A 25-mm-diameter copper sphere with a low emissivity coating is removed from an oven at a uniform temperature of 85°C and allowed to cool in a quiescent fluid maintained at 25°C.

(a) Calculate convection coefficients associated with the initial condition for immersion in air and water.

(b) Using two different approaches, estimate the time for the sphere to reach 30°C when immersed in air and water. In the simpler, but more approximate, approach, use an average convection coefficient based on the average temperature of the sphere during the cooling process. In the more accurate method, treat the convection coefficient as a variable and numerically integrate the energy balance equation.