Chapter 2, Problem 2.23P

A method for determining the thermal conductivity k and the specific heat $c_p$ of a material is illustrated in thesketch. Initially the two identical samples of diameter $D=60\text{mm}$ and thickness $L=10\text{mm}$ and the thinheater are at a uniform temperature of $T_i=23.00°\text{C,}$ while surrounded by an insulating powder. Suddenlythe heater is energized to provide a uniform heat flux $q_o^{"}$ on each of the sample interfaces, and the heat flux ismaintained constant for a period of time, $\Delta t_o.$ A shorttime after sudden heating is initiated, the temperature atthis interface $T_o$ is related to the heat flux as $T_o\left(t\right)-T_i=2q_0^{"}{\left(\frac{t}{\pi \rho c_{p}k}\right)}^{1/2}$ For a particular test run, the electrical heater dissipates15.0 W for a period of $\Delta t_o=120\text{s,}$ and the temperatureat the interface is $T_o\left(30s\right)=24.57°\text{C}$ after 30 s of heating.A long time after the heater is deenergized, $\text{t}\gg \Delta t_o.$ the samples reach the uniform temperature of $T_o\left(\infty \right)=33.50°\text{C}\text{.}$ The density of the sample materials,determined by measurement of volume and mass, is $\rho \text{=3965}{\text{kg/m}}^{\text{3}}.$

Determine the specific heat and thermal conductivityof the test material. By looking at values of the thermophysicalproperties in Table A.1 or A.2, identify thetest sample material.