Unsteady-state heat conduction in an iron sphere, an iron sphere of 1-in. diameter has the following physical properties: k = 30 Btu/hr ∙ ft ∙ F, C_p = 0.12 Btu/lb_m ∙ F. and p = 436lbm/ft^3, initially the sphere is at a temperature of 70°F. 

(a) What is the thermal diffusivity of the sphere? 

(b) If the sphere is suddenly plunged into a large body of fluid of temperature 270°F, how much time is needed for the center of the sphere to attain a temperature of 128°F? 

(c) A sphere of the same size and same initial temperature, but made of another material, requires twice as long for its center to reach 128°F. What is its thermal diffusivity? 

(d) The chart used in the solution of (b) and (c) was prepared from the solution to a partial differential equation. What is that differential equation?