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Equivalent air cavities thermal conductivity calculator

air cavity thermal conductivity calculator

QuickField thermal analysis modules may be applied for the simulation of temperature and heat flux distribution in building components. But the heat transfer across the air filled cavities, present in such models, includes convection and radiation, and formally speaking requires the complicated CFD analysis.
However, the international standard ISO 10077-2:2012 Thermal performance of windows, doors and shutters -- Calculation of thermal transmittance -- Part 2: Numerical method for frames offers the practical method of calculating the equivalent thermal conductivity of the air filled cavities. The calculations are based on the replacement of arbitrary shaped cavity by the equivalent rectangle, oriented along the direction of the heat flux along the cavity. Then using the maximum temperature difference on the cavity boundary and this equivalent rectangle dimensions, formulas provide both convective and radiative thermal conductivity coefficients. Using these two coefficients the equivalent thermal conductivity of the air filled cavity is then calculated, and for slightly ventilated cavities the value should be doubled.

Т1 =
°C

Air in the window frame cavity

Width b= mm

Height d= mm

Т2 =
°C

Equivalent thermal conductivity W/m-K

Excel spreadsheet was developed to implement this method using ActiveField interface (macros should be enabled). It interacts with the corresponding QuickField Static Heat transfer problem, which should be open. Air cavities in QuickField problem should be marked by separate block labels. Spreadsheet consists of three worksheets - UI, ContourCalculations and CavityCoeffs.

User Interface (UI) worksheet is the only page where user should enter the input data for calculations: air block labels, their ventilation type (1-non-ventilated, 2-slightly ventilated), and their initial thermal conductivities. Clicking on the button "Clear data" clears all the calculated data from the previous run. Clicking "Make the next step" replaces the thermal conductivities in the QuickField data file by the currently displayed values in the table, and one iteration of the equivalent air cavity conductivity calculations runs. These steps should be repeated till the relative errors of air blocks conductivities are less than 1e-6 (all zeroes in the "error" column). This accuracy is more than required by ISO 10077-2:2012 validation guidelines.
ContourCalculations worksheet has the formulas for equivalent rectangle calculations and maximum temperature differences for all air blocks, and CavityCoeffs worksheet uses these results in formulas for convective, radiative and equivalent heat transfer coefficient calculations. VBA Macros assure interaction with QuickField and input/output at the UI page.

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