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Related Concept Videos

Boundary Layer Characteristics01:18

Boundary Layer Characteristics

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When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...
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Steady, Laminar Flow Between Parallel Plates01:17

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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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Viscosity01:27

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Viscosity is a property of fluids that measures their resistance to flow. It is influenced by factors such as the surface area of contact, the gradient of flow speed, and the fluid's viscosity constant, called the coefficient of viscosity. The coefficient of viscosity, also known as dynamic viscosity, is denoted by the symbol η. It determines the proportionality between the viscous force and the gradient of flow speed.Newton's law of viscosity states that the viscous force on a...
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When a fluid flows through a pipe, it experiences energy losses due to frictional resistance along the pipe walls, known as major losses. These energy losses result in a pressure drop, which varies based on the flow conditions — whether laminar or turbulent — and the specific physical properties of the fluid and pipe.
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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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Numerical solution of boundary layer MHD flow with viscous dissipation.

S R Mishra1, S Jena2

  • 1Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Khandagiri, Bhubaneswar, Odisha 751030, India.

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Summary

This study examines fluid flow over a shrinking sheet, considering magnetic fields and heat generation. Results show how parameters affect fluid velocity, temperature, and heat transfer rates.

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Area of Science:

  • Fluid Dynamics
  • Magnetohydrodynamics
  • Heat Transfer

Background:

  • Investigates steady, 2D, laminar flow of viscous, incompressible, electrically conducting fluids.
  • Considers flow over a shrinking sheet with a transverse magnetic field and viscous dissipation.

Purpose of the Study:

  • To analyze the impact of magnetic fields and viscous dissipation on fluid flow and heat transfer.
  • To numerically solve the transformed governing equations for velocity and temperature profiles.

Main Methods:

  • Employs similarity transformations to convert partial differential equations into ordinary differential equations.
  • Utilizes the fourth-order Runge-Kutta method with a shooting technique for numerical solutions.

Main Results:

  • Presents detailed graphical analysis of velocity and temperature profiles for various governing parameters.
  • Provides numerical evaluations of skin friction and Nusselt number.

Conclusions:

  • The study offers insights into the complex interplay of magnetic fields, viscous dissipation, and sheet shrinkage on fluid dynamics and thermal behavior.
  • The numerical approach provides accurate solutions for this class of problems.