Theoretical Temperature Profile of AC Calorimetric Sensor

Language: Python / Matlab

Part A: Image Processing (Construct a 3D array for finite element calculation) 

1) Take a picture of the calorimeter first, 

2) Trace color, extract feature and apply geometric transformation. Delete noisy data if necessary . 

Part B: Numerical Physics (Finite Element Method)

Apply time-dependent heat equation to calculate the thermal profile of the calorimeter as a function of time.

The calorimeter is put in vacuum chamber. Radiative loss on all surfaces are considered. The chip is heated by time-dependent current source.

The thermal map of the AC calorimetric sensor without sample is simulated. 

The thermocouple pairs are aligned in V-shape

The silicon chip (red area) is suspended by four wires on XY plane.  Two wires are for current injection while the other wires are designed for thermocouple. The input heating power of the chip can be converted from the values of electrical resistance & current. 

The geometric ratios of the chip are X : Z = 60 and Y : Z = 40, respectively. Z refers to the thickness of the chip

The copper block (blue area) acts as a heat sink. 

The sinusoidal heater (0.3W, 7.14Hz) provides thermal energy by sending current to the levitating silicon chip

Surrounding temperature in vacuum= 299.9K 

Theoretical results: (Error: 8% when compared to experiment values)

*The DC temperature offset between two thermocouple ends is 0.481K 

*Amplitude of the AC modulation in Kelvin is 0.0041K. 

The above results are obtained by solving time-dependent heat equation numerically where the parameters are listed below

Q is the heating power in a given volume
P' is the radiation power loss in a given volume
k is thermoconductance
T is temperature
t is time
p is density
c is specific heat

The sample will be put on top of the silicon chip during measurement. For the sample with large heat capacity, the thermocouple voltage becomes smaller. (vice versa)

*Please watch the video to see how the temperature (or the vertical color bar) changes. A high-quality screen is required to display the tiny variation in temperature.