Heat and Mass Transfer
The time constant of a thermocouple is

The time taken to attain the final temperature to be measured
Determined by the time taken to reach 100°C from 0°C
The time taken to attain 63.2% of the value of initial temperature difference
The time taken to attain 50% of the value of initial temperature difference

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Heat and Mass Transfer
The heat transfer by conduction through a thick cylinder (Q) is given by (where T₁ = Higher temperature, T₂ = Lower temperature, r₁ = Inside radius, r₂ = Outside radius, l = Length of cylinder, and k = Thermal conductivity)

Q = 2.3 log (r₂/r₁)/[2πlk (T₁ - T₂)]
Q = = 2πlk/2.3 (T₁ - T₂) log (r₂/r₁)
Q = [2πlk (T₁ - T₂)]/2.3 log (r₂/r₁)
Q = [2π (T₁ - T₂)]/2.3 lk log (r₂/r₁)

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