An experimental nuclear core simulation device consists of a long thin?walled metallic tube with diameter D and length L. It is electrically heated to produce a sinusoidal surface heat flux distribution: ??" = sin(pi x/L)
?
where x is the distance from the tube inlet. Fluid flows through the tube with a
flowrate of ?? and an inlet temperature of Tm, i and can be considered turbulent and fully developed over
its entire length. Using the supplied variables, develop expressions for:
(a) the total rate of heat transfer (??) from the tube to the fluid
(b) the fluid outlet temperature Tm, a
(c) the axial distribution of the wall temperature, ??s(X)
(d) the magnitude and x?location of the highest wall temperature.

Asteel wire of 2 mm diameter is fixed between two points located 2 m apart. the tensile force in the wire is 250n, if its density of steel is given by 7830 kg/m3 the fundamental frequency of vibration hz? ?

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?

Arigid tank contains 10 kg of air at 137 kpa (abs) and 21°c. more air is added to the tank until the pressure and temperature rise to 242 kpa (abs) and 32°c, respectively. determine the amount of air added to the tank. [r-0.287 kj/kg k]