A spherical metal ball of radius ro is heated in an oven to a temperature of

$600\backslash$deg F throughout and is then taken out of the oven and allowed to cool in

ambient air at T$`578\backslash$deg F The thermal conductivity of the ball material is k $58\mathrm{.}3$ Btu$/$h$$ft$$R$,$ and the average convection heat transfer coefficient on the outer surface of the ball is evaluated to be h $54\mathrm{.}5$

Btu$/$h$$ft$2$R$.$ The emissivity of the outer surface of the ball is e $50\mathrm{.}6,$ and the

average temperature of the surrounding surfaces is Tsurr $5525$ R$.$ Assuming

the ball is cooled uniformly from the entire outer surface, express the initial

and boundary conditions for the cooling process of the ball, and solve the question with values provided