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- Thread starter Waqar Amin
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then how kinematic viscosity is termed as momentum diffusivity, i m very confused with these terms.

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The heat equation:

[tex]\frac{\partial \phi}{\partial t} = c^2\nabla^2 \phi[/tex]

The incompressible Navier-Stokes equation:

[tex]\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v}\cdot\nabla\mathbf{v}=-\frac{1}{\rho}\nabla p + \nu\nabla^2\mathbf{v} + \mathbf{f}[/tex]

The heat equation is a simplified version of the diffusion equation that describes the diffusion of basically any quantity through a material. In heat transfer, [itex]c^2=\alpha=\frac{k}{\rho c_p}[/itex] is the thermal diffusivity.

In the Navier-Stokes equations, notice that the [itex]\nu\nabla^2\mathbf{v}[/itex] term takes the same form, only the N-S equations are a momentum balance, so the kinematic viscosity, [itex]\nu[/itex], is essentially a diffusivity constant that describes how momentum diffuses through the medium. In other words, it describes one particle's ability to affect the momentum of the adjacent particles.

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i have understand. thanxx for your help boneh3ad. :)

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