Question

4 (20pointsexperiments are conducted to investigate-the thermal properties of a new coating material. Two steel cylinders of equal radius, R, and height, H, are exposed to-air on all sides. One

cylinder is uncoated,whereas the surface of the second Problem total):cylinder is completely coated with the new material. The radius of the cylinders R is 100 mm and the height H is 100 mm.The steel has a density, p, of 7800 kg/m²and a specific heat capacity, c, of 486J/kg-°C. Initially, both cylinders are at room temperature To = 20°C. Then they are both placed in an annealing furnace,which was heated up before to Tenv500°C. The temperatures of the two cylinders are measured as a function of time (un coated – blue curve, coated - red%3Dcurve) (a) (5 points) Estimate the heat transfer coefficient, h1, for the coated cylinder (red curve) and the heat transfer coefficient, h2, for the uncoated cylinder (blue curve). The mass of the coating can be neglected. h_{1}=[] \frac{W}{m^{2}-{ }^{\circ} C} h_{2}=[] \frac{W}{m^{2}-{ }^{2} C} ) (10 points) To improve the economic and energy efficiency of the heat treatment, the cylinders (initial temperature Teyl,0the same time, an induction heater is turned on with an additional input power P(t)Po is in Watts. Assuming the total power/heat exchange is the sum of the power from the induction and heat exchange with the environment, derive the temperature of the coated cylinder, T,(t), and the uncoated cylinder, T2(t), in symbolic form. Your answers should include the symbols Tenv , To ,Po, m, A, c, t, and the heat transfer coefficient h, or h,.20°C) are exposed to a reduced temperature furnace, Tenv, at the time t = 0. AtPo · u(t) where c) (5 points) Using the result of problem 2 (b), suppose Po the coated cylinder has been measured with great precision and is equal to 10.61 W/m² °C (Note that this is not the answer to part (a)). Calculate the steady state temperature reached by the coated cylinder?= 200 W, Teny = 350°C, To= 20°C, and h,for

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