A1. A thermocouple, which is initially at 20°C, is inserted...

A1. A thermocouple, which is initially at 20°C, is inserted in a stream of hot gas at T. After 3 seconds the thermocouple reads 80°C while after 6 seconds it reads 110°C. Assuming applicability of the lumped thermal capacity model, estimate the temperature of the hot gas. What would be the temperature of the thermocouple after 10 seconds in the hot gas stream? Please note that, $a \ln x = \ln x^a$

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00:01 In this question we are given with the value of so density which is equal to 8800 kg per meter cube and we are given with the value of specific heat constant which is equal to 330 joule per kg kelvin and we are given with the height which is 210 or the heat coefficient.

00:19 So heat transfer coefficient which is equal to 210 watt per meter square kelvin.

00:24 Then we are given with a diameter as 1 millimeter which is equal to so then it implies radius will be 1 by 2 which is 0 .5 millimeter.

00:34 Then we have to find the characteristic length.

00:38 So characteristic length given by lc is equal to v by a where v is the volume a is the area.

00:47 So assuming it as a spherical path we have 4 by 3 pi into r square so r naught cube divided by 4 pi r square so which is equal to so 4 pi 4 pi get cancels we have so r square and r square get cancels we have r by 3 which is equal to 0 .5 into 10 power minus 3 by 3.

01:11 So we have the characteristic length is 1 .66 into 10 power minus 4 meter.

01:16 Then we have to find the biot number.

01:18 So biot number is given by bi is equal to h into lc by k where we have given with the values so h is 210 into characteristics length is found which is 1 .66 into 10 power minus 4 divided by k value is 38.

01:40 So here k is given the thermal conductivity which is 38 watt per meter kelvin.

01:46 So we have this is 38 which is equal to 9 .21 into 10 power minus 4.

01:52 So we have the condition that if biot number is less than the 0 .1 then we can say that lumped system analysis can be applied analysis applied...

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