter cylindrical rod has a uniform internal heat generation of q, = 7*107 W/m³. With steady-state conditions, the equation for the temperature distribution is T(r) = a + br², where T is in Celsius, r is in meters, a = 900°C, and b = -5.40*105 °C/m². The rod properties are k=25 W/(m K), density= 1100 kg/m³, and cp = 750 J/(kg K). (a) What is the heat transferred (in Watts) at r=0 (centerline) and r=r. (outer surface) if the rod is 3 m long? (b) The heat generation is increased to ġ2 =1*10° W/m³. At t=0, what is the time rate of %3D temperature change evaluated at r=0 and r=r,?
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
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Transcribed Image Text:4. A 100 mm diameter cylindrical rod has a uniform internal heat generation of q, = 7*107 W/m³.
With steady-state conditions, the equation for the temperature distribution is T(r) = a + br²,
where T is in Celsius, r is in meters, a = 900°C, and b = -5.40*105 °C/m². The rod properties
are k=25 W/(m K), density= 1100 kg/m³, and cp = 750 J/(kg K).
(a) What is the heat transferred (in Watts) at r=0 (centerline) and r=r, (outer surface) if the rod
is 3 m long?
(b) The heat generation is increased to ġ2 =1*109 W/m³. At t=0, what is the time rate of
temperature change () evaluated at r=0 and r=r,?
Expert Solution
Step 1 Description
This question is the heat transfer in a cylinder
Heat generation q1 is given as
q1=7*107 W/m3
T=a+br2
a=900
b=-5.40*10-5
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