An investigation is made to study the heat transfer in boundary layer stagnationpoint flow over a non-isothermal permeable shrinking sheet with suction/injection.In this study,power-law variation of sheet temperature...An investigation is made to study the heat transfer in boundary layer stagnationpoint flow over a non-isothermal permeable shrinking sheet with suction/injection.In this study,power-law variation of sheet temperature is considered.By similarity transformation,the governing equations with the boundary conditions are transformed to self-similar nonlinear ordinary differential equations and then those are solved numerically by shooting method.In presence of variable sheet temperature,the variation of temperature is analysed.For larger shrinking rate compared to that of straining rate,dual solutions for velocity and temperature are obtained.It is found that for positive value of power-law exponent of variable sheet temperature heat transfer at the sheet as well as heat absorption at the sheet with temperature overshoot near the sheet occur and for negative value heat transfer from the sheet occurs though there is overshoot away from the sheet.With increasing positive power-law exponent heat transfer reduces for first solution and heat absorption enhances for second solution.Whereas,with increasing magnitude of negative power-law exponent heat transfer increases for second solution and for first solution the heat transfer increases for larger shrinking rate and it decreases for smaller shrinking rate.Due to suction heat transfer/absorption increases in all cases and for injection heat transfer/absorption increases for first solution and decreases for second solution.Also,interesting effects of suction/injection and Prandtl number on temperature distribution are observed when the sheet temperature varies(directly/inversely)along the sheet.展开更多
A unified mathematical model is established to simulate the nonlinear unsteady percolation of shale gas with the consideration of the nonlinear multi-scale effects such as slippage, diffusion, and desorption. The cont...A unified mathematical model is established to simulate the nonlinear unsteady percolation of shale gas with the consideration of the nonlinear multi-scale effects such as slippage, diffusion, and desorption. The continuous inhomogeneous models of equivalent porosity and permeability are proposed for the whole shale gas reservoir includ- ing the hydraulic fracture, the micro-fracture, and the matrix regions. The corresponding semi-analytical method is developed by transforming the nonlinear partial differential governing equation into the integral equation and the numerical discretization. The nonlinear multi-scale effects of slippage and diffusion and the pressure dependent effect of desorption on the shale gas production are investigated.展开更多
We have constrained a small-scale,dome-shaped low-velocity structure near the core-mantle boundary(CMB)of Earth beneath Perm(the Perm anomaly)using travel-time analysis and three-dimensional(3-D)forward waveform model...We have constrained a small-scale,dome-shaped low-velocity structure near the core-mantle boundary(CMB)of Earth beneath Perm(the Perm anomaly)using travel-time analysis and three-dimensional(3-D)forward waveform modeling of seismic data sampling of the mantle.The best-fitting dome-shaped model centers at 60.0°E,50.5°N,and has a height of 400 km and a radius that increases from 200 km at the top to 450 km at the CMB.Its velocity reduction varies from 0%at the top to–3.0%at 240km above the CMB to–3.5%at the CMB.A surrounding 240-km-thick high-velocity D''structure has also been detected.The Perm anomaly may represent a stable smallscale chemical pile in the lowermost mantle,although the hypothesis of a developing mantle plume cannot be ruled out.展开更多
Although there has been significant progress in the seismic imaging of mantle heterogeneity, the outstanding issue that remains to be resolved is the unknown distribution of mantle temperature anomalies in the distant...Although there has been significant progress in the seismic imaging of mantle heterogeneity, the outstanding issue that remains to be resolved is the unknown distribution of mantle temperature anomalies in the distant geological past that give rise to the present-day anomalies inferred by global tomography models. To address this question, we present 3-D convection models in compressible and self-gravitating mantle initialised by different hypothetical temperature patterns. A notable feature of our forward convection modelling is the use of self-consistent coupling of the motion of surface tectonic plates to the underlying mantle flow, without imposing prescribed surface velocities （i.e., p/ate-like boundary condition）. As an approximation for the surface mechanical conditions before plate tectonics began to operate we employ the no-slip （rigid） boundary condition. A rigid boundary condition dem- onstrates that the initial thermally-dominated structure is preserved, and its geographical location is fixed during the evolution of mantle flow. Considering the impact of different assumed surface boundary conditions （rigid and plate-like） on the evolution of thermal heterogeneity in the mantle we suggest that the intrinsic buoyancy of seven superplumes is most-likely resolved in the tomographic images of present-day mantle thermal structure. Our convection simulations with a plate-like boundary condition reveal that the evolution of an initial cold anomaly beneath the Java-lndonesian trench system yields a long-term, stable pattern of thermal heterogeneity in the lowermost mantle that resembles the present- day Large Low Shear Velocity Provinces （LLSVPs）, especially below the Pacific. The evolution of sub- duction zones may be, however, influenced by the mantle-wide flow driven by deeply-rooted and long- lived superplumes since Archean times. These convection models also detect the intrinsic buoyancy of the Perm Anomaly that has been identified as a unique slow feature distinct from the two principal LLSVPs. We find there is no need for dense chemical ＇piles＇ in the lower mantle to generate a stable distribution of temperature anomalies that are correlated to the LLSVPs and the Perm Anomaly. Our tomography-based convection simulations also demonstrate that intraplate volcanism in the south-east Pacific may be interpreted in terms of shallow small-scale convection triggered by a superplume beneath the East Pacific Rise.展开更多
文摘An investigation is made to study the heat transfer in boundary layer stagnationpoint flow over a non-isothermal permeable shrinking sheet with suction/injection.In this study,power-law variation of sheet temperature is considered.By similarity transformation,the governing equations with the boundary conditions are transformed to self-similar nonlinear ordinary differential equations and then those are solved numerically by shooting method.In presence of variable sheet temperature,the variation of temperature is analysed.For larger shrinking rate compared to that of straining rate,dual solutions for velocity and temperature are obtained.It is found that for positive value of power-law exponent of variable sheet temperature heat transfer at the sheet as well as heat absorption at the sheet with temperature overshoot near the sheet occur and for negative value heat transfer from the sheet occurs though there is overshoot away from the sheet.With increasing positive power-law exponent heat transfer reduces for first solution and heat absorption enhances for second solution.Whereas,with increasing magnitude of negative power-law exponent heat transfer increases for second solution and for first solution the heat transfer increases for larger shrinking rate and it decreases for smaller shrinking rate.Due to suction heat transfer/absorption increases in all cases and for injection heat transfer/absorption increases for first solution and decreases for second solution.Also,interesting effects of suction/injection and Prandtl number on temperature distribution are observed when the sheet temperature varies(directly/inversely)along the sheet.
基金supported by the National Basic Research Program of China(973 Program)(No.2013CB228002)
文摘A unified mathematical model is established to simulate the nonlinear unsteady percolation of shale gas with the consideration of the nonlinear multi-scale effects such as slippage, diffusion, and desorption. The continuous inhomogeneous models of equivalent porosity and permeability are proposed for the whole shale gas reservoir includ- ing the hydraulic fracture, the micro-fracture, and the matrix regions. The corresponding semi-analytical method is developed by transforming the nonlinear partial differential governing equation into the integral equation and the numerical discretization. The nonlinear multi-scale effects of slippage and diffusion and the pressure dependent effect of desorption on the shale gas production are investigated.
基金the National Natural Science Foundation of China(grant 41474042)the Key Research Program of the Institute of Geology&Geophysics,Chinese Academy of Sciences(IGGCAS)+1 种基金grant IGGCAS-201904the Computer Simulation Lab,IGGCAS and NSF(grants 0911319 and 1214215).
文摘We have constrained a small-scale,dome-shaped low-velocity structure near the core-mantle boundary(CMB)of Earth beneath Perm(the Perm anomaly)using travel-time analysis and three-dimensional(3-D)forward waveform modeling of seismic data sampling of the mantle.The best-fitting dome-shaped model centers at 60.0°E,50.5°N,and has a height of 400 km and a radius that increases from 200 km at the top to 450 km at the CMB.Its velocity reduction varies from 0%at the top to–3.0%at 240km above the CMB to–3.5%at the CMB.A surrounding 240-km-thick high-velocity D''structure has also been detected.The Perm anomaly may represent a stable smallscale chemical pile in the lowermost mantle,although the hypothesis of a developing mantle plume cannot be ruled out.
基金provided by the Natural Sciences and Engineering Research Council of Canadathe Canadian Institute for Advanced Research(Earth System Evolution Program)
文摘Although there has been significant progress in the seismic imaging of mantle heterogeneity, the outstanding issue that remains to be resolved is the unknown distribution of mantle temperature anomalies in the distant geological past that give rise to the present-day anomalies inferred by global tomography models. To address this question, we present 3-D convection models in compressible and self-gravitating mantle initialised by different hypothetical temperature patterns. A notable feature of our forward convection modelling is the use of self-consistent coupling of the motion of surface tectonic plates to the underlying mantle flow, without imposing prescribed surface velocities （i.e., p/ate-like boundary condition）. As an approximation for the surface mechanical conditions before plate tectonics began to operate we employ the no-slip （rigid） boundary condition. A rigid boundary condition dem- onstrates that the initial thermally-dominated structure is preserved, and its geographical location is fixed during the evolution of mantle flow. Considering the impact of different assumed surface boundary conditions （rigid and plate-like） on the evolution of thermal heterogeneity in the mantle we suggest that the intrinsic buoyancy of seven superplumes is most-likely resolved in the tomographic images of present-day mantle thermal structure. Our convection simulations with a plate-like boundary condition reveal that the evolution of an initial cold anomaly beneath the Java-lndonesian trench system yields a long-term, stable pattern of thermal heterogeneity in the lowermost mantle that resembles the present- day Large Low Shear Velocity Provinces （LLSVPs）, especially below the Pacific. The evolution of sub- duction zones may be, however, influenced by the mantle-wide flow driven by deeply-rooted and long- lived superplumes since Archean times. These convection models also detect the intrinsic buoyancy of the Perm Anomaly that has been identified as a unique slow feature distinct from the two principal LLSVPs. We find there is no need for dense chemical ＇piles＇ in the lower mantle to generate a stable distribution of temperature anomalies that are correlated to the LLSVPs and the Perm Anomaly. Our tomography-based convection simulations also demonstrate that intraplate volcanism in the south-east Pacific may be interpreted in terms of shallow small-scale convection triggered by a superplume beneath the East Pacific Rise.
