Page 25 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

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INTRODUCTION
Exercise 1.9.11 A long, thin copper wire of radius r and length L has an electrical resis-
tance of ρ per unit length. The wire is initially kept at a room temperature of T a and subjected
to an electric current flow of I. The heat generation due to the current flow is simultaneously
lost to the ambient by convection. Set up an equation to determine the temperature of the
wire as a function of time. Mention the assumptions made in the derivation of the equation.
Exercise 1.9.12 In a continuous casting machine, the billet moves at a rate of u m/s. The hot
billet is exposed to an ambient temperature of T a . Set up an equation to find the temperature
of the billet as a function of time in terms of the pertinent parameters. Assume that radiation
also plays a role in the dissipation of heat to ambient.

Exercise 1.9.13 In a double-pipe heat exchanger, hot fluid (mass flow M kg/s and specific
◦
heat c kJ/kg C) flows inside a pipe and cold fluid (mass flow m kg/s and specific heat c
kJ/kg C) flows outside in the annular space. The hot fluid enters the heat exchanger at
◦
T h1 and leaves at T h2 , whereas the cold fluid enters at T c1 and leaves at T c2 . Set up the
differential equation to determine the temperature variation (along the heat exchanger) for
hot and cold fluids.

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