A spherical metal ball of radius r_o is heated in an oven to a temperature of T_i throughout and is then taken out of the oven and allowed to cool in ambient air at T∞ by convection and radiation. The emissivity of the outer surface of the cylinder is e, and the temperature of the surrounding surfaces is T_surr. The average convection heat transfer coefficient is estimated to be h. Assuming variable thermal conductivity and transient one-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary and initial conditions) of this heat conduction problem. Do not solve.

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Metal ball 0 T₁ Tsurr Radiation Convection To To h