Accurately solving transient nonlinear inverse heat conduction problems in complex structures is of great importance to provide key parameters for modeling coupled heat transfer process and the structure’s optimizati...Accurately solving transient nonlinear inverse heat conduction problems in complex structures is of great importance to provide key parameters for modeling coupled heat transfer process and the structure’s optimization design.The finite element method in ABAQUS is employed to solve the direct transient nonlinear heat conduction problem.Improved particle swarm optimization(PSO)method is developed and used to solve the transient nonlinear inverse problem.To investigate the inverse performances,some numerical tests are provided.Boundary conditions at inaccessible surfaces of a scramjet combustor with the regenerative cooling system are inversely identified.The results show that the new methodology can accurately and efficiently determine the boundary conditions in the scramjet combustor with the regenerative cooling system.By solving the transient nonlinear inverse problem,the improved particle swarm optimization for solving the transient nonlinear inverse heat conduction problem in a complex structure is verified.展开更多
The flow of an Oldroyd 8-constant fluid between coaxial cylinders with variable viscosity is considered.The heat transfer analysis is also taken into account.An analytical solution of the non-linear problem is obtaine...The flow of an Oldroyd 8-constant fluid between coaxial cylinders with variable viscosity is considered.The heat transfer analysis is also taken into account.An analytical solution of the non-linear problem is obtained usinghomotopy analysis method.The behavior of pertinent parameters is analyzed and depicted through graphs.展开更多
The existence of classical solutions to a stationary simplified quantum energytransport model for semiconductor devices in 1-dimensional space is proved.The model consists of a nonlinear elliptic third-order equation ...The existence of classical solutions to a stationary simplified quantum energytransport model for semiconductor devices in 1-dimensional space is proved.The model consists of a nonlinear elliptic third-order equation for the electron density,including a temperature derivative,an elliptic nonlinear heat equation for the electron temperature,and the Poisson equation for the electric potential.The proof is based on an exponential variable transformation and the Leray-Schauder fixed-point theorem.展开更多
With the help of some reductions of the self-dual Yang Mills(briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of(2 + 1)-dimensional equations. Its first reductio...With the help of some reductions of the self-dual Yang Mills(briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of(2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation,the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new(2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of(2 + 1)-dimensional integrable couplings of a new(2 + 1)-dimensional integrable nonlinear equation.展开更多
In this paper we analyze the influence of free convection on nonlinear peristaltic transport of a Jeffrey fluid in a finite vertical porous stratum using the Brinkman model. Heat is generated within the fluid by both ...In this paper we analyze the influence of free convection on nonlinear peristaltic transport of a Jeffrey fluid in a finite vertical porous stratum using the Brinkman model. Heat is generated within the fluid by both viscous and Darcy dissipations. The coupled nonlinear governing equations are solved analytically. The expressions for the temperature, the axial velocity, the local wall shear stress and the pressure gradient are obtained. The effects of various physical parameters such as the Jeffrey parameter λ1, the permeability parameter σ and the heat source/sink parameter β are analyzed through graphs, and the results are discussed in detail. It is observed that the velocity field increases with increasing values of the Jeffrey parameter but it decreases with increasing values of the permeability parameter. It is found that the pressure rise increases with decreasing Jeffrey parameter and increasing permeability parameter. We notice that the effect of the permeability parameter a is the strongest on the bolus trapping phenomenon. For λ1 = 0, N =0, the results of the present study reduce to the results of Tripathi [Math. Comput.Modelling 57 （2013） 1270-1283]. Further the effect of viscous and Darcy dissipations is to reduce the rate of heat transfer in the finite vertical porous channel under peristalsis.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12172078,51576026)Fundamental Research Funds for the Central Universities in China(No.DUT21LK04)。
文摘Accurately solving transient nonlinear inverse heat conduction problems in complex structures is of great importance to provide key parameters for modeling coupled heat transfer process and the structure’s optimization design.The finite element method in ABAQUS is employed to solve the direct transient nonlinear heat conduction problem.Improved particle swarm optimization(PSO)method is developed and used to solve the transient nonlinear inverse problem.To investigate the inverse performances,some numerical tests are provided.Boundary conditions at inaccessible surfaces of a scramjet combustor with the regenerative cooling system are inversely identified.The results show that the new methodology can accurately and efficiently determine the boundary conditions in the scramjet combustor with the regenerative cooling system.By solving the transient nonlinear inverse problem,the improved particle swarm optimization for solving the transient nonlinear inverse heat conduction problem in a complex structure is verified.
文摘The flow of an Oldroyd 8-constant fluid between coaxial cylinders with variable viscosity is considered.The heat transfer analysis is also taken into account.An analytical solution of the non-linear problem is obtained usinghomotopy analysis method.The behavior of pertinent parameters is analyzed and depicted through graphs.
基金the Vital Science Research Foundation of Henan Province Education Department(No.12A110024)
文摘The existence of classical solutions to a stationary simplified quantum energytransport model for semiconductor devices in 1-dimensional space is proved.The model consists of a nonlinear elliptic third-order equation for the electron density,including a temperature derivative,an elliptic nonlinear heat equation for the electron temperature,and the Poisson equation for the electric potential.The proof is based on an exponential variable transformation and the Leray-Schauder fixed-point theorem.
基金Supported by the Fundamental Research Funds for the Central Universities(2013XK03)the National Natural Science Foundation of China under Grant No.11371361
文摘With the help of some reductions of the self-dual Yang Mills(briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of(2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation,the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new(2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of(2 + 1)-dimensional integrable couplings of a new(2 + 1)-dimensional integrable nonlinear equation.
文摘In this paper we analyze the influence of free convection on nonlinear peristaltic transport of a Jeffrey fluid in a finite vertical porous stratum using the Brinkman model. Heat is generated within the fluid by both viscous and Darcy dissipations. The coupled nonlinear governing equations are solved analytically. The expressions for the temperature, the axial velocity, the local wall shear stress and the pressure gradient are obtained. The effects of various physical parameters such as the Jeffrey parameter λ1, the permeability parameter σ and the heat source/sink parameter β are analyzed through graphs, and the results are discussed in detail. It is observed that the velocity field increases with increasing values of the Jeffrey parameter but it decreases with increasing values of the permeability parameter. It is found that the pressure rise increases with decreasing Jeffrey parameter and increasing permeability parameter. We notice that the effect of the permeability parameter a is the strongest on the bolus trapping phenomenon. For λ1 = 0, N =0, the results of the present study reduce to the results of Tripathi [Math. Comput.Modelling 57 （2013） 1270-1283]. Further the effect of viscous and Darcy dissipations is to reduce the rate of heat transfer in the finite vertical porous channel under peristalsis.
