TAILIEUCHUNG - Heat Conduction Basic Research Part 13

Tham khảo tài liệu 'heat conduction basic research part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Self-Similar Hydrodynamics with Heat Conduction 289 quantities just for readers comprehension. The behavior of the velocity for V OT may seem physically unacceptable at least in a rigorous sense. As a matter of fact however there are a number of examples for implosions and explosions in which the velocity profile is approximately linear with the radius Sedov 1959 Bernstein 1978 . In addition the physical condition at enough large radii f 1 will not affect the core dynamics for an intermediate time period. Therefore when we restrict our considerations to a finite closed volume containing the core the present self-similar solution is expected to be an approximation of the core evolution at higher densities and temperatures. Normalized density g Fig. 7. g - 1 diagram showing the optimization process of the eigenvalue Kv Fig. 8. Eigenstructure of the self-similar solution. 290 Heat Conduction - Basic Research Under the condition that the right integrated curve is to converge to g T 0 each curve has already optimized with respect to K2 as was shown in Fig. 6. Other fixed parameters are the same as in Fig. 6. The normalized physical quantities are obtained as a result of the two-dimensional eigenvalue problem with fixed parameters m 2 n 13 2 and Y 5 3. 5. Conclusions The crucial role of dimensional analysis and self-similarity are discussed in the introduction and the three subsequent examples. Self-similar solutions for individual cases have been demonstrated to be derivable by applying the Lie group analysis to the set of PDE for the hydrodynamic system taking nonlinear heat conductivity into account as the decisive physical ingredient. The scaling laws for thermally conductive fluids are conspicuously different from those for adiabatic fluids not discussed in the present chapter see references by Murakami et al. 2002 2005 for details . The former has one freedom less than the latter due to the additional constraint of thermal conductivity. If a thermo-hydrodynamic .

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