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Problem 1 An endothermic reaction is conducted in a tubular reactor with length of 10 m. The wall has uniform volumetric energy generation of 40 kW/m³ and thermal conductivity of 4 W/m-K. The inner diameter is 20 cm, and the outer diameter is 30 cm. The outer surface is at 25°C and is exposed to air at 20°C with convection coefficient h = 90 W/m². a) Draw a simple schematic of the problem, indicating the heat transfer rates involved. b) What is the heat rate consumed by the endothermic reaction? c) If we insulate the outer surface perfectly, what is the new necessary volumetric energy generation? Consider that the heat rate consumed by the reaction is unchanged d) For this new scenario in item c., consider that the temperature of the inner surface is 50°C. What two boundary conditions can be used for obtaining a temperature profile? e) Considering items c. and d., derive the temperature profile for the reactor wall. What is the temperature at the outer surface of the reactor?