Governing Equations(Contd) Define B, the volumetric thermal expansion coefficient B pa7丿p For an ideal gas:P、RT RT Thus: B For liquids and non-ideal gases, see appendix a In general 1△, B p△Tp1-7 p≈pB(T-7 Density gradient is due to the temperature gradient Heat Transfer Su Yongkang School of Mechanical EngineeringHeat Transfer Su Yongkang School of Mechanical Engineering # 9 Governing Equations (Cont’d) • Define , the volumetric thermal expansion coefficient. • In general, T Thus RT RT P P T P 1 : For an ideal gas : 1 = =  =         = −       For liquids and non-ideal gases, see appendix A T T −T − = −    −         1 1 ( )   −    T −T Density gradient is due to the temperature gradient