In a thermal heat sink the heat flux variation along the axis of a cooling passage is appr...

In a thermal heat sink the heat flux variation along the axis of a cooling passage is approximated as

where x is measured along the passage axis and L is its total length.

A large installation involves a stack of plates with a 3-mm air space between them. The flow passages are 1.22 m long, and the heat flux in the plates varies according to the above equation where a = 900 W/m2 and v = 2500 W/m2. Air enters at 100°C with a mass velocity (the product of ρV) of 7.5 kg/s · m2. The surface coefficient along the flow passage can be considered constant with a value of 56W/m2 · K.

Generate a plot of heat flux, mean air temperature, and plate surface temperature as functions of x. Where does the maximum surface temperature occur and what is its value?