QUESTION $1$

One method to determine the thermal diffusivity, $a,$ of a material is to expose it to an energy

pulse and then to measure the resulting increase in surface temperature. A material with a

known thermal conductivity of $0\mathrm{.}05\frac{W}{m}.K$ but unknown density and specific heat is

measured using a laser pulse with an energy flux of $10E4\frac{J}{m^2}.$ Initially, the material is at

thermal equilibrium with the room at $25C,$ and after $10$ s the surface temperature measured

by a specialized thermocouple reads $100C.$ Consider the material surface as a flat plane and

the material thick, such that the surface temperature is only influenced by the laser pulse.

You can neglect the impact of natural convection and radiation at the surface.

a$)$ Would you consider this material to be an insulator or a conductor? Why?

b$)$ What is the thermal diffusivity of this material?

c$)$ Determine the surface temperature at $t=30s$ and the temperatures at a distance

of $2$ mm from the surface at $t=10s$ and $t=30s.$ If you were unable to calculate

the diffusivity in part b$),$ use a value of $10E-8\frac{m^2}{s}.$

d$)$ Using your calculations from part c$),$ draw a graph $($temperature on the $y-$axis,

distance from the surface on the $x-$axis$)$ of the temperature profile at $t=10s$ for a

distance of $x=0$ to $2$ mm and the same at $t=30s.$ Also, be sure to sketch the

temperature profile of the material at the given initial condition for $t=0s.$