(Solved): Consider spheres (p=3000kg/m3,cp=850J/kgK,k=20W/mK) of 40mm diameter that are hea ...

Consider spheres $\left(p=3000\mathrm{kg}/{\mathrm{m}}^3,c_p=850\mathrm{J}/\mathrm{kg}\cdot \mathrm{K},k=20\mathrm{W}/\mathrm{m}\cdot \mathrm{K}\right)$ of $40-\mathrm{mm}$ diameter that are heated to a uniform temperature of $400^{\circ }\mathrm{C}$, then suddenly removed from an oven and placed in a forced-air bath operating at $25^{\circ }\mathrm{C}$ with a corvection coefficient of 200 $\mathrm{W}/{\mathrm{m}}^2.\mathrm{K}$. Find the time, in seconds, the spheres must remain in the bath for $85\%$ of the thermal energy to be removed as well as the centerline temperature, in ${}^{\circ }\mathrm{C}$, at that time. $\begin{array}{l}t=\\ T(0,t)={}^{\circ }\mathrm{C}\end{array}$