Skip to content
Quanscient logo Quanscient Allsolve Docs

Laminar flow

This page describes the governing equations for incompressible laminar fluid flow in Allsolve. Laminar flow is the fluid dynamics physics used in conjugate heat transfer simulations, where it supplies the velocity field that transports heat through the fluid domain.

Governing equations

Section titled “Governing equations”

The Laminar flow physics solves the incompressible Navier-Stokes equations,

∇⋅vf=0\nabla \cdot \boldsymbol{v}_{\mathrm{f}} = 0 \\[5pt] ρf(∂vf∂t+vf⋅∇vf)=−∇pf+∇⋅(μf(∇vf+(∇vf)T)),\rho_{\mathrm{f}} \left( \frac{\partial \boldsymbol{v}_{\mathrm{f}}}{\partial t} + \boldsymbol{v}_{\mathrm{f}} \cdot \nabla \boldsymbol{v}_{\mathrm{f}} \right) = - \nabla p_{\mathrm{f}} + \nabla \cdot \left( \mu_{\mathrm{f}} \left( \nabla \boldsymbol{v}_{\mathrm{f}} + \left( \nabla \boldsymbol{v}_{\mathrm{f}} \right)^T \right) \right),

where

  • ρf [kg/m3]\rho_{\mathrm{f}} ~ \rm [kg/m³] is fluid density,
  • μf [Pa⋅s]\mu_{\mathrm{f}} ~ \rm [Pa \cdot s] is the dynamic viscosity of the fluid,
  • pf [Pa]p_{\mathrm{f}} ~ \rm [Pa] is pressure, and
  • vf [m/s]\boldsymbol{v}_{\mathrm{f}} ~ \rm [m/s] is the flow velocity of the fluid.

The first equation enforces incompressibility (mass conservation), and the second is the momentum balance.

Couplings to other physics

Section titled “Couplings to other physics”

This formulation supports the following couplings:

  • Thermal fluid — Heat fluid, to advect the temperature field with the flow
  • Fluid structure interaction — Solid mechanics, Elastic waves

In a conjugate heat transfer setup, Laminar flow is combined with Heat fluid and Heat solid. See Heat fluid for how the three physics fit together.

Compatibilities with analysis types

Section titled “Compatibilities with analysis types”

Laminar flow supports all analysis types: Static, Harmonic, Multiharmonic, Transient, and Eigenmode.

See the full compatibility table in Simulations overview.

Use cases

Section titled “Use cases”