2. (3 pt) Heat Transfer from Tubular Reactor (Problem 8 from Midterm #1) Hint: Read through ALL SUBPARTS of this problem, before starting. Consider a tubular reactor for which the wall

is a cylindrical glass shell of inside radius r₁ = 1.0 cm and outside radius r₂ = 2.0 cm, and length L = 0.5 m. Inside the tube core (inside r₁) is a reaction mixture of uniform temperature T₁ = 60 °C, which generates q = 5 x 105 W/m³ heat due to exothermic reaction. A. The design goal calls for the temperature of the outer wall (7₂) to be less than 35 °C, for safety reasons. Is this goal met? Use k = 0.8 W/m-K for the glass wall and assume steady state and that the fluid inside the tube core is well-mixed, so that its resistance may be neglected. The two ends of the reactor are insulated. Hint: There is no generation in the glass tube walls; generation only occurs in the fluid mixture inside. B. The following equation can be found on your equation sheet for this class, under the section 3. Hollow spheres and cylinders with generation in core: T(r) = T(₁) + (q/4k)(r² - r²) Explain why this equation is not applicable for this particular scenario. C. Now, suppose the ambient air temperature in the room containing the reactor is To = 25 °C. A fan blows air over the reactor (perpendicular to the cylinder axis) at a velocity v = 0.25 m/s. Is the resulting forced convection enough to carry away the heat generated by the reactor? Use T₂ = 35 °C (rather than your result from Part A), along with Kair= 0.025 W/mK, Vair 1.6 x 10-5 m²/s, and Pr = 0.7 for air. D. Explain why the finding that Nup > 1 or even Nup >> 1 in Part C is insufficient to justify whether the resulting forced convection is enough to carry away the heat generated by the reactor.