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Solution for Engineering Heat Transfer 2nd Edition Chapter 1, Problem 2

by William S. Janna
196 Solutions 12 Chapters 16650 Studied ISBN: 9780849321269 Physics 5 (1)

Chapter 1, Problem Example 2 : Example 1.2 Figure I .8 is...

Example 1.2

Figure I .8 is a schematic of a device used to measure thermal conductivity. It consists of a hot

plate as a heat source. In contact with the hot plate is a 2.5-cm-diameter rod miide of stainless steel of known thermal conductivity that has thermocouples attached for obtaining temperature readings. Resting on the stainless steel is a 2.5-cm-diameter aluminum rod of unknown therinal conductivity that also contains thermocouples. On top of the aluininuin is a water-cooled chamber that acts as ii heat sink. The rods and water chamber :ire surrounded completely by thick insulation. The stainless steel rod has ;I thermal conductivity of 14.4 W/(m.K), and the following steady-state temperature data were obtained for one setting of the hot plate thermostat:

 

Step-By-Step Solution

Example 1.2


 

Short answer

Determine the thermal conductivity of the aluminum

Solution

The insulation is heated, as is the stainless steel. Just as a gradient in the axial direction exists

in the metals, one will exist wifhin the insulation. The difference is that the metal transfers heat

Par better than the insulation does. The existing axial gradients also produce temperature

differences in the radial direction so that heat is transferred through the insulation to the surrounding air.

 

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