Pustam | पुस्तम | পুস্তম🇳🇵<p>Convection–diffusion equation<br />The convection-diffusion equation is a more general version of the scalar transport equation. It is a combination of the diffusion and convection (advection) equations. It describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection.<br />\[\dfrac{\partial c}{\partial t} = \mathbf{\nabla} \cdot (D \mathbf{\nabla} c - \mathbf{v} c) + R\]</p><p>\[\dfrac{\partial c}{\partial t} = \underbrace{\mathbf{\nabla} \cdot (D \mathbf{\nabla} c)}_{\text{diffusion}}-\overbrace{\underbrace{\mathbf{\nabla}\cdot (\mathbf{v} c)}_{\text{advection}}}^\text{convection} + \overbrace{\underbrace{R}_\text{destruction}}^\text{creation}\] </p><p>\(\mathbf{\nabla} \cdot (D \mathbf{\nabla} c)\) is the contribution of diffusion.<br />\(- \mathbf{\nabla}\cdot (\mathbf{v} c)\) is the contribution of convection or advection.<br />\(R\) describes the creation or destruction of the quantity.</p><p>where<br />\(c\) is the variable of interest.<br />\(D\) is the diffusivity.<br />\(\mathbf{v}\) is the velocity field, and<br />\(R\) is the sources or sinks of the quantity \(c\).</p><p><a href="https://mathstodon.xyz/tags/Convection" class="mention hashtag" rel="tag">#<span>Convection</span></a> <a href="https://mathstodon.xyz/tags/Diffusion" class="mention hashtag" rel="tag">#<span>Diffusion</span></a> <a href="https://mathstodon.xyz/tags/Transport" class="mention hashtag" rel="tag">#<span>Transport</span></a> <a href="https://mathstodon.xyz/tags/Advection" class="mention hashtag" rel="tag">#<span>Advection</span></a> <a href="https://mathstodon.xyz/tags/Equation" class="mention hashtag" rel="tag">#<span>Equation</span></a> <a href="https://mathstodon.xyz/tags/ConvectionDiffusionEquation" class="mention hashtag" rel="tag">#<span>ConvectionDiffusionEquation</span></a> <a href="https://mathstodon.xyz/tags/DifferentialEquations" class="mention hashtag" rel="tag">#<span>DifferentialEquations</span></a> <a href="https://mathstodon.xyz/tags/AdvectionEquation" class="mention hashtag" rel="tag">#<span>AdvectionEquation</span></a> <a href="https://mathstodon.xyz/tags/DiffusionEquation" class="mention hashtag" rel="tag">#<span>DiffusionEquation</span></a> <a href="https://mathstodon.xyz/tags/TransportEquation" class="mention hashtag" rel="tag">#<span>TransportEquation</span></a> <a href="https://mathstodon.xyz/tags/ConvectionEquation" class="mention hashtag" rel="tag">#<span>ConvectionEquation</span></a></p>