Copper tubing is joined to a solar collector plate of thickness t, and the working fluid maintains the temperature of the plate above the tubes at To. There is a uniform net radiation heat flux q"rad to the top surface of the plate, while the bottom surface is well insulated. The top surface is also exposed to a fluid at T[infinity] that provides for a uniform convection coefficient h. a. Derive the differential equation that governs the temperature distribution T(x) in the plate.
b. Obtain a solution to the differential equation for appropriate boundary conditions.

Steel is coated with a thin layer of ceramic to protect against corrosion. what do you expect to happen to the coating when the temperature of the steel is increased significantly? explain.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Prove the equivalence between the two statements of the 2nd law of thermodynamics (i. e., a violation of one statement leads to the violatio the other statement)