This study investigates laminar convection in three regimes(forced convection,mixed convection,and natural convection)of a bi-nanofluid(Cu-Al_(2)O_(3)-water)/mono-nanofluid(Al_(2)O_(3)-water)inside a square enclosure ...This study investigates laminar convection in three regimes(forced convection,mixed convection,and natural convection)of a bi-nanofluid(Cu-Al_(2)O_(3)-water)/mono-nanofluid(Al_(2)O_(3)-water)inside a square enclosure of sliding vertical walls which are kept at cold temperature and moving up,down,or in opposite directions.The enclosure bottom is heated partially by a central heat source of various sizes while the horizontal walls are considered adiabatic.The thermal conductivity and dynamic viscosity are dependent on temperature and nanoparticle size.The conservation equations are implemented in the solver ANSYS R2(2020).The numerical predictions are successfully validated by comparison with data from the literature.Numerical simulations are carried out for various volume fractions of solid mono/hybrid-nanoparticles(0≤ϕ≤5%),Richardson numbers(0.001≤Ri≤10),and hot source lengths((1/5)H≤ε≤(4/5)H).Isothermal lines,streamlines,and average Nusselt numbers are analyzed.The thermal performance of nanofluids is compared to that of the base heat transfer fluid(water).Outcomes illustrate the flow characteristics significantly affected by the convection regime,hot source size,sidewall motion,and concentration of solid nanoparticles.In the case of sidewalls moving downward,using hybrid nanofluid(Cu-Al_(2)O_(3)-water)shows the highest heat transfer rate in the enclosure at Ri=1,ε=(4/5)H and volume fraction ofφ=5%where a significant increment(25.14%)of Nusselt number is obtained.展开更多
This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference m...This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference method(HOCDM)with computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4))is suggested,whereτ,h_(x),h_(y) denote the temporal and spatial stepsizes of the method,respectively.In order to improve the temporal computational accuracy of this method,the Richardson extrapolation technique is used and thus a new two-level HOCDMis derived,which is proved to be convergent of order four both in time and space.Although the new two-level HOCDM has the higher computational accuracy in time than the previous one,it will bring a larger computational cost.To overcome this deficiency,a three-level HOCDM with computational accuracy O(τ^(4)+h_(x)^(4)+h_(y)^(4))is constructed.Finally,with a series of numerical experiments,the theoretical accuracy and computational efficiency of the above methods are further verified.展开更多
In a world of Google and AI, developing an encyclopedic coverage of a theme that is of great interest to biologists, social scientists, politicians and environmental managers, is a daunting challenge. Wattles is a boo...In a world of Google and AI, developing an encyclopedic coverage of a theme that is of great interest to biologists, social scientists, politicians and environmental managers, is a daunting challenge. Wattles is a book that presents new knowledge, makes interesting reading, and has the potential to stimulate research in a variety of disciplines. We learn that Acacia, commonly known as the wattles or acacias, is a genus of shrubs and trees comprising 1,083 species of which 417 are known to have been introduced to areas outside their native range. We are surprised to read that Australian acacias are found almost everywhere, in virtually all terrestrial habitats, including woodlands, grasslands, alpine settings,rainforests, coastal dunes and deserts, causing major environmental and socio-economic changes in the invaded regions. Until recently, Acacia comprised a group of plant species native to Africa, South America and Australasia, but the name is now reserved for species predominantly from Australia, including some from Southeast Asia. The genus name Acacia is Neo-Latin, and refers to a preparation extracted from the leaves and fruit pods of Vachellia nilotica, the original type of the genus.展开更多
Richardson迭代法是求解ℳ张量多线性系统的一种有效方法。为了进一步加快其收敛速度,本文给出一个新的预处理子并提出一种新预处理Richardson迭代法。理论上证明所提预处理Richardson迭代法的收敛性。最后,通过数值例子验证该方法的有...Richardson迭代法是求解ℳ张量多线性系统的一种有效方法。为了进一步加快其收敛速度,本文给出一个新的预处理子并提出一种新预处理Richardson迭代法。理论上证明所提预处理Richardson迭代法的收敛性。最后,通过数值例子验证该方法的有效性和可行性。The Richardson iterative method is an effective method for solving multi-linear systems with ℳ-tensors. In this paper, a new preconditioner and new preconditioned Richardson iterative method are proposed to accelerate the convergence of multi-linear systems with ℳ-tensors. In the theory, the convergence of the preconditioned Richardson iterative method is proved. Finally, a numerical example is given to verify the effectiveness and feasibility of the proposed method.展开更多
文摘This study investigates laminar convection in three regimes(forced convection,mixed convection,and natural convection)of a bi-nanofluid(Cu-Al_(2)O_(3)-water)/mono-nanofluid(Al_(2)O_(3)-water)inside a square enclosure of sliding vertical walls which are kept at cold temperature and moving up,down,or in opposite directions.The enclosure bottom is heated partially by a central heat source of various sizes while the horizontal walls are considered adiabatic.The thermal conductivity and dynamic viscosity are dependent on temperature and nanoparticle size.The conservation equations are implemented in the solver ANSYS R2(2020).The numerical predictions are successfully validated by comparison with data from the literature.Numerical simulations are carried out for various volume fractions of solid mono/hybrid-nanoparticles(0≤ϕ≤5%),Richardson numbers(0.001≤Ri≤10),and hot source lengths((1/5)H≤ε≤(4/5)H).Isothermal lines,streamlines,and average Nusselt numbers are analyzed.The thermal performance of nanofluids is compared to that of the base heat transfer fluid(water).Outcomes illustrate the flow characteristics significantly affected by the convection regime,hot source size,sidewall motion,and concentration of solid nanoparticles.In the case of sidewalls moving downward,using hybrid nanofluid(Cu-Al_(2)O_(3)-water)shows the highest heat transfer rate in the enclosure at Ri=1,ε=(4/5)H and volume fraction ofφ=5%where a significant increment(25.14%)of Nusselt number is obtained.
文摘This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference method(HOCDM)with computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4))is suggested,whereτ,h_(x),h_(y) denote the temporal and spatial stepsizes of the method,respectively.In order to improve the temporal computational accuracy of this method,the Richardson extrapolation technique is used and thus a new two-level HOCDMis derived,which is proved to be convergent of order four both in time and space.Although the new two-level HOCDM has the higher computational accuracy in time than the previous one,it will bring a larger computational cost.To overcome this deficiency,a three-level HOCDM with computational accuracy O(τ^(4)+h_(x)^(4)+h_(y)^(4))is constructed.Finally,with a series of numerical experiments,the theoretical accuracy and computational efficiency of the above methods are further verified.
文摘In a world of Google and AI, developing an encyclopedic coverage of a theme that is of great interest to biologists, social scientists, politicians and environmental managers, is a daunting challenge. Wattles is a book that presents new knowledge, makes interesting reading, and has the potential to stimulate research in a variety of disciplines. We learn that Acacia, commonly known as the wattles or acacias, is a genus of shrubs and trees comprising 1,083 species of which 417 are known to have been introduced to areas outside their native range. We are surprised to read that Australian acacias are found almost everywhere, in virtually all terrestrial habitats, including woodlands, grasslands, alpine settings,rainforests, coastal dunes and deserts, causing major environmental and socio-economic changes in the invaded regions. Until recently, Acacia comprised a group of plant species native to Africa, South America and Australasia, but the name is now reserved for species predominantly from Australia, including some from Southeast Asia. The genus name Acacia is Neo-Latin, and refers to a preparation extracted from the leaves and fruit pods of Vachellia nilotica, the original type of the genus.
文摘Richardson迭代法是求解ℳ张量多线性系统的一种有效方法。为了进一步加快其收敛速度,本文给出一个新的预处理子并提出一种新预处理Richardson迭代法。理论上证明所提预处理Richardson迭代法的收敛性。最后,通过数值例子验证该方法的有效性和可行性。The Richardson iterative method is an effective method for solving multi-linear systems with ℳ-tensors. In this paper, a new preconditioner and new preconditioned Richardson iterative method are proposed to accelerate the convergence of multi-linear systems with ℳ-tensors. In the theory, the convergence of the preconditioned Richardson iterative method is proved. Finally, a numerical example is given to verify the effectiveness and feasibility of the proposed method.
