In this paper,the natural convection of a complex fluid that contains both nanoparticles and gyrotactic microorganisms in a heated square cavity is considered.The Buongiorno model is applied to descirbe the nanofluid ...In this paper,the natural convection of a complex fluid that contains both nanoparticles and gyrotactic microorganisms in a heated square cavity is considered.The Buongiorno model is applied to descirbe the nanofluid behaviours.Both the top and bottom horizontal walls of the cavity are adiabatic,and there is a temperature difference between the left and right vertical walls.The non-dimensional governing equations are obtained when the stream-vorticity formulation of function is used,which are solved by the recently developed robust Coiflet wavelet homotopy analysis method.A rigid verification for the solver is given.Besides,the effects of various physics parameters including the Rayleigh number,the buoyancy ratio parameter,the bioconvection Rayleigh number,the Prandtl number,the Brownian motion parameter,the thermophoresis parameter,the heat generation parameter,the Lewis number,the bioconvection Peclet number and the Schmidt number on this complicated natural convection are examined.It is known that natural convection is closely related to our daily life owing to its wide existence in nature and engineering applications.We believe that our work will make a significant contribution to a better understanding of the natural convection of a complex fluid in a cavity with suspensions of both inorganic nanoparticles and organic microorganisms.展开更多
The Coiflet wavelet-homotopy Galerkin method is extended to solve unsteady nonlinear wave equations for the first time.The Korteweg-de Vries(KdV)equation,the Burgers equation and the Korteweg-de Vries-Burgers(KdVB)equ...The Coiflet wavelet-homotopy Galerkin method is extended to solve unsteady nonlinear wave equations for the first time.The Korteweg-de Vries(KdV)equation,the Burgers equation and the Korteweg-de Vries-Burgers(KdVB)equation are examined as illustrative examples.Validity and accuracy of the proposed method are assessed in terms of relative variance and the maximum error norm.Our results are found in good agreement with exact solutions and numerical solutions reported in previous studies.Furthermore,it is found that the solution accuracy is closely related to the resolution level and the convergence-control parameter.It is also found that our proposed method is superior to the traditional homotopy analysis method when dealing with unsteady nonlinear problems.It is expected that this approach can be further used to solve complicated unsteady problems in the fields of science and engineering.展开更多
基金H.Xu is supported by the National Natural Science Foundation of China(Grant No.11872241)This work was partially supported by the Australian Research Council(ARC)through Grants DE150100169,FT160100357 and CE140100003。
文摘In this paper,the natural convection of a complex fluid that contains both nanoparticles and gyrotactic microorganisms in a heated square cavity is considered.The Buongiorno model is applied to descirbe the nanofluid behaviours.Both the top and bottom horizontal walls of the cavity are adiabatic,and there is a temperature difference between the left and right vertical walls.The non-dimensional governing equations are obtained when the stream-vorticity formulation of function is used,which are solved by the recently developed robust Coiflet wavelet homotopy analysis method.A rigid verification for the solver is given.Besides,the effects of various physics parameters including the Rayleigh number,the buoyancy ratio parameter,the bioconvection Rayleigh number,the Prandtl number,the Brownian motion parameter,the thermophoresis parameter,the heat generation parameter,the Lewis number,the bioconvection Peclet number and the Schmidt number on this complicated natural convection are examined.It is known that natural convection is closely related to our daily life owing to its wide existence in nature and engineering applications.We believe that our work will make a significant contribution to a better understanding of the natural convection of a complex fluid in a cavity with suspensions of both inorganic nanoparticles and organic microorganisms.
文摘The Coiflet wavelet-homotopy Galerkin method is extended to solve unsteady nonlinear wave equations for the first time.The Korteweg-de Vries(KdV)equation,the Burgers equation and the Korteweg-de Vries-Burgers(KdVB)equation are examined as illustrative examples.Validity and accuracy of the proposed method are assessed in terms of relative variance and the maximum error norm.Our results are found in good agreement with exact solutions and numerical solutions reported in previous studies.Furthermore,it is found that the solution accuracy is closely related to the resolution level and the convergence-control parameter.It is also found that our proposed method is superior to the traditional homotopy analysis method when dealing with unsteady nonlinear problems.It is expected that this approach can be further used to solve complicated unsteady problems in the fields of science and engineering.
