The temperature of a gas stream is measured by a thermocouple whose junction can be approximated as a 1.2mm diameter sphere.
The properties of the junction are:
K = 40.5 W/m*k p= 7950 kg/m^3 Cp= 345 J/kg*k
The heat transfer coefficient between the junction and the air where h= 250 W/m^2 * K
Determine how long it will take the thermocouple to read 50% and 99% of the initial temperature.
Sphere: diameter = 1.2mm
Please see attachment.
We will assume that heat is released (absorbed) by the spherical thermocouple to (from) the air mass flow by forced convection at the sphere surface. We will neglect the conduction, since this gives in general errors in thermocouples measurements.
T = actual temperature of the sphere surface
T0 = initial temperature of the sphere surface
Ta = air temperature
Let's suppose also that the sphere is warmer than the air ...
This solution contains step-by-step calculations to determine how long it will take the thermocouple to read 50% and 99% of the initial temperature.