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# ChE 350 Problem Set 8 Due Thursday March 24, 2016 1.

I need help with my heat tranfer hw please .........

ChE 350 Problem Set 8 Due Thursday March 24, 2016 1. A cylindrical composite particle with a diameter of 1 cm is composed of a 4- cm- long cylindrical silver segment ( ρ = 10,500 kgm -3 ; c = 230 Jkg -1 K -1 ; k = 420 Wm -1 K -1 ) attached (on its end) to a 4- cm- long cylindrical tin segment ( ρ = 7,300 kgm -3 ; c = 230 Jkg -1 K -1 ; k = 60 Wm -1 K -1 ), with a thin layer of a perfect thermal insulator separating the two segments. The composite cylinder is initially at 20 ˚C and then passes through a 550 ˚C environment with a heat transfer coefficient of 2,000 Wm -2 K -1 on all exposed surfaces . a. If the melting point of tin is 505 ˚C , how long will it take for the tin segment to begin to melt? b. What is the temperature difference across the insulating layer on the surface of the particle when the tin segment begins to melt? c. What is the difference between the average temperatures of the two segments when the tin segment begins to melt? d. (Extra credit) If the composite were made in spherical form (using the same amounts of silver and tin as in the original particle), with a perfect insulator separating silver and tin hemispheres, how long would it take for the tin segment to begin to melt? What is the temperature at the coldest point in the tin segment when it begins to melt? What is the largest such particle for which the tin segment would begin to melt at the same time everywhere? 2. A spherical stainless steel ( ρ = 7,800 kgm -3 ; c = 460 Jkg -1 K -1 ; k = 17 Wm -1 K -1 ) reactor with 1.0 m inner diameter and wall thickness of 5 mm is f lled with reactants ( ρ = 1,100 kgm -3 ; c = 2,400 Jkg -1 K -1 ) that are initially at 25 ˚C . Exothermic reactions within the reactor release energy at a rate of 10 kWm -3 , while the exterior surface of the reactor is exposed to 25 ˚C ambient air with a convective heat transfer coef f cient of 5 Wm -2 K -1 . The reactant mixture is well stirred so that the temperature within the reactor is uniform, and the thermal capacitance of the reactor wall is negligible so that the instantaneous heat transfer rate through the reactor wall is equal to the instantaneous rate of heat loss to the air by convection. a. What is the temperature of the reactant mixture after 5 hours of process time? b. What is the temperature at the outer surface of the reactor at that time?
3. The 7- mm -thick base plate of an iron is made of an aluminum alloy ( ρ = 2,700 kgm -3 ; c = 950 Jkg -1 K -1 ; k = 200 Wm -1 K -1 ; ε = 0.8) and has a surface area of 0.04 m 2 . An electrical resistance heater applies a uniform heat flux of 12.5 kWm -2 to the inner surface of the base plate when the iron is turned on. The outer surface of the base plate is exposed to 25 ˚C ambient air with a convective heat transfer coefficient of 20 Wm -2 K -1 and exchanges radiation with large surroundings at 25 ˚C . Estimate the time required for the base plate to reach 140 ˚C from an initial temperature of 25 ˚C . Use the NDSolve command in Mathematica for numerical integration of the governing differential equation.

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