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Message ID: 2191     Entry time: Fri May 25 14:20:55 2018
Author: shruti 
Type: DailyProgress 
Category: TempCtrl 
Subject: Simulation and measurement of thermal conductivity time constant - Vacuum Can 

A model of vacuum can was constructed taking into account the heat conduction across the foam, neglecting the geometry of the foam and approximating an effective cross-sectional area and thickness.

The analytically calculated time for the decay of temperature to 1/e of the initial value  (time constant) = d*m*C/k/A = 2.99 hours, with constant ambient temperature and no heating. The parameters used in this calculation :

Material and dimensional parameters of vac can
Mass of assembly m 15.76 kg
Specific heat of steel can C 505 J/kg-K
Heat conduction cross sec area A 1.3 m^2
Thickness d 5.08e-2 m
Thermal conductivity constant k 1.136*25.4e-3 W/m-K

'A' is not known very accurately and could even be as low as 0.48 m^2, and since the time constant is very sensitive to A a better estimate is required for a more accurate model. The units for 'k' in the spec sheet was confusingly W/m^2-K, nonetheless an approximation was made assuming it scales by thickness. An experiment to measure the time constant is now underway. This will give us a better idea of the values.

In order to study the evolution of temperature, scipy.odeint was used to perform numerical integration of the following equation:

\frac{\text{d}T_{can}}{\text{d}t} = -\frac{kA}{mC}\frac{(T_{can}-T_{amb})}{d} + \frac{H}{mC},

where 'H' is the heating power.

This can be done even in the presence of fluctuating ambient temperatures and variable heating power (taken as a lists, piecewise functions).

In the two trial plots shown, the ambient temperature was stepped up from 300K to 315K at 10000 s (~2.77hours). One plot shows the evolution without heating and the other with a heating power of 18.46 W.

Attachment 1: Temp_18W_StepTempAmbient.pdf  50 kB  Uploaded Fri May 25 15:21:55 2018  | Hide | Hide all
Temp_18W_StepTempAmbient.pdf
Attachment 2: Temp_NoHeat_StepTempAmbient.pdf  63 kB  Uploaded Fri May 25 15:22:11 2018  | Hide | Hide all
Temp_NoHeat_StepTempAmbient.pdf
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