Brīvās konvekcijas koeficients

Horizontāli novietotam cilindram

1. Ja dots plūsmas garums L (puse no apkārtmēra)

\alpha = {{{Nu__L} \cdot \lambda } \over L} L = \frac{\pi}{2} \cdot D
{Nu__L} = {\left\{ {0.752 + {{0.387Ra_L^{{1 \mathord{\left/ {\vphantom {1 6}} \right. \kern-\nulldelimiterspace} 6}} } \over {\left[ {1 + \left( {{{0.559} \mathord{\left/ {\vphantom {{0.559} {\Pr }}} \right. \kern-\nulldelimiterspace} {\Pr }}} \right)^{{9 \mathord{\left/ {\vphantom {9 {16}}} \right. \kern-\nulldelimiterspace} {16}}} } \right]^{{8 \mathord{\left/ {\vphantom {8 {27}}} \right. \kern-\nulldelimiterspace} {27}}} }}} \right\}^2 }
{Ra__L} = {Gr__L} \cdot \Pr
{Gr__L} = {{g\beta (T_s - T_\infty )L^3 } \over {\nu ^2 }}

2. Ja dots diametrs D

\alpha = {{{Nu__D} \cdot \lambda } \over D}
{Nu__D} = \left\{ {0.600 + {{0.387{Ra__D}^{{1 \mathord{\left/ {\vphantom {1 6}} \right. \kern-\nulldelimiterspace} 6}} } \over {\left[ {1 + \left( {{{0.559} \mathord{\left/ {\vphantom {{0.559} {\Pr }}} \right. \kern-\nulldelimiterspace} {\Pr }}} \right)^{{9 \mathord{\left/ {\vphantom {9 {16}}} \right. \kern-\nulldelimiterspace} {16}}} } \right]^{{8 \mathord{\left/ {\vphantom {8 {27}}} \right. \kern-\nulldelimiterspace} {27}}} }}} \right\}^2  {Ra__D} \lesssim 10^{12}
{Ra__D} = {Gr__D} \cdot \Pr
{Gr__D} = {{g\beta (T_s - T_\infty )D^3 } \over {\nu ^2 }}

Apzīmējumi

\alpha – konvekcijas koeficients;
Nu – Nusselta skaitlis; temperatūras gradients pie virsmas, bezdimensiju lielums;
\lambda – gāzes/šķidruma siltumvadīšanas koeficients;
Pr – Prandtla skaitlis; dots no tabulām; “ratio of the momentum diffusivity \nu to the thermal diffusivity \alpha” (cits \alpha); bezdimensiju lielums;
Gr – Grasshofa skaitlis; “ratio of the buoyancy forces to the viscous forces”; analogs Reinoldsa skaitlim Re, kas ir “ratio of the inertial to viscous forces”;
g – brīvās krišanas paātrinājums 9.81 m/s^2;
\beta – termālās izplešanās koeficients; ideālām gāzēm = 1/T;
T_s – virsmas temperatūra;
T_\infty – apkārtējās vides temperatūra;
\nu – viskozitāte.

Formulas ņemtas no Incropera (izmantojot D) un Warmewatlas (izmantojot L), un ir ekvivalentas.

  1. Incropera F.P. Fundamentals of Heat and Mass Transfer. 6th ed. Hoboken (NJ) : Wiley, 2006. 1024 p.
  2. VDI-Wärmeatlas. 9. Aufl. Berlin : Springer, 2002.

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