HW3 Solutions - ME 364 HW 3 Solutions Problem 1 You have...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ME 364 HW 3 Solutions Problem 1: You have been contracted by ASHRAE (the American Society of Heating, Refrigeration, and Air- Conditioning Engineers) to measure the thermal conductivity of various, new materials for insulating pipes. Your contract specifies that you will measure the thermal conductivity to within 10%. Your initial design for the test setup is shown in Fig. 1. Figure 1: Test facility for measuring pipe insulation The test facility consists of a pipe (with conductivity k pipe = 120 W/m-K) with inner diameter, D i,pipe = 6.0 inch and thickness th pipe = 0.5 inch that carries a flow of chilled water, T water = 10°C. The heat transfer coefficient between the water and the internal surface of the pipe is h water = 300 W/m 2 -K. The pipe is covered by a th ins =2.0 inch thick layer of the insulation (with conductivity k ins ) that is being tested. Two thermocouples are embedded in the insulation, one connected to the outer surface ( T ins , out ) and the other to the inner surface ( T ins,in ). The insulation material is surrounded by a th m =3.0 inch thick layer of a material with a well-known thermal conductivity, k m = 2.0 W/m-K. Two thermocouples are embedded in the material at its inner and outer surface ( T m,in and T m,out , respectively). Finally, a band heater is wrapped around the outer surface of the material. Assume that the thickness of the band heater is negligibly small. The band heater provides band q =3 kW for every m of its length. The outer surface of the band heater is exposed to ambient air at T air = 20°C and has a heat transfer coefficient, h air = 10 W/m 2 -K and emissivity = 0.5. A contact resistance of c R  =1e-4 m 2 -K/W is present at all 3 interfaces in the problem (i.e., between the pipe and the insulation, the insulation and the material, and the material and the band heater). You may assume that the problem is 1-D (i.e., there are no variations along the length of the pipe) and do the problem on a per unit length of pipe ( L =1 m) basis. a.) Draw a resistance network that represents the test facility. Clearly label each resistance and indicate what it represents. Be sure to indicate where in the network the heat input from the band heater will be applied and also the location of the thermocouples mentioned in the problem statement.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The resistance network is shown in Fig. 2 and includes convection with the water and the air ( R conv,w and R air ), conduction through the pipe, insulation, and material ( R pipe , R cond,ins , and R cond,m ), contact resistances between the pipe and insulation ( R c, 1 ), the insulation and material ( R c, 2 ), and the material and the band heater ( R c ,3 ), and radiation ( R rad ). Figure 2: Resistance network representing the test facility. b.) If the insulating material under test has a conductivity of k ins = 1.0 W/m-K then predict the heater temperature, T htr , and determine how much of the heater power is transferred through the insulation ( ins q ).
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern