Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperatur...Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H1 norm error estimates are given.展开更多
Thermal convection in a three-dimensional tilted rectangular cell with aspect ratio 0.5 is studied using direct nu- merical simulations within both Oberbeck-Boussinesq （OB） approximation and strong non-Oberbeck-Bous...Thermal convection in a three-dimensional tilted rectangular cell with aspect ratio 0.5 is studied using direct nu- merical simulations within both Oberbeck-Boussinesq （OB） approximation and strong non-Oberbeck-Boussinesq （NOB） effects. The considered Rayleigh numbers Ra range from 105 to 107, the working fluid is air at 30OK, and the corresponding Prandtl number Pr is 0.71. Within the OB approximation, it is found that there exist multiple states for Ra = 105 and hysteresis for Ra = 106. For a relatively small tilt angle/3, the large-scale circulation can either orient along one of the the vertical diagonal planes （denoted by Ma mode） or orient parallel to the front wall （denoted by Mp mode）. Which of the two modes transports heat more efficiently is not definitive, and it depends on the Rayleigh number Ra. For/Ta = 107 and β = 0°, the time-averaged flow field contains four rolls in the upper half and lower half of the cell, respectively, Md and Mp modes only developing in tilted cells. By investigating NOB effects in tilted convection for fixed/Ta = 106, it is found that the NOB effects on the Nusselt number Nu, the Reynolds number Re and the central temperature Tc for different β ranges are different. NOB effects can either increase or decrease Nu, Re and Tc when β is varied.展开更多
Molecular dynamics simulations are employed to investigate the effect of thermal convection induced only by dissipative lateral walls on density segregation of the strongly driven binary granular gases under low gravi...Molecular dynamics simulations are employed to investigate the effect of thermal convection induced only by dissipative lateral walls on density segregation of the strongly driven binary granular gases under low gravity conditions. It is found that the thermal convection due to dissipative lateral walls has significant influence on the segregation intensity of the system. The dominant factor in determining the degree of segregation achieved by the system is found to be the relative convection rate between differing species. Moreover, a qualitative explanation is proposed for the relationship between the thermal convection due to dissipative lateral walls and the observed segregation intensity profiles.展开更多
Fluid flow through porous spaces with variable porosity has wide-range applications,notably in biomedical and thermal engineering,where it plays a vital role in comprehending blood flow dynamics within cardiovascular ...Fluid flow through porous spaces with variable porosity has wide-range applications,notably in biomedical and thermal engineering,where it plays a vital role in comprehending blood flow dynamics within cardiovascular systems,heat transfer and thermal management systems improve efficiency using porous materials with variable porosity.Keeping these important applications in view,in current study blood-based hybrid nanofluid flow has considered on a convectively heated sheet.The sheet exhibits the properties of a porous medium with variable porosity and extends in both the x and y directions.Blood has used as base fluid in which the nanoparticles of Cu and Cu O have been mixed.Thermal radiation,space-dependent,and thermal-dependent heat sources have been incorporated into the energy equation,while magnetic effects have been integrated into the momentum equations.Dimensionless variables have employed to transform the modeled equations into dimensionless form and facilitating their solution using bvp4c approach.It has concluded in this study that,both the primary and secondary velocities augmented with upsurge in variable porous factor and declined with escalation in stretching ratio,Casson,magnetic,and slip factors along x-and y-axes.Thermal distribution has grown up with upsurge in Casson factor,magnetic factor,thermal Biot number,and thermal/space-dependent heat sources while has retarded with growth in variable porous and stretching ratio factors.The findings of this investigation have been compared with the existing literature,revealing a strong agreement among present and established results that ensured the validation of the model and method used in this work.展开更多
基金Supported by National Natural Science Foundation of China(10071044)the Research Fund of Doctoral Program of High Education by State Education Ministry of China.
文摘Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H1 norm error estimates are given.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11572314,11232011 and 11621202the Fundamental Research Funds for the Central Universities
文摘Thermal convection in a three-dimensional tilted rectangular cell with aspect ratio 0.5 is studied using direct nu- merical simulations within both Oberbeck-Boussinesq （OB） approximation and strong non-Oberbeck-Boussinesq （NOB） effects. The considered Rayleigh numbers Ra range from 105 to 107, the working fluid is air at 30OK, and the corresponding Prandtl number Pr is 0.71. Within the OB approximation, it is found that there exist multiple states for Ra = 105 and hysteresis for Ra = 106. For a relatively small tilt angle/3, the large-scale circulation can either orient along one of the the vertical diagonal planes （denoted by Ma mode） or orient parallel to the front wall （denoted by Mp mode）. Which of the two modes transports heat more efficiently is not definitive, and it depends on the Rayleigh number Ra. For/Ta = 107 and β = 0°, the time-averaged flow field contains four rolls in the upper half and lower half of the cell, respectively, Md and Mp modes only developing in tilted cells. By investigating NOB effects in tilted convection for fixed/Ta = 106, it is found that the NOB effects on the Nusselt number Nu, the Reynolds number Re and the central temperature Tc for different β ranges are different. NOB effects can either increase or decrease Nu, Re and Tc when β is varied.
基金Supported by the National Natural Science Foundation of China under Grant No 11404104the Natural Science Foundation of Hubei Province of China under Grant No 2014CFC1127
文摘Molecular dynamics simulations are employed to investigate the effect of thermal convection induced only by dissipative lateral walls on density segregation of the strongly driven binary granular gases under low gravity conditions. It is found that the thermal convection due to dissipative lateral walls has significant influence on the segregation intensity of the system. The dominant factor in determining the degree of segregation achieved by the system is found to be the relative convection rate between differing species. Moreover, a qualitative explanation is proposed for the relationship between the thermal convection due to dissipative lateral walls and the observed segregation intensity profiles.
基金supported via funding from Prince Sattam bin Abdulaziz University(Grant No.PSAU/2024/R/1446)。
文摘Fluid flow through porous spaces with variable porosity has wide-range applications,notably in biomedical and thermal engineering,where it plays a vital role in comprehending blood flow dynamics within cardiovascular systems,heat transfer and thermal management systems improve efficiency using porous materials with variable porosity.Keeping these important applications in view,in current study blood-based hybrid nanofluid flow has considered on a convectively heated sheet.The sheet exhibits the properties of a porous medium with variable porosity and extends in both the x and y directions.Blood has used as base fluid in which the nanoparticles of Cu and Cu O have been mixed.Thermal radiation,space-dependent,and thermal-dependent heat sources have been incorporated into the energy equation,while magnetic effects have been integrated into the momentum equations.Dimensionless variables have employed to transform the modeled equations into dimensionless form and facilitating their solution using bvp4c approach.It has concluded in this study that,both the primary and secondary velocities augmented with upsurge in variable porous factor and declined with escalation in stretching ratio,Casson,magnetic,and slip factors along x-and y-axes.Thermal distribution has grown up with upsurge in Casson factor,magnetic factor,thermal Biot number,and thermal/space-dependent heat sources while has retarded with growth in variable porous and stretching ratio factors.The findings of this investigation have been compared with the existing literature,revealing a strong agreement among present and established results that ensured the validation of the model and method used in this work.
