outside temperature after insulation 3

[Enkelaar]

Currently we have a vessel with an assumed wall temperature of 450ºC insulated with 200 mm Rockwool. As there are instruments installed outside the insulation capable of a temperature of approx 65ºC we wish to make sure the temperature increase through the insulation is not a problem.

The way I see it is as follows.

Heat Loss through the insulation is approx 30 kW/100 m2, therefore 300 W per m; 300 J/s.

Assuming the instrument is placed approx 30 cm outside the insulation, approx 0,3 m3 of air between instrument and insultaion will be heated; ~ 0,4 kg. Thermal conductivity of air; 1205 J/Kg/K, so for a temperature increase off 1º approx 500 J is required.

So the instant rise would be approx 0,6/0.7 ºC/K, however every second new heat loss through the insulation appears. Can I assume that due to normal convection, wind etc I can neglect the temperature to increase >>10ºC ? The instrument is located on the cone of the vessel, so it is not heated from below.

 

[25362]

Knowing the pipe temperature, the insulation conductivity, its thickness and the heat flux of 300 W/m² = 300 J.m^-2.s^-1; IMHO one could estimate the insulation's external surface temperature.

Also, apart from convection by air movement, radiation effects can introduce appreciable errors in the thermometer reading.

Besides, the value of 1205 J.kg^-1.K^-1 is not air's thermal conductivity but its specific heat capacity, and the value at, say, 300 K and atmospheric pressure, is about 1006 J.kg^-1.K^-1.
Air's thermal conductivity at 300 K is taken at 0.0262 W.m^-1.K^-1. Data taken from J.P. Holman's: Heat Transfer.

There is a nomograph by V. Ganapathy on the Chemical Engineering issue of February 20, 1984, that may be helpful. Its title: Estimate convective heat losses from surfaces

 

[ione]

Heat flux of 300 W/m^2 with 450 °C wall vessel temperature and 200 mm insulation thickness?

Naaah.

With 200 mm insulation thickness (thermal conductivity of insulation 0,0595 W/(m*K)) and 20°C ambient temperature I got approx 125 W/m^2 heat flux.
Further to surface temperature I got 32.5 °C.

 

[Enkelaar]

Ione,

Doesn't the thermal conductivity of the rockwool vary with the mean temperature of the insulations (0.043^(0.0035*(Tmean))? I used 450ºC giving 0.208 W/m/K, but mean temperature would indeed be 235ºC giving 0.098 W/m/K. In that case I get a heat flux of approx 210 W/m^2.

Heatloss = 0.098 * (450-20) / 0.200

But how did you calculate the surface temperature from your 125 W/m^2?

 

[ione]

With 0.098 W/(m*K) as thermal conductivity, which is anyway a quite high value for mineral wool at 235 °C, I got approx 40 °C as surface temperature and a heat flux of 201 W/m^2.

You can go with an iterative procedure (take a glance here

http://www.eng-tips.com/viewthread.cfm?qid=268145

) or use a software as I usually do.

 

[25362]

Holman's book, mentions the following thermal conductivities for rockwool, 10 lb/ft³, loosely packed: 0.087 W.m^-1.K^-1 at 260^oC; 0.067 W.m^-1.K^-1 at 150^oC, and 0.04 W.m^-1.K^-1 at 32^oC.

With a heat flux of 201 W/m², the above-mentioned nomograph gives a much larger [Δ]T between the temperature of the surface of a vertical cylinder and the surrounding air, in natural convection.

 

[ione]

25362,

I don't know why a discrepancy in results has arisen, but I'd really appreciate if you could give me an idea of the value which Holman's nomograph foresees as I don't have access to this book.

What I can say is that:
1)I've taken the cylindrical tank as it were a flat vertical plate
2) htc for the outer surface is 10 W/(m^2*K), taking into account natural convection plus radiative heat transfer contribution

 

[25362]

To ione,

The nomograph by Ganapathy appeared in an old ChE issue, not in Holman's book. Based on a vertical plate, it gives a ?T of 80^oF ~ 44^oC due to natural convection only.

You have rightly assumed a convection plus radiation effect.

If we assume Holman's simplified equation for the free convection coefficient for air taking GrPr > 10⁹, h_c = 0,95(?T)^1/3, using ?T = 20 K, we get h_c ~ 2.6 W.m^-2.K^-1.

The question is, of course, what is the radiation h_r component, which depends not only on the temperatures, but also on the coefficient of emissivity.

If aluminium sheets are used to cover the rockwool insulation (a fact Enkelaar has not detailed), the value of h_r may be quite low, and the combined h_c+ h_r may be lower than 10 W.m^-2.K^-1.

Do you agree?

 

[ione]

25362,

Thanks for your reply.

For a vertical plane, natural convection and a deltaT of 20 K, I got h = 3.6 W/(m^2*K). This is probably due to the fact the simplified formula I’ve got for this scenario is:

h = 1.35*(deltaT)^1/3

I had considered an aluminium cover too, but what really matters is I committed an error entering 0.9 for aluminium emissivity instead of 0.09 (it’s not by chance you’re the best in the heat transfer forum).


Rerunning….. a much more realistic heat transfer coefficient would be approx 5 W/(m^2*K) and this will rise the outside temperature up to 54 °C (assuming an average thermal conductivity of 0.085 W/(m*K) for the insulation).

 

[25362]

It's you who did the calculation. Therefore you deserve a star.