The numerical solution of compressible flows has become more prevalent than that of incompressible flows.With the help of the artificial compressibility approach,incompressible flows can be solved numerically using th...The numerical solution of compressible flows has become more prevalent than that of incompressible flows.With the help of the artificial compressibility approach,incompressible flows can be solved numerically using the same methods as compressible ones.The artificial compressibility scheme is thus widely used to numerically solve incompressible Navier-Stokes equations.Any numerical method highly depends on its accuracy and speed of convergence.Although the artificial compressibility approach is utilized in several numerical simulations,the effect of the compressibility factor on the accuracy of results and convergence speed has not been investigated for nanofluid flows in previous studies.Therefore,this paper assesses the effect of this factor on the convergence speed and accuracy of results for various types of thermo-flow.To improve the stability and convergence speed of time discretizations,the fifth-order Runge-Kutta method is applied.A computer program has been written in FORTRAN to solve the discretized equations in different Reynolds and Grashof numbers for various grids.The results demonstrate that the artificial compressibility factor has a noticeable effect on the accuracy and convergence rate of the simulation.The optimum artificial compressibility is found to be between 1 and 5.These findings can be utilized to enhance the performance of commercial numerical simulation tools,including ANSYS and COMSOL.展开更多
Heat exchangers are utilized extensively in different industries and technologies.Consequently,optimizing heat exchangers has been a major concern among researchers.Although various studies have been conducted to impr...Heat exchangers are utilized extensively in different industries and technologies.Consequently,optimizing heat exchangers has been a major concern among researchers.Although various studies have been conducted to improve the heat transfer rate,the use of a wavy wall in the presence of different types of heat transfer mechanisms has not been investigated.This study thus investigates the mixed heat transmission behavior of fluid in a horizontal channel with a cavity and a hot,wavy wall.The fluid flow in the channel is considered laminar,and the governing equations including continuity,momentum,and energy are all solved numerically.The numerical solution is stabilized by using a first-order multi-dimensional characteristic-based scheme in combination with a fifth-order Runge-Kutta method.The flow and heat transfer effects of varying Richardson numbers,Reynolds numbers,wave amplitude,wavelength,channel height,and cavity width are examined.The results indicate that the mean Nusselt number increases with an increase in Reynolds number,wave amplitude,and cavity width,while it decreases with an increase in Richardson number,wavelength,and channel height.The minimum Nusselt number is calculated to be 0.7,whereas the maximum Nusselt number is 27.09.The Nusselt number has only increased by 40%in the higher depths of the cavity,despite the Richardson number being 10,000 times larger.But this figure increases to 130%at lower depths.The mean Nusselt number is thus significantly influenced by channel height and cavity width.The influence of wave amplitude on the mean Nusselt number is twice that of wavelength.展开更多
基金The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through the Large Groups Project under grant number RGP.2/235/43.
文摘The numerical solution of compressible flows has become more prevalent than that of incompressible flows.With the help of the artificial compressibility approach,incompressible flows can be solved numerically using the same methods as compressible ones.The artificial compressibility scheme is thus widely used to numerically solve incompressible Navier-Stokes equations.Any numerical method highly depends on its accuracy and speed of convergence.Although the artificial compressibility approach is utilized in several numerical simulations,the effect of the compressibility factor on the accuracy of results and convergence speed has not been investigated for nanofluid flows in previous studies.Therefore,this paper assesses the effect of this factor on the convergence speed and accuracy of results for various types of thermo-flow.To improve the stability and convergence speed of time discretizations,the fifth-order Runge-Kutta method is applied.A computer program has been written in FORTRAN to solve the discretized equations in different Reynolds and Grashof numbers for various grids.The results demonstrate that the artificial compressibility factor has a noticeable effect on the accuracy and convergence rate of the simulation.The optimum artificial compressibility is found to be between 1 and 5.These findings can be utilized to enhance the performance of commercial numerical simulation tools,including ANSYS and COMSOL.
文摘Heat exchangers are utilized extensively in different industries and technologies.Consequently,optimizing heat exchangers has been a major concern among researchers.Although various studies have been conducted to improve the heat transfer rate,the use of a wavy wall in the presence of different types of heat transfer mechanisms has not been investigated.This study thus investigates the mixed heat transmission behavior of fluid in a horizontal channel with a cavity and a hot,wavy wall.The fluid flow in the channel is considered laminar,and the governing equations including continuity,momentum,and energy are all solved numerically.The numerical solution is stabilized by using a first-order multi-dimensional characteristic-based scheme in combination with a fifth-order Runge-Kutta method.The flow and heat transfer effects of varying Richardson numbers,Reynolds numbers,wave amplitude,wavelength,channel height,and cavity width are examined.The results indicate that the mean Nusselt number increases with an increase in Reynolds number,wave amplitude,and cavity width,while it decreases with an increase in Richardson number,wavelength,and channel height.The minimum Nusselt number is calculated to be 0.7,whereas the maximum Nusselt number is 27.09.The Nusselt number has only increased by 40%in the higher depths of the cavity,despite the Richardson number being 10,000 times larger.But this figure increases to 130%at lower depths.The mean Nusselt number is thus significantly influenced by channel height and cavity width.The influence of wave amplitude on the mean Nusselt number is twice that of wavelength.
