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Related Concept Videos

Couette Flow01:22

Couette Flow

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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...
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Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

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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.
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Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

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Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
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Irrotational Flow01:28

Irrotational Flow

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Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
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Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

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Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
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Laminar and Turbulent Flow01:07

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Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the...
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Updated: Sep 21, 2025

Evolution of Staircase Structures in Diffusive Convection
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Double-diffusive convection in Jeffery-Hamel flow.

Noureen1, Dil Nawaz Khan Marwat2

  • 1Department of Mathematics, Faculty of Technologies and Engineering Sciences, Islamia College Peshawar, University Campus, Jamrod Road, Peshawar, Khyber Pakhtunkhwa, 25120, Pakistan. noureenusman2018@gmail.com.

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This study explores double-diffusive convection in a viscous fluid channel with heated, inclined walls. New methods analyze fluid flow, heat, and mass transfer, offering insights into real-world physical phenomena.

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Area of Science:

  • Fluid Dynamics
  • Heat and Mass Transfer
  • Convection

Background:

  • Investigates double-diffusive convection within a horizontal channel.
  • Features heated, inclined, and rectangular plane walls with a non-uniform temperature and variable species concentration on the upper wall.

Purpose of the Study:

  • To analyze double-diffusive convection in a viscous fluid flow.
  • To explore Jeffery-Hamel flow with two non-zero velocity components using novel procedures.
  • To provide analytical and numerical solutions for fluid flow, heat, and mass transfer.

Main Methods:

  • The problem is formulated using four partial differential equations (PDEs) and boundary conditions (BCs) in Cartesian Coordinates.
  • A transformation reduces the PDEs to a system of ordinary differential equations (ODEs).
  • The ODEs are solved using multiple methods, including approximate analytical and accurate numerical solutions.

Main Results:

  • Solutions are validated through comparison of analytical and numerical methods.
  • Skin friction and the rate of two diffusions are investigated.
  • Analysis covers assisting (opposing) and converging (diverging) flow scenarios.

Conclusions:

  • The study provides a comprehensive analysis of double-diffusive convection under specific channel conditions.
  • The findings are applicable to real-world physical problems involving similar circumstances.
  • The employed methodology offers a robust approach for similar fluid dynamics investigations.