A copper sphere initially at a uniform temperature To is immersed in a fluid. Electric heaters are placed in the fluid and controlled so that the temperature of the fluid follows a periodic variation given by Too - Tm = A sin wt where Tm = time-average mean fluid temperature A = amplitude of temperature wave @= = frequency Derive an expression for the temperature of the sphere as a function of time and the heat-transfer coefficient from the fluid to the sphere. Assume that the tempres of the sphere and fluid are uniform at any instant so that the lumped-capacity method of analysis may be used.
A copper sphere initially at a uniform temperature To is immersed in a fluid. Electric heaters are placed in the fluid and controlled so that the temperature of the fluid follows a periodic variation given by Too - Tm = A sin wt where Tm = time-average mean fluid temperature A = amplitude of temperature wave @= = frequency Derive an expression for the temperature of the sphere as a function of time and the heat-transfer coefficient from the fluid to the sphere. Assume that the tempres of the sphere and fluid are uniform at any instant so that the lumped-capacity method of analysis may be used.
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:A copper sphere initially at a uniform temperature To is immersed in a fluid. Electric
heaters are placed in the fluid and controlled so that the temperature of the fluid
follows a periodic variation given by
Too - Tm A sin wt
where
Tm = time-average mean fluid temperature
A = amplitude of temperature wave
@= frequency
Derive an expression for the temperature of the sphere as a function of time and the
heat-transfer coefficient from the fluid to the sphere. Assume that the temperares
of the sphere and fluid are uniform at any instant so that the lumped-capacity method
of analysis may be used.
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