1.) Electric current flows through a flat steel plate that is 1 cm thick. Electrical power is dissipated via Joule heating of the plate. At steady state, the temperature distribution across the thickness of the plate is given by: TT(xx) = 2.5 K�1 − xx2 (0.5 cm)2� + 10 K � xx 0.5 cm� + 313 K The two surfaces of the plate are located at x = -0.5 cm and x = 0.5 cm.
The thermal conductivity of the plate is 50 W/m/K.
a. How much electric power is dissipated per unit area of the plate?
b. What are the values of heat flux at the two surfaces of the plate?
c. For each surface, is the heat flux directed toward or away from the surface?

The drive force for diffusion is 7 fick's first law can be used to solve the non-steady state diffusion. a)-true b)-false

Acertain flow of air (at stp) has a velocity distribution given by v i (in ft/s). if this flow is going through a 4 ft square area in the yz-plane (centered at the origin), what is the mass flow rate (in lbm/s)?

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?