Question 1: one dimensional steady state conduction with uniform internal

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1 Question 1: one dimensional steady state conduction with uniform internal energy generation occurs in plane wall with thickness of 50mm and a constant thermal conductivity of 5 m.k.for this conditions, the temperature distribution has the form, T x = a + bx + cx 2.The surface at x = 0 Has a temperature of T 0 = T o = 120 and experiences convection with fluid for which T = 20 and h = 500 m 2.K.The surface at x = L is well insulated. (a)applying an overall energy balance to the wall, calculate the internal energy generation rate q. (b)determine the coefficient a, b and c by apply the boundary conditions to the prescribed temperature distribution. (c) Consider condition s for which the convection coefficient is halved, but the internal energy generation rate remains unchanged. Determine the new values of a, b and c and use the results to the plot the temperature distribution.hint: recognize that T (0) is no longer 120. (d)under condition for which the internal energy generation rate is doubled, and the convection coefficient remains unchanged ( h = 500 m 2.K ), determine the new values of a, b and c and plot the corresponding temperature distribution.

2 Referring to the results of Parts (b),(c),and (d) as Case 1.2,and 3,respectively,compare to the temperature distribution for the three cases and discuss the effects of h and q on the distribution. Question 2: Passage of an electric current through long conducting rod of radius r i and thermal conductivity K r results in uniform volumetric heating at rate of q.the conducting rod is wrapped in an electrically nonconducting cladding material of outer radius r o and thermal conductivity k c, and convection cooling is provided by adjoining fluid. For steady-state conditions, write appropriate forms of the heat equations for the rod and the cladding.express appropriate boundary conditions for the solution of these equations.

3 Question3: A Cylindrical liquid oxygen (LOX) had a diameter of 4 ft, a length of 20 ft, and hemispherical ends. The boiling point of LOX is -29.An insulation is sought that will reduce the boil-off rate in steady state to no more than 25 lb/hr.the heat vaporization of LOX is 92 /lb.if the thickness of insulation is to be more than 3in.,what would the value of its thermal conductivity have to be?

4 Question 4: A standard 4-in.steel pipe (ID=4.026in.,OD=4.500 in)carries superheated steam at 1200 in an enclosed space where a fire hazard exists, limiting the outer surface temperature to 100.In order to minimize the insulation cost,two materials are to be used :first high-temperature (relatively expensive)insulation is to be applied to the pipe,and then magnesia (a less expensive material )will be applied on the outside. The maximum temperature of the magnesia is to be 600.The following constants are known: Steam side coefficient h = 100 hr.ft 2. High-temperature insulation conductivity k = 0.06 Magnesia conductivity k = Outside heat transfer coefficient h = 2.0 Steel conductivity k = 25 Ambient temperature T a = 70 hr.ft 2.

5 (a)specify the thickness for each insulation material.(b)calculate the overall heat transfer coefficient based on pipe OD.(c) hat fraction of total resistance is due (1)steam-side resistance,(2)steel pipe resistance,(3)insulation (the combination of the two),and (4)outside resistance?(d)how much is heat transferred per hour per foot length of pipe? Question 5: two large steel plates at temperatures of 90 and 70 are separated by a steel rod 0.3 m long and 2.5 cm in diameter. The rod is welded to each plate. The space between the plates is filled with insulation that also insulates the circumference of the rod.because of the voltage difference between the two plates, current flows through the rod, dissipating electrical energy at a rate of 12.Determine the maximum temperature in the rod and the heat flow rate at each ends with the total rate of heat generation.