A copper sphere of diameter 5 cm is initially at temperature 200°C. It cools in air by convection…

A copper sphere of diameter 5 cm is initially at temperature 200°C. It cools in air by convection and radiation. The temperature T of the sphere is governed by the equation here ρ is the density of copper, C its specific heat, V0 the volume of the sphere, t the time, ε a property of the surface known as emissivity, σ a constant known as the Stefan–Boltzmann constant, T∞ the ambient temperature, A the surface area of the sphere, and h the convective heat transfer coefficient. The initial condition is as follows: At t I = = 0 : 200°C Using Heun’s method, without iteration, solve this differential equation to find the temperature variation with time, until the temperature drops below 50°C. Use the following values: ρ ε σ = = = = × − ∞ 9000 5 67 10 8 4 kg/m 400 J/kg K 0.5 W/m K 3 2 C . T = ° 25 C h = 15 W/m2 K Employ time steps of 0.5 and 1.0 min, and compare the results obtained in the two cases.

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