A two-dimensional(2D)laminar flow of nanofluids confined within a square cavity having localized heat source at the bottom wall has been investigated.The governing Navier–Stokes and energy equations have been non dim...A two-dimensional(2D)laminar flow of nanofluids confined within a square cavity having localized heat source at the bottom wall has been investigated.The governing Navier–Stokes and energy equations have been non dimensionalized using the appropriate non dimensional variables and then numerically solved using finite volume method.The flow was controlled by a range of parameters such as Rayleigh number,length of heat source and nanoparticle volume fraction.The numerical results are represented in terms of isotherms,streamlines,velocity and temperature distribution as well as the local and average rate of heat transfer.A comparative study has been conducted for two different base fluids,ethylene glycol and water as well as for two different solids Cu and Al_(2)O_(3).It is found that the ethylene glycol-based nanofluid is superior to the water-based nanofluid for heat transfer enhancement.展开更多
A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented.The discretization of the spatial operators in the method is shown to be self-...A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented.The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface,Dirichlet and periodic boundary conditions.The fully discrete version of the method conserves a discrete energy to machine precision.展开更多
We present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed...We present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed.We prove stability for a second-order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition.The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials.The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners.The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.展开更多
基金The third author acknowledges the Ministry of Science and Technology(MOST),the People’s Republic of Bangladesh(https://most.gov.bd/),for providing the financial support for this research gratefully(Grant No.441-EAS)The third author also acknowledges gratefully to the North South University for the financial support as a Faculty Research Grant(CTRG-20-SEPS-15)(http://www.northsouth.edu/research-office/).
文摘A two-dimensional(2D)laminar flow of nanofluids confined within a square cavity having localized heat source at the bottom wall has been investigated.The governing Navier–Stokes and energy equations have been non dimensionalized using the appropriate non dimensional variables and then numerically solved using finite volume method.The flow was controlled by a range of parameters such as Rayleigh number,length of heat source and nanoparticle volume fraction.The numerical results are represented in terms of isotherms,streamlines,velocity and temperature distribution as well as the local and average rate of heat transfer.A comparative study has been conducted for two different base fluids,ethylene glycol and water as well as for two different solids Cu and Al_(2)O_(3).It is found that the ethylene glycol-based nanofluid is superior to the water-based nanofluid for heat transfer enhancement.
基金This work performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
文摘A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented.The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface,Dirichlet and periodic boundary conditions.The fully discrete version of the method conserves a discrete energy to machine precision.
文摘We present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed.We prove stability for a second-order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition.The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials.The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners.The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.
