Heat transfer in fluids

This page describes the governing equations for heat transfer in fluids in Allsolve. Heat fluid resolves the temperature field inside a fluid domain, where heat is both advected by the flow and diffused through the fluid.

Governing equations

The Heat fluid physics solves the advection-diffusion equation for the temperature field in the fluid domain,

\rho_{\mathrm{f}} \, C_{\mathrm{p,f}} \left(\frac{\partial T}{\partial t} + \boldsymbol{v}_{\mathrm{f}} \cdot \nabla T \right) = \nabla \cdot \left( k_{\mathrm{f}} \nabla T \right),

where

$T ~ \rm [K]$ is fluid temperature,
$\rho_{\mathrm{f}} ~ \rm [kg/m³]$ is fluid density,
$\boldsymbol{v}_{\mathrm{f}} ~ \rm [m/s]$ is the flow velocity of the fluid,
$C_{\mathrm{p,f}} ~ \rm [J/(kg \cdot K)]$ is the specific heat capacity of the fluid at constant pressure (assumed constant), and
$k_{\mathrm{f}} ~ \rm [W/(m \cdot K)]$ is the thermal conductivity of the fluid.

The velocity field $\boldsymbol{v}_{\mathrm{f}}$ comes from Laminar flow through the Thermal fluid coupling. Without that coupling the advection term vanishes and the equation reduces to pure diffusion.

Conjugate heat transfer

Conjugate heat transfer (CHT) simulations resolve the temperature field across both a fluid and a solid domain. They require three physics,

Laminar flow
Heat fluid
Heat solid

as well as their strongly coupled interactions.

The temperature field $T$ is continuous across the fluid and the solid domains. Thus, the interaction is strongly coupled and no material specific suffixes are required.

Couplings to other physics

This formulation supports the following couplings:

Thermal fluid — Laminar flow, to advect the temperature field with the flow
Thermal expansion — Solid mechanics, Elastic waves

Compatibilities with analysis types

Heat fluid supports all analysis types: Static, Harmonic, Multiharmonic, Transient, and Eigenmode.

See the full compatibility table in Simulations overview.