$(2)$ Air at $27C(1$atm$)$ is flowing over a sphere $($diameter $=6cm)$ with a velocity of $3\mathrm{.}5\frac{m}{s}.$ If

the surface temperature of the sphere is constant at $90C,$ determine the heat transfer rate from

the sphere. You might use the Whitaker's correlation to predict the heat transfer coefficient,

${}_D=2+(0\mathrm{.}4R{e}^{\frac{1}{2}}+0\mathrm{.}06R{e}^{\frac{2}{3}})P{r}^{0\mathrm{.}4}(\frac{{}_{}}{{}_S}{)}^{\frac{1}{4}}$

All properties are evaluated at $T_{}$ except for ${}_s,$ which is evaluated at the surface temperature.

The density, viscosity, thermal conductivity, and Prandtl number of air at $300K$ are given by $$

$=1\mathrm{.}18k\frac{g}{m^3},=1\mathrm{.}85**{10}^{-5}Pa.s,k=0\mathrm{.}026\frac{W}{m}-K,$ and $Pr=0\mathrm{.}708,$ respectively. The viscosity

of air at $363K$ is given by $={2\mathrm{.}18}^{**}{10}^{-5}Pa.$s$.$ State your assumptions, if any.