Quick Measurement of Thermal Conductivity by a Small Spherical Heat Source

Abstract

An apparatus of spherical shell type of the radius s of a few mm having uniformly distributed point heat sources on its surface is used for measuring thermal conductivity.
The thermal conductivity is given by the equation
k=q₀/4πθ·1/s_??_
on the assumption of no heat loss, Θ∞ being the temperature rise of the center of the shell after infinite time, q₀ the heat input per unit time.
Correction for the heat loss through the lead wires of the heater and thermocouples is performed by the equation k_??_k+b√k_m, where k_m is the thermal conductivity by the aforementioned equation assuming no heat loss, k the true conductivity and b a certain constant of the apparatus. This equation is derived by the condition of heat conservation q₀=q_l∞+q_∞ at infinite time where q_l∞ is the heat loss through leads and q∞ the heat input to the shell, both per unit time.