# Laminar Flow Through a Pipe With Imposed Heat Flux

In this application, AcuSolve is used to simulate the flow of mercury through a heated pipe. The AcuSolve results are compared with analytical results for pressure drop as described in White (1991), and with temperature changes as described in Incropera and DeWitt (1981). The close agreement of AcuSolve results with analytical results validates the ability of AcuSolve to model cases with flow and imposed heat flux.

## Problem Description

^{2}. The laminar velocity field is modeled as periodic to achieve a fully developed velocity profile. As the fluid moves through the pipe it is slowly heated by the heat flux on the wall, resulting in an increased centerline temperature. Pressure decreases along the pipe length due to the friction imposed by the viscous stresses near the pipe wall.

## AcuSolve Results

Analytical solution | AcuSolve solution | Percent deviation from analytical | |

Pressure drop (Pa) | 0.991 | 0.994 | 0.303 |

Centerline temperature of flow at outlet (K) | 316.917 | 316.269 | 0.204 |

## Summary

The AcuSolve solution compares well with analytical results for flow through a pipe with an imposed heat flux. In this application, the pressure drop in the fluid region is driven by the viscous stresses near the pipe wall. The temperature in the fluid region is influenced by the imposed heat flux on the walls. The values of pressure and temperature that are predicted by AcuSolve are within 0.3 percent of the analytical solution.

## Simulation Settings for Laminar Flow Through a Pipe With Imposed Heat Flux

SimLab database file: <your working directory>\pipe_laminar_heat\pipe_laminar_heat.slb

Global

- Problem Description
- Flow - Steady State
- Temperature equation - Advective Diffusive
- Turbulence equation - Laminar

- Auto Solution Strategy
- Relaxation Factor -
`0.2`

- Relaxation Factor -
- Material Model
- Mercury
- Density -
`13579.0`kg/m3 - Viscosity -
`0.001548`kg/m-sec

- Density -

Model

- Mercury
- Volume
- Fluid
- Element Set
- Material model - Mercury

- Element Set

- Fluid
- Surfaces
- Inflow
- Simple Boundary Condition - (disabled to allow for periodic conditions to be set)
- Advanced Options
- Integrated Boundary Conditions
- Mass Flux
- Type - Constant
- Constant value -
`-1.33e-3`kg/sec

- Mass Flux
- Temperature
- Type - Constant
- Constant value -
`300.0`K

- Integrated Boundary Conditions

- Outflow
- Simple Boundary Condition - (disabled to allow for periodic conditions to be set)

- Wall
- Simple Boundary Condition
- Type - Wall
- Temperature BC type - Flux
- Heat flux -
`2000.0`W/m2

- Simple Boundary Condition

- Inflow
- Periodics
- Periodic 1
- Individual Periodic BCs
- Velocity
- Type - Periodic

- Pressure
- Type - Single Unknown Offset

- Temperature
- Type - Single Unknown Offset

- Velocity

- Individual Periodic BCs

- Periodic 1

## References

F. M. White. "Viscous Fluid Flow". Section 3-2.1. McGraw-Hill Book Co., Inc.. New York. 1991.

F. P. Incropera and D. P. DeWitt. "Fundamentals of Heat Transfer". John Wiley & Sons. New York. 1981.