Forced air at T$\backslash$infty $=25\backslash$deg C and V $=10$ m$/$s is used to cool electronic elements on a circuit board. One such element is a chip, $4$ mm $\backslash$times $4$ mm$,$ located $120$ mm from the leading edge of the board. Experiments have revealed that flow over the board is disturbed by the elements and that convection heat transfer is correlated by an expression of the form Nu$=0\mathrm{.}04$Rex$^0\mathrm{.}85*$Pr$^1/3.$ The cooling system is designed and tested at sea level $($p $1$ atm$),$ but the circuit board is sold to a customer in Mexico City, with an elevation of $2250$ m and atmospheric pressure of $76\mathrm{.}5$ kPa.

The chip dissipates $30$ mW$.$

$($a$)$ Estimate the surface temperature of the chip when the board is designed at sea level.

$($b$)$ Estimate the surface temperature of the chip when the board is operated in Mexico City. Hint: To a good approximation, the dynamic viscosity $\backslash$mu $,$ the thermal conductivity k$,$ and the specific heat cp are independent of pressure. Based on this, and considering air as an ideal gas, first determine how other relevant parameters vary with pressure.

$($c$)$ It is desirable for the chip operating temperature to be independent of the location of the customer. What air velocity is required for operation in Mexico City if the chip temperature is to be the same as at sea level?