A high-temperature gas reactor (HTGR) consists of spherical, uranium oxide fuel elements in which there is uniform volumetric heating(q). Each fuel element is embedded in a graphite spherical shell, which is cooled by a helium gas flow at 1 atm. Consider steady-state condition for which radiation effects may be neglected, the gas velocity and temperature are V=20m/s and T?=500K, the pellet and shell diameters are Di=10mm and Do=12mm, and the shell surface temperature is Ts,o=1300K. The uranium oxide and graphite each have a thermal conductivity of kp=kg=2W/m?K. Properties: Helium: ?= 290 × 10-6m2/s, k = 0.22 W/m?K, Pr =0.67, µ= 283 × 10-7 N?s/m2; (Ts,o = 1300 K, with extrapolation): µ = 592 × 10-7 N?s/m2. (a) What is the rate of heat transfer from a single pellet to the gas stream? (b) What is the volumetric rate of heat generation in the pellet and what is the temperature at the pellet- graphite interface (Ts,i) ? (c) Obtain an expression for the radial temperature distribution, T(r), in the pellet, express the result in terms of temperature at center of the pellet, T(0). Evaluate T(0) for the prescribed conditions.