In order to solve the heat damages in deep mines, a cool-wall cooling technology and its working model are proposed based on the principles of heat absorption and insulation in this paper. During this process, the dif...In order to solve the heat damages in deep mines, a cool-wall cooling technology and its working model are proposed based on the principles of heat absorption and insulation in this paper. During this process, the differential equation of thermal equilibrium for roadway control unit is built, and the heat adsorption control equation of cool-wall cooling system is derived by an integral method, so as to obtain the quantitative relationship among the heat absorption capacity of cooling system, the heat dissipating capacity of surrounding rock and air temperature change. Then, the heat absorption capacity required by air temperature less than the standard value for safety is figured out by section iterative method with the simultaneous solution of heat absorption control equation and the heat dissipation density equation of surrounding rock. Finally, the results show that as the air temperature at the inlet of roadway is 25 ℃, the roadway wall is covered by heat-absorbing plate up to 39% of the area, as well as the cold water is injected into the heat-absorbing plate with a temperature of 20 ℃ and a mass flow of 113.6 kg/s, the air flow temperature rise per kilometer in the roadway can be less than 3 ℃.展开更多
This paper deals with positive solutions of a degenerate parabolic system: u t= Δ u m+ v p ln α(h+u), v t= Δ v n+u q ln β(h+v) with homogeneous Dirichlet boundary conditions and positive in...This paper deals with positive solutions of a degenerate parabolic system: u t= Δ u m+ v p ln α(h+u), v t= Δ v n+u q ln β(h+v) with homogeneous Dirichlet boundary conditions and positive initial conditions. This system describes the processes of diffusion of heat and burning in two component continuous media with nonlinear conductivity and volume energy release. We obtain the global existence and blow up results of the solution relying on comparison with carefully constructed upper solutions and lower solutions.展开更多
In this paper,we have numerically examined the steady boundary layer of a viscous incompressible nanofluid and its heat and mass transfers above a horizontal flat sheet.The boundary conditions considered were a nonlin...In this paper,we have numerically examined the steady boundary layer of a viscous incompressible nanofluid and its heat and mass transfers above a horizontal flat sheet.The boundary conditions considered were a nonlinear magnetic field,a nonlinear velocity and convection.Such nonlinearity in hydrodynamic and heat transfer boundary conditions and also in the magnetic field has not been addressed with the great details in the literature.In this investigation,both the Brownian motion and thermophoretic diffusion have been considered.A similarity solution is achieved and the resulting ordinary differential equations (nonlinear) are worked numerically out.Upon validation,the following hydrodynamic and heat and mass transfers parameters were found:the reduced Sherwood and Nusselt numbers,the reduced skin friction coefficient,and the temperature and nanoparticle volume fraction profiles.All these parameters are found affected by the Lewis,Biot and Prandtl numbers,the stretching,thermophoretic diffusion,Brownian motion and magnetic parameters.The detailed trends observed in this paper are carefully analyzed to provide useful design suggestions.展开更多
We have considered the basic dynamic homogeneous system of partial differential equations of generalized Green-Lindsay couple-stress thermodiffusion on the plane for homogeneous, isotropic elastic media with the centr...We have considered the basic dynamic homogeneous system of partial differential equations of generalized Green-Lindsay couple-stress thermodiffusion on the plane for homogeneous, isotropic elastic media with the centre of symmetry. We have constructed regular solution of the boundary problems on the line. In the works are obtained in quadrates the solution of the boundary-value problem of the generalized Green-Lindsay theory of couple-stress thermodiffusion, when on border of area are given： the component of normal of displacement vector, the component of touching of stress vector, rotations, flow of heat and flow of diffusion.展开更多
基金Project(2018CXNL08) supported by the Fundamental Research Funds for the Central Universities,China。
文摘In order to solve the heat damages in deep mines, a cool-wall cooling technology and its working model are proposed based on the principles of heat absorption and insulation in this paper. During this process, the differential equation of thermal equilibrium for roadway control unit is built, and the heat adsorption control equation of cool-wall cooling system is derived by an integral method, so as to obtain the quantitative relationship among the heat absorption capacity of cooling system, the heat dissipating capacity of surrounding rock and air temperature change. Then, the heat absorption capacity required by air temperature less than the standard value for safety is figured out by section iterative method with the simultaneous solution of heat absorption control equation and the heat dissipation density equation of surrounding rock. Finally, the results show that as the air temperature at the inlet of roadway is 25 ℃, the roadway wall is covered by heat-absorbing plate up to 39% of the area, as well as the cold water is injected into the heat-absorbing plate with a temperature of 20 ℃ and a mass flow of 113.6 kg/s, the air flow temperature rise per kilometer in the roadway can be less than 3 ℃.
文摘This paper deals with positive solutions of a degenerate parabolic system: u t= Δ u m+ v p ln α(h+u), v t= Δ v n+u q ln β(h+v) with homogeneous Dirichlet boundary conditions and positive initial conditions. This system describes the processes of diffusion of heat and burning in two component continuous media with nonlinear conductivity and volume energy release. We obtain the global existence and blow up results of the solution relying on comparison with carefully constructed upper solutions and lower solutions.
文摘In this paper,we have numerically examined the steady boundary layer of a viscous incompressible nanofluid and its heat and mass transfers above a horizontal flat sheet.The boundary conditions considered were a nonlinear magnetic field,a nonlinear velocity and convection.Such nonlinearity in hydrodynamic and heat transfer boundary conditions and also in the magnetic field has not been addressed with the great details in the literature.In this investigation,both the Brownian motion and thermophoretic diffusion have been considered.A similarity solution is achieved and the resulting ordinary differential equations (nonlinear) are worked numerically out.Upon validation,the following hydrodynamic and heat and mass transfers parameters were found:the reduced Sherwood and Nusselt numbers,the reduced skin friction coefficient,and the temperature and nanoparticle volume fraction profiles.All these parameters are found affected by the Lewis,Biot and Prandtl numbers,the stretching,thermophoretic diffusion,Brownian motion and magnetic parameters.The detailed trends observed in this paper are carefully analyzed to provide useful design suggestions.
文摘We have considered the basic dynamic homogeneous system of partial differential equations of generalized Green-Lindsay couple-stress thermodiffusion on the plane for homogeneous, isotropic elastic media with the centre of symmetry. We have constructed regular solution of the boundary problems on the line. In the works are obtained in quadrates the solution of the boundary-value problem of the generalized Green-Lindsay theory of couple-stress thermodiffusion, when on border of area are given： the component of normal of displacement vector, the component of touching of stress vector, rotations, flow of heat and flow of diffusion.
