Self Test $3$

$($Unsteady State energy balance$)$

Problem Statement

A hot, thin copper disk of mass $"M"$ and temperature $"$T$"$ is suddenly immersed in an oil bath containing $"m"$ kilograms of cold oil at temperature $"$t$".$ The oil in the bath is very well mixed. Convective heat transfer $($h$)$ cools the copper disk.

a$)$ Formulate differential equations and initial conditions describing the change of the temperature of the oil and the temperature of the disc as a function of time.

Self Test $3$

$($Unsteady State energy balance$)$

b$)$ Solve the differential equations.

c$)$ Make a sketch of the solution $($show the temperature of the disc and the temperature of the oil as a function of time$)$

d$)$ How long will it take for this system to reach thermal equilibrium and what will be the temperature of the oil and the disc at that time?

Assumptions $($Open Discussion$)$

Illustration

List of Variables

$\backslash$table$[[M=,$mass of the disk,$kg$