3. A sphere of radius 3 in is initially at a uniform temperature of 70 F. How long after being immersed in a liquid at 1000 F with an associated heat transfer coefficient h of 10 BTU/(h-ft-F) will the temperature at the center of the sphere reach 907 F if the sphere is made from (a) Copper, k=212 BTU/(h-ft-F), p = 555 lb/ft³, cp = 0.092 BTU/(lb-F) (b) Asbestos, k = 0.08 BTU/(h-ft-F), p = 36 lb/ft³, cp = 0.25 BTU/(lb-F) In each case determine if a lumped analysis applies or a distributed analysis applies. Note that the Biot number is defined as Bi = A Consequently, for a sphere, Bi = hR where k 3k R is the sphere radius. Also, there is no need to derive any results.
3. A sphere of radius 3 in is initially at a uniform temperature of 70 F. How long after being immersed in a liquid at 1000 F with an associated heat transfer coefficient h of 10 BTU/(h-ft-F) will the temperature at the center of the sphere reach 907 F if the sphere is made from (a) Copper, k=212 BTU/(h-ft-F), p = 555 lb/ft³, cp = 0.092 BTU/(lb-F) (b) Asbestos, k = 0.08 BTU/(h-ft-F), p = 36 lb/ft³, cp = 0.25 BTU/(lb-F) In each case determine if a lumped analysis applies or a distributed analysis applies. Note that the Biot number is defined as Bi = A Consequently, for a sphere, Bi = hR where k 3k R is the sphere radius. Also, there is no need to derive any results.
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 sphere of radius 3 in is initially at a uniform temperature of 70 F. How long after
being immersed in a liquid at 1000 F with an associated heat transfer coefficient h of
10 BTU/(h-ft-F) will the temperature at the center of the sphere reach 907 F if the sphere
is made from
(a) Copper, k = 212 BTU/(h-ft-F), p = 555 lb/ft³, Cp 0.092 BTU/(lb-F)
(b) Asbestos, k = 0.08 BTU/(h-ft-F), p= 36 lb/ft³, cp = 0.25 BTU/(lb-F)
In each case determine if a lumped analysis applies or a distributed analysis applies. Note
that the Biot number is defined as Bi = h'/. Consequently, for a sphere, Bi
hR
where
k
3k
R is the sphere radius. Also, there is no need to derive any results.
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