Natural Convection: Fluid Flow using FEniCS, University of Colorado Boulder

Under the influence of a gravitational field, a differential temperature applied to opposite sides of a cavity causes buoyancy-driven convective flow. In practical analysis, the specification of a heat transfer convection coefficient drives the modeling of natural convection. However, high sensitivity to the chosen constant convection coefficient is a source of error for heat transfer analysis. Hence, the idea of this numerical study is to model convection coupling the following:

  • Navier Stokes Equations – Conservation of momentum
  • Advection-Diffusion Equation – Conservation of thermal energy

The initial validation of the solution of equations was conducted by simulating a steady recirculating flow in a square cavity. After the solution was validated, the main study focused on a practical engineering application: analyzing the natural convective flow around a heated plate geometry (a good use case would be, for example, estimating the convection from inclined
solar panel.)

The final problem was implementing Unsteady Convection in a Differential Heated Cavity using Monolithic Solve solution algorithm.

Description of domain and boundary conditions in square cavity (left), and the structured mesh we used for simulation of our problem
Representations of Isotherms from our analysis (top), reference results from Donea Huerta’s Finite Element Methods for Flow Problems (bottom)
Temperature (Upper) and Velocity (Lower) Contours, Steady Convection Flow around Incline Plate Geometry,
Unsteady Convective Flow: Problem Setup
Unsteady Convective Flow: Temperature Contour Plots.

Related Posts