Integral quantities in heat transfer
For the heat transfer analysis, the most interesting integral values are: the heat flux, mean volume temperature.
The following notations are used in formulas:
G – vector of temperature gradient;
F – vector of heat flux density;
T – temperature.
Name, |
Formula and Description |
Heat flux qfInt_KGrad_n_ds |
Φ = s∫ (F·n)ds Heat flux through a particular surface. |
Temperature difference qfInt_Grad_t_dl |
ΔT = L∫ (G·t)dl The temperature difference between starting and ending points of a contour can be calculated as an integral over the contour of the temperature gradient. |
Average surface temperature qfInt_Potential_ds |
TS = 1/S s∫ T·ds |
Average volume temperature qfInt_Potential_dv |
TV = 1/V v∫ T·dv |
Average volume temperature gradient qfInt_Grad_dv |
Ga = 1/V v∫ G·dv Mean vector of temperature gradient in a volume. |
Average volume heat flux density qfInt_KGrad_dv |
Fa = 1/V v∫ F·dv Mean vector of heat flux density in a volume. |
Average volume temperature gradient qfInt_Grad2_dv |
Ga2 = 1/V v∫ G2·dv |
Mean square heat flux densisty qfInt_KGrad_dv |
Fa2 = 1/V v∫ F2·dv |
Line integral of heat flux density qfInt_KGrad_t_dl |
x = L∫ (F·t)dl |
Surface integral of grad(T) qfInt_Grad_n_ds |
x = s∫ (G·n)ds |