# Laminar Flow Through a Channel with Heated Walls

In this application, AcuSolve is used to simulate high Peclet number laminar flow through a channel with heated walls. AcuSolve results are compared with analytical results adapted from Hua and Pillai (2010). The close agreement of AcuSolve results with analytical results validates the ability of AcuSolve to model cases involving heat transfer to a moving fluid with a high Peclet number.

## Problem Description

## AcuSolve Results

## Summary

The AcuSolve results compare well with the analytical results for the development of a thermal boundary layer in a heated channel. In this application, the model is set up to yield large gradients as the flow convects away from the inlet. The boundary conditions and mesh size were chosen specifically to yield a high Peclet number. The element Peclet number in the flow direction in this case is Pe=30.0, as calculated from the following equation.

where $\rho $ is the density, $CP$ the heat capacity, ν the velocity, $he$ the length, and k the thermal conductivity.

This example shows the robustness of the stabilized technique in AcuSolve when element Peclet number is high. Note that standard Galerkin finite element formulations become unstable when the element Peclet number is greater than 1.0.

## Simulation Settings for Laminar Flow Through a Channel with Heated Walls

AcuConsole database file: <your working directory>\channel_laminar_heat\channel_laminar_heat.acs

Global

- Problem Description
- Analysis type - Steady State
- Temperature equation - Advective Diffusive
- Turbulence equation - Laminar

- Auto Solution Strategy
- Relaxation factor -
`0.4`

- Relaxation factor -
- Material Model
- Fluid_Material
- Density -
`1000.0`kg/m3 - Specific Heat -
`1000`J/kg-K - Viscosity -
`1.0e-12`kg/m-sec - Conductivitiy - 1.0 W/m-K

- Density -

Model

- Fluid_Material
- Volumes
- Fluid
- Element Set
- Material model - Fluid_Material

- Element Set

- Fluid
- Surfaces
- Inlet
- Simple Boundary Condition
- Type - Inflow
- Inflow type - Velocity
- X velocity -
`0.003`m/sec - Temperature -
`20`°C

- Simple Boundary Condition
- Outlet
- Simple Boundary Condition
- Type - Outflow

- Simple Boundary Condition
- Symm_MaxZ
- Simple Boundary Condition
- Type - Slip

- Simple Boundary Condition
- Symm_MinY
- Simple Boundary Condition
- Type - Slip

- Simple Boundary Condition
- Symm_MinZ
- Simple Boundary Condition
- Type - Slip

- Simple Boundary Condition
- Wall
- Simple Boundary Condition
- Type - Wall
- Temperature BC type - Value
- Temperature -
`75`°C

- Simple Boundary Condition

- Inlet

## References

Hua Tan and K. M. Pillai. "Numerical Simulation of Reactive Flow in Liquid Composite Molding Using Flux-Corrected Transport (FCT) Based Finite Element/Control Volume (FE/CV) Method". International Journal of Heat and Mass Transfer. 53:2256-2271, 2010.