Steps in Determining Thermal Conductivity

Flash Method

• To determine thermal conductivity, thermal diffusivity and heat capacity, take a high-intensity short-duration flash lamp and a thermally insulated specimen a few millimeters thick, coated with camphor black. Direct the light pulse to the specimen. Measure the temperature history of the rear surface using a thermocouple. Record your measure with an oscilloscope and camera. Determine the thermal diffusivity by the shape of the temperature versus time curve at the rear surface, the heat capacity by the maximum temperature indicated by the thermocouple and the thermal conductivity by the product of multiplying the heat capacity, the thermal diffusivity and the density.

Mathematical Method

• Although the \"k\" of the particular material can be found in the thermal conductivity table, this co-efficient can be calculated by using formula: k = Q * L / [A (?T)]

Data Collection

• You need to know the heat transferred under steady condition \"Q;\" the thickness of the material \"L;\" the cross-sectional area of the surface \"A;\" and the temperature differential \"?T\" that can be found through the final (outer) temperature and initial (inner) temperatures. Convert all your units required in the problem to the same standard.

Example Problem

• Find the thermal conductivity of an aluminum pan that has a flat bottom at a 10cm radius and a thickness at 0.4 cm. Heat is transferred steadily to boiling water in the pan through the bottom at a rate of 800W. The inner surface temperature of the pan bottom is 105 degrees C and the temperature of the outer surface of the bottom of the pan is 105.43 degrees C.

Calculation

• Convert cm into meters: 10cm=0.1m
  0.4cm=0.004m

  Find an area of the surface of the pan \"A\" by multiplying the number 3.14 (pi) by radius square to the second power.

  A= 3.14*0.1²=0.0314m²

  Subtract the outer temperature from the inner temperature. Be sure that both are in Celsius.
  ?T= 105.43-105=0.43°C

  Calculate the value of thermal conductivity \"k\" by using the calculator and the formula below:

  k=Q*L/A*?T=800*0.004/0.0314*0.43=237 W/m*°C

  This will be your answer in watts/meter*degrees Celsius.