Tham khảo tài liệu 'two phase flow phase change and numerical modeling part 18', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 500 Two Phase Flow Phase Change and Numerical Modeling y Y or y i 0 div direction normal to the inclined plane dimensionless y granular material constitutive coefficients i 0 to 5 volume fraction bulk density reference density temperature divergence operator gradient symbol outer product 3. Governing equations The balance laws in the absence of chemical and electromagnetic effects are the conservation of mass linear momentum angular momentum and energy Truesdell Noll 1992 . The conservation of mass in the Eulerian form is given by div pu o 1 where u is the velocity is the density and t is the partial derivative with respect to time. The balance of linear momentum is du . m p-j divT pb 2 where d dt is the total time derivative given by grad . u 3 dt t where b is the body force and T is the Cauchy stress tensor. The balance of angular momentum in the absence of couple stresses yields the result that the Cauchy stress is symmetric. The energy equation in general can have the form p - divq r QC0K0 4 dt where denotes the specific internal energy q is the heat flux vector r is the radiant heating Q is the heat of reaction Co is the initial concentration of the reactant species Ko is the reaction rate expression which is a function of temperature and L is the velocity gradient. For most common applications where there are no chemical reactions or heat generation the last term on the right hand side is ignored. It should also be noted that the form of the energy equation for a complex fluid is in general not the same as the standard energy equation given in many books and articles where the substantial or total time derivative of the temperature appears on the left hand side of Eqn 4 instead of the internal energy. For the detailed derivation of Eqn 4 and the assumptions implicit in obtaining this form using the First Law of Thermodynamics see Appendix A. Heat Transfer in Complex Fluids 501 Thermodynamical considerations require the application of the second law of .
