Question $2)[50$ Pts$]$

A stainless steel ball having a diameter of $25$ cm and a density of $8055k\frac{g}{m^3}$ and a specific heat capacity of $480\frac{J}{k}g.K$ is removed from the oven at a uniform temperature of $300C.$ The ball is then subjected to the flow of air at $1$ atm and $25C$ with a velocity of $3\frac{m}{s}.$ The surface temperature of the ball eventually drops to $200C.$

The dynamic viscosity of air at the average surface temperature is $2\mathrm{.}76{10}^{-5}k\frac{g}{m}.s.$

At $1$ atm and $25C,$ air has a thermal conductivity of $0\mathrm{.}02551\frac{W}{m}.k,$ a kinematic viscosity of $1\mathrm{.}562{10}^{-5}m\frac{2}{s},$ a dynamaic visosity of $1\mathrm{.}849{10}^{-5}k\frac{g}{m}.s$ and a Pr of $0\mathrm{.}7296.$

Estimate the following.

A$)$ Reynolds Number $[10$ Pts$]$

B$)$ Nusselt Number $[15$ Pts$]$

C$)$ Convective heat transfer coefficient $[10$ Pts$]$

D$)$ Heat transfer rate $[15$ Pts$]$