Thermal expansion coefficient of air as applied to convective heat transfer
The thermal exchange coefficient used in calculating the convective heat transfer is dependent on the Rayleigh number.
For horizental tubes the Rayleigh number is calculated with the following formula
Ra = gB(Ts-Ta)D^3/va
In this formula B denotes the thermal expansion coefficient of air.
The Lugano testers in the report state about this coefficient :
β[K–1] is the volumetric thermal expansion coefficient, which, for an ideal gas (applied here to air for simplicity) is= 1/T
Indeed, for ideal gases the thermal expansion coefficient is 1/T.
While for many calculations air can be treated as an ideal gas, this is not true for it's volumetric thermal expansion coefficient.
In those cases that the thermal expansion coefficient does not follow the ideal gas law 1/T the data can be found in tables. Such a table also exist for the thermal expansion coefficient of air.
The differences for air between the tabulated values and the ideal law can be found in the folowing figure.
As can be seen the difference between the ideal thermal expansion coefficient and the real value can be quite large. The errors are for different temperatures shown in the following table
---Temp-----------Error
------K----------------%
----250------------- -0.8
----300--------------12.8
----350--------------15.2
----400--------------12.4
----450--------------11.0
----500--------------10.6
These errors result in an incorrect calculated convective heat transfer coefficient.
However since in the final calculation of the convective heat transfer coefficient the Rayleigh numer is raised to the power .25 for the temperature ranges used in Lugano, the error will be lower and reduced to a value between 2.3 % and 4.2 %.
The question is if the Lugano testers applied 1/T for the thermal expension coefficient for simplicity only as they state in their example calculation in the Lugano report, only for the calculation of the dummy run, or for all calculations.
If they used 1/T throughout then their calculated convective heat transfer was somewhat under estimated.