$(35$ pts $.)$ A solid sphere $(d=0\mathrm{.}200m)$ is initially at a uniform temperature of $888C.$ It is suddenly submerged in a fluid $(444C)$ flow with a convection coefficient of $275\frac{W}{m^2}K.$ Determine the temperature at a radial distance one$-$fourth of the way from the midpoint $($center$)$ of the sphere to its outer surface after the sphere has been in the fluid flow for $2468$ seconds.

Solid Material Properties: $=6543\frac{kg}{m^3},Cp=987\frac{J}{kg}*K,k=13\mathrm{.}75\frac{W}{m}*K$

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