7. Heat Transfer of Laminar Free Convection of Polyatomic Gas

Based on the study of Chap. 6, the temperature-dependent specific heat is further considered for investigation of laminar free convection of polyatomic gases with consideration of variable physical properties. The viscosity, thermal conductivity, and specific heat parameters are provided for a series of polyatomic gases. The governing energy ordinary differential equation is further derived out for consideration of temperature-dependent specific heat, by using the new similarity analysis method. A system of numerical solutions are obtained for variation of the temperature parameters \(n_\upmu , n_\lambda \), and \(n_{c_\mathrm{p} } \), Prandtl number, and the boundary temperature ratio . It is seen from the numerical results that there are obvious effects of variable physical properties on velocity and temperature fields, as well as heat transfer of free convection of polyatomic gases. The theoretical equations of heat transfer of polyatomic gas free convection created based on the heat transfer analysis contain a only one no-given variable, the wall temperature gradient. Based on the system of numerical solutions on the wall dimensionless temperature gradient, the prediction equation of the wall temperature gradient is created by means of a curve-fitting method, and then, the theoretical equations on heat transfer are available for prediction of heat transfer. It is found that the gas temperature parameters, Prandtl number, and the boundary temperature ratio dominate the heat transfer of laminar free convection of polyatomic gases. Because the temperature parameters are based on the typical experimental data, these equations on heat transfer are reliable for engineering prediction of laminar free convection of polyatomic gas.