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Related Concept Videos

Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
Fluid Pressure over Flat Plate of Variable Width01:02

Fluid Pressure over Flat Plate of Variable Width

When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.
The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate. Thus, the magnitude of the force is equal to the...
Fluid Pressure over Curved Plate of Constant Width01:12

Fluid Pressure over Curved Plate of Constant Width

When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the...
Couette Flow01:22

Couette Flow

Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
Fluid Pressure over Flat Plate of Constant Width01:05

Fluid Pressure over Flat Plate of Constant Width

When a body is submerged in water, it experiences fluid pressure acting normal on its surface and distributed over its area. For better design structures, it is crucial to determine the magnitude and location of the resultant force acting on the surface. In the case of a rectangular plate of constant width submerged in water, the pressure increases with depth, resulting in a linearly varying trapezoidal pressure distribution from the upper to the lower edge of the plate.
The resultant force...
Navier–Stokes Equations01:28

Navier–Stokes Equations

For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...

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A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment
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Dynamic equations for fluid-loaded porous plates using approximate boundary conditions.

Peter D Folkow1, Martin Johansson

  • 1Department of Applied Mechanics, Chalmers University of Technology, SE-412 96 Goteborg, Sweden.

The Journal of the Acoustical Society of America
|May 12, 2009
PubMed
Summary

New equations accurately predict fluid-loaded thin poroelastic layer behavior. This Biot theory-based model, using series expansion, offers a flexible approach for analyzing plate dynamics under various conditions.

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Area of Science:

  • Acoustics
  • Solid Mechanics
  • Materials Science

Background:

  • Poroelastic materials exhibit complex behavior influenced by fluid flow within pores.
  • Accurate modeling of thin, fluid-loaded poroelastic layers is crucial for applications in acoustics and structural engineering.
  • Existing models may lack the precision or flexibility needed for diverse configurations.

Purpose of the Study:

  • To systematically derive and present equations for fluid-loaded thin poroelastic layers under time-harmonic conditions.
  • To develop a model based on Biot theory applicable to both open and closed pore systems.
  • To validate the accuracy of the derived equations against established theories.

Main Methods:

  • Application of Biot theory for modeling poroelasticity with open and closed pores.
  • Utilizing series expansion techniques in the thickness variable.
  • Formulating separate symmetric and antisymmetric plate equations with approximate boundary conditions.

Main Results:

  • Derived asymptotically correct plate equations that can be truncated to arbitrary order.
  • Presented analytical and numerical results for the developed theory.
  • Demonstrated accurate prediction of plate behavior through comparisons with exact 3D theory and flexural plate theory.

Conclusions:

  • The presented systematically derived equations provide an accurate method for analyzing fluid-loaded thin poroelastic layers.
  • The model's flexibility allows for arbitrary truncation order, enhancing its applicability.
  • The findings validate the effectiveness of Biot theory combined with series expansion for this class of problems.