A horizontal cylindrical pipe (k = 10 W/m·K) has an outer diameter of 15 cm and a wall thickness of 5 cm. The pipe is situated in a stationary air, where the air and surrounding temperature is 27°C. The outer surface temperature of the pipe is 127°C, and the pipe surface has an emissivity of 0.5. Determine the inner surface temperature of the pipe. Use the following air properties for the analysis:
k = 0.03 W/m∙K, ν = 20.92 × 10−6 m2 /s, α = 29.90 × 10−6 m2 /s, Pr = 0.70

The filament of an incandescent lamp has a temperature of 2000k. calculate the fraction of radiation emitted in the visible light band if the filament is approximated as blackbody

A2-m rigid tank initially contains saturated water vapor at 100 kpa. the tank is connected to a supply line through a valve. steam is flowing in the supply line at 600 kpa and 300 c. the valve is opened, and steam is allowed to enter the tank until the pressure in the tank reaches the line pressure, at which point the valve is closed. a thermometer placed in the tank indicates that the temperature at the final state is 200°c. determine (a) the mass of steam that has entered the tank (b) the amount of heat transfer.

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)?