Plane, transverse MHD flow through a porous structure is considered in this work. Solution to the governing equations is obtained using an inverse method in which the streamfunction of the flow is considered linear in...Plane, transverse MHD flow through a porous structure is considered in this work. Solution to the governing equations is obtained using an inverse method in which the streamfunction of the flow is considered linear in one of the space variables. Expressions for flow quantities are obtained for finitely conducting and infinitely conducting fluids.展开更多
Flow through a channel bounded by a porous layer is considered when a transition layer exists between the channel and the medium. The variable permeability in the transition layer is chosen such that Brinkman’s equat...Flow through a channel bounded by a porous layer is considered when a transition layer exists between the channel and the medium. The variable permeability in the transition layer is chosen such that Brinkman’s equation governing the flow reduces to a generalized inhomogeneous Airy’s differential equation. Solution to the resulting generalized Airy’s equation is obtained in this work and solution to the flow through the transition layer, of the same configuration, reported in the literature, is recovered from the current solution.展开更多
Third- and fourth-order accurate finite difference schemes for the first derivative of the square of the speed are developed, for both uniform and non-uniform grids, and applied in the study of a two-dimensional visco...Third- and fourth-order accurate finite difference schemes for the first derivative of the square of the speed are developed, for both uniform and non-uniform grids, and applied in the study of a two-dimensional viscous fluid flow through an irregular domain. The von Mises transformation is used to transform the governing equations, and map the irregular domain onto a rectangular computational domain. Vorticity on the solid boundary is expressed in terms of the first partial derivative of the square of the speed of the flow in the computational domain, and the schemes are used to calculate the vorticity at the computational boundary grid points using up to five computational domain grid points. In all schemes developed, we study the effect of coordinate clustering on the computed results.展开更多
In this work, we consider the flow through composite porous layers of variable permeability, with the middle layer representing a porous core bounded by two Darcy layers. Brinkman’s equation is valid in the middle la...In this work, we consider the flow through composite porous layers of variable permeability, with the middle layer representing a porous core bounded by two Darcy layers. Brinkman’s equation is valid in the middle layer and has been reduced to an Airy’s inhomogeneous differential equation. Solution is obtained in terms of Airy’s functions and the Nield-Kuznetsov function.展开更多
In this work we consider coupled-parallel flow through a finite channel bounded below by a porous layer that is either finite or infinite in depth. The porous layer is one in which Darcy’s equation is valid under the...In this work we consider coupled-parallel flow through a finite channel bounded below by a porous layer that is either finite or infinite in depth. The porous layer is one in which Darcy’s equation is valid under the assumption of variable permeability. A suitable permeability stratification function is derived in this work and the resulting variable velocity profile is analyzed. It will be shown that when an infinite porous layer is implemented, Darcy’s equation must be used with a constant permeability.展开更多
文摘Plane, transverse MHD flow through a porous structure is considered in this work. Solution to the governing equations is obtained using an inverse method in which the streamfunction of the flow is considered linear in one of the space variables. Expressions for flow quantities are obtained for finitely conducting and infinitely conducting fluids.
文摘Flow through a channel bounded by a porous layer is considered when a transition layer exists between the channel and the medium. The variable permeability in the transition layer is chosen such that Brinkman’s equation governing the flow reduces to a generalized inhomogeneous Airy’s differential equation. Solution to the resulting generalized Airy’s equation is obtained in this work and solution to the flow through the transition layer, of the same configuration, reported in the literature, is recovered from the current solution.
文摘Third- and fourth-order accurate finite difference schemes for the first derivative of the square of the speed are developed, for both uniform and non-uniform grids, and applied in the study of a two-dimensional viscous fluid flow through an irregular domain. The von Mises transformation is used to transform the governing equations, and map the irregular domain onto a rectangular computational domain. Vorticity on the solid boundary is expressed in terms of the first partial derivative of the square of the speed of the flow in the computational domain, and the schemes are used to calculate the vorticity at the computational boundary grid points using up to five computational domain grid points. In all schemes developed, we study the effect of coordinate clustering on the computed results.
文摘In this work, we consider the flow through composite porous layers of variable permeability, with the middle layer representing a porous core bounded by two Darcy layers. Brinkman’s equation is valid in the middle layer and has been reduced to an Airy’s inhomogeneous differential equation. Solution is obtained in terms of Airy’s functions and the Nield-Kuznetsov function.
文摘In this work we consider coupled-parallel flow through a finite channel bounded below by a porous layer that is either finite or infinite in depth. The porous layer is one in which Darcy’s equation is valid under the assumption of variable permeability. A suitable permeability stratification function is derived in this work and the resulting variable velocity profile is analyzed. It will be shown that when an infinite porous layer is implemented, Darcy’s equation must be used with a constant permeability.
