HomeworkSolutions_C8 - Problem #1: Consider a circular...

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Problem #1: Consider a circular steel pipe having an inner diameter of 2.067 in., and wall thickness of 0.154 in. The pipe carrying steam is insulted with 2 in. of 85% magnesia covered in turn with 2 in. of cork. Estimate the heat loss per hour per foot of pipe if the inner surface of the pipe is at 250 o F and the outer surface of the cork is at 90 o F. The thermal conductivities (in Btu/hr.ft.F) of the substances concerned are: steel, 26.1; 85% magnesia, 0.04; cork, 0.03. Answer: See Example 10.6-1 (or 9.6-1) in the textbook, 2 nd (or 1 st ) edition, for the notation and the derivation of the energy equations in terms of temperature for individual layers. The final forms of these equations are as follow: ( ) () 10 0 1 00 0 1 01 21 1 2 1 2 12 32 23 0 0 2 3 0 0 23 Zone 01 (steel): Zone 12 (magnesia): Zone 23 (cor k): ln ln ln rr dT k r rq T T dr k dT T T dr k dT T T dr k =⇒ = = = Addition of these above equation gives 03 01 12 23 ln ln ln TT kkk = ++ Thus, the heat loss over the inner surface of the pipe with an area of 0 2 Lr π
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( ) () 03 00 0 10 21 32 01 12 23 2 2 ln ln ln LT T QL r q rr kkk π == ++ Or the heat loss per hour per foot of the pipe ( ) 0 01 12 23 2 ln ln ln TT Q L = The r i for this problem are 1 2 3 2.067/ 2 1.0335 in. 1.0335 0.154 1.19 in. 1.19 2 3.19 in. 3.19 2 5.19 in. o r r r r =+= =+ = = Insertion of numerical values into the above formula gives: 24.58 Btu/hr-foot o Q L = Problem # 2: An oil is acting as a lubricant for a pair of cylindrical surfaces such as those shown in Fig. 9.4-1 (see section 9-4 in the textbook, 1 st edition) or Fig.10.4-1 (2 nd edition). The angular velocity of the outer cylinder is 7908 rpm. The outer cylinder has a radius of 5.06 cm, and the clearance between the cylinders is 0.027 cm. What is the maximum temperature in the oil if both wall temperatures are know to be 158 o F? The physical properties of the oil are assumed constant at the following values: Viscosity: 92.3 cp Density: 1.22 g/cm 3 Thermal conductivity: 0.0055 cal/s.cm.C Answer: The parallel-plate approximation in Example 10.4 in the textbook (or 9.4 in the 1 st edition) is used here to estimate the temperature rise. Multiplication of Eq. 10.4-9 (or 9.4
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HomeworkSolutions_C8 - Problem #1: Consider a circular...

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