The convection coefficient for flow over a solid sphere may be determined by submerging the sphere which is initial1y at 25°C, into the flow, which is at 75°C, and measuring its surface temperature at some time during the transient heating process.

(a) If the sphere has a diameter of 0.1 m, a thermal conductivity of 15 W/m ∙ K, and a thermal diffusivity of 10^-5 m²/s, at what time wil1 a surface temperature of 60°C be recorded if the convection coefficient is 300 W/m² ∙ K?

(b) Assess the effect of thermal diffusivity on the thermal response of the material by computing center and surface temperature histories for a = 10^-6, 10^-5, and 10^-4 m²/s. Plot your results for the period o < t < 300 s. In a similar manner, assess the effect of thermal conductivity by considering values of k = 1.5, 15 and 150 W/m ∙ K.