Question

An long cylindrical vaccuum chamber shown in Figure 1, is used to anneal single titanium rods by maintaining their temperature at 800 °C for an extended period of time. Heat is introduced into the rods internally by induction. The insulation surrounding the chamber has a thicknesss of 50 mm and thermal conductivity of 0.1 W/m.K. The convective heat transfer coefficient on the outer surface of the insulation is 10 W/m2.K. 2 Chamber wall (thin) T=30°C inner= 250 mm Insulation Titanium Rod mm Figure 1: Annealing chamber The inner surface of the chamber and the titanium rods both have an emissivity of e 0.8. (a) Determine expressions for the following heat transfer rates: (i) from the rod to the inner wall of the chamber (ii) from the chamber inner wall to the ambient, assuming radiation from the outer surface of the insulation to be negligible (10 Marks) (b) Show that the temperature of the inner surface of the vacuum chamber is 763.8 °C during steady operation (12 Marks) (c) Calculate the temperature at the outer surface of the insulation. (4 Marks The emissivity of the outer surface of the insulation is subsequently measured as 0.1 (d) Estimate the error introduced in assuming radiation from the outer surface of the chamber to be negligible in Part (a)(ii). State whether this assumption is reasonable (4 Marks) (e) If radiation at the outer surface of the insulation was to be included in the analysis, outline how you would: (i) determine an expression for the temperature at the inner surface of the chamber (ii solve the resulting expression to find this temperature (6 Marks) The following additional information is provided: In(ro/ri (i) The thermal resistance for a cylindrical shell is R = 2πkL (ii) The Stefan-Boltzmann constant, o, is 5.7 x 108 W/m2.K4 (Total 36 Marks)

The heat question and would like to have work solution. The answers are (c) 136.6 (d) < 2%. thank you.

Answer 1

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