Problem

A 2.5-cm-diameter and 8-cm-long cylindrical sample of a material is used to determine its...

A 2.5-cm-diameter and 8-cm-long cylindrical sample of a material is used to determine its thermal conductivity experimentally. In the thermal conductivity apparatus, the sample is placed in a well-insulated cylindrical cavity to ensure one-dimensional heat transfer in the axial direction, and a heat flux generated by a resistance heater whose electricity consumption is measured is applied on one of its faces (say, the left face). A total of 9 thermocouples are imbedded into the sample, 1 cm apart, to measure the temperatures along the sample and on its faces. When the power consumption was fixed at 83.45 W, it is observed that the thermocouple readings are stabilized at the following values:

Distance from left face, cm	Temperature, °C
0	89.38
1	83.25
2	78.28
3	74.10
4	68.25
5	63.73
6	49.65
7	44.40
8	40.00

Plot the variation of temperature along the sample, and calculate the thermal conductivity of the sample material. Based on these temperature readings, do you think steady operating conditions are established? Are there any temperature readings that do not appear right and should be discarded? Also, discuss when and how the temperature profile in a plane wall will deviate from a straight line.