An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time.This solution is valid for both H1 and H2 boundary conditions,which are relate...An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time.This solution is valid for both H1 and H2 boundary conditions,which are related to fully developed convective heat transfer under constant heat flux at the duct walls.The separation of variables method and various other mathematical techniques are used to find the closed form of the temperature distribution.The local and mean Nusselt numbers are also obtained as functions of the aspect ratio.A new physical constraint is presented to solve the Neumann problem in non-dimensional analysis for the H2 boundary conditions.This is one of the major innovations of the current study.The analytical results indicate a singularity occurs at a critical aspect ratio of 2.4912 when calculating the local and mean Nusselt numbers.展开更多
In this study,natural convection flow in a porous cavity with sinusoidal temperature distribution has been analyzed by a new double multi relaxation time(MRT)Lattice Boltzmann method(LBM).We consider a copper/water na...In this study,natural convection flow in a porous cavity with sinusoidal temperature distribution has been analyzed by a new double multi relaxation time(MRT)Lattice Boltzmann method(LBM).We consider a copper/water nanofluid filling a porous cavity.For simulating the temperature and flow fields,D2Q5 and D2Q9 lattices are utilized respectively,and the effects of different Darcy numbers(Da)(0.001-0.1)and various Rayleigh numbers(Ra)(10^(3)-10^(5))for porosity(ε)between 0.4 and 0.9 have been considered.Phase deviation(θ)changed from 0 toπand the volume fraction of nanoparticles(∅)varied from 0 to 6%.The present results show a good agreement with the previous works,thus confirming the reliability the new numerical method proposed in this paper.It is indicated that the heat transfer rate increases at increasing Darcy number,porosity,Rayleigh number,the volume fraction of nanoparticles and phase deviation.However,the most sensitive parameter is the Rayleigh number.The maximum Nusselt deviation is 10%,32%and 33%for Ra=10^(3),10^(4) and 10^(5),respectively,withε=0.4 toε=0.9.It can be concluded that the effect of Darcy number on the heat transfer rate increases at increasing Rayleigh number,yielding a maximum enhancement of the average Nusselt number around 12%and 61%for Ra=10^(3) and Ra=10^(5),respectively.展开更多
基金Project supported by the Shahrood University of Technology (No. 17024),Iran
文摘An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time.This solution is valid for both H1 and H2 boundary conditions,which are related to fully developed convective heat transfer under constant heat flux at the duct walls.The separation of variables method and various other mathematical techniques are used to find the closed form of the temperature distribution.The local and mean Nusselt numbers are also obtained as functions of the aspect ratio.A new physical constraint is presented to solve the Neumann problem in non-dimensional analysis for the H2 boundary conditions.This is one of the major innovations of the current study.The analytical results indicate a singularity occurs at a critical aspect ratio of 2.4912 when calculating the local and mean Nusselt numbers.
文摘In this study,natural convection flow in a porous cavity with sinusoidal temperature distribution has been analyzed by a new double multi relaxation time(MRT)Lattice Boltzmann method(LBM).We consider a copper/water nanofluid filling a porous cavity.For simulating the temperature and flow fields,D2Q5 and D2Q9 lattices are utilized respectively,and the effects of different Darcy numbers(Da)(0.001-0.1)and various Rayleigh numbers(Ra)(10^(3)-10^(5))for porosity(ε)between 0.4 and 0.9 have been considered.Phase deviation(θ)changed from 0 toπand the volume fraction of nanoparticles(∅)varied from 0 to 6%.The present results show a good agreement with the previous works,thus confirming the reliability the new numerical method proposed in this paper.It is indicated that the heat transfer rate increases at increasing Darcy number,porosity,Rayleigh number,the volume fraction of nanoparticles and phase deviation.However,the most sensitive parameter is the Rayleigh number.The maximum Nusselt deviation is 10%,32%and 33%for Ra=10^(3),10^(4) and 10^(5),respectively,withε=0.4 toε=0.9.It can be concluded that the effect of Darcy number on the heat transfer rate increases at increasing Rayleigh number,yielding a maximum enhancement of the average Nusselt number around 12%and 61%for Ra=10^(3) and Ra=10^(5),respectively.
