A very thick plate with thermal diffusivity and conductivity k is initially at a uniform temperature Ti. Suddenly one of its surface is exposed to a coolant and, instantaneously, it adopts the temperature of the coolant Ts. Assume that the temperature in the solid varies according to T (x, t), where t is time. Define the coordinate system with the origin (x = 0) on the surface which is being cooled. (a) Write the governing equation, and appropriate boundary and initial conditions to determine the temperature profile T (x, t), if the heat transfer rate in the plate is modeled as a semi-infinite body (b) Estimate the heat flux q (kW/m2) at the surface after one-minute of cooling. Set = 15 106 m2/s, k = 20 W/m K, Ts = 20 C, To = 100 C. (d) An experiment is conducted and the heat flux is measured for two different materials undergoing similar cooling treatments. All properties and experimental conditions are the same, except that the thermal conductivity of each material is different. For material A, kA = 20 W/m K and q A at the surface is measured to be 10 kW/m2. If the thermal conductivity of material B is kB = 40 W/m K, what is the anticipated heat flux q for material B at its surface (kW/m2)