This module covers natural convection in a fluid-saturated, permeable material. A number of recent graduate-level heat transfer texts cover this topic. The problem is analogous to classical Rayleigh-Benard natural convection in homogeneous fluid layers. The fluid is assumed to be “Boussinesq,” i.e., the fluid density is only a function of temperature and variable only in the body force term. In addition, it completely fill all interstices. The Darcy equations govern the fluid motion. Heating is from the bottom of the layer or from side to side.
Module Description
Inputs
Before any run the user selects the aspect ratio of the layer and the number of grid points to be used in the vertical direction. The model uses the same grid spacing in both directions. That being the case, we accomodate different aspect ratios by simply adding or subtracting columns of grid points in the horizontal direction. The user may not change these two parameters once a calculation is begun. Before as well during a run the user may set the Rayleigh number for the calculation. They may also change the heating mode from either bottom-to-top or side-to-side. (The remaining sides are taken as adiabatic.)
Display
Unless the user elects to stop prematurely, the program runs to a prescribed non-dimensional time. During that interval a succession of 200 color contour plots of temperature are drawn in the left-hand window creating an animation effect. Contours of stream function are superimposed on top if the user selects that option. The Nusselt number computed at both the bottom and top (or at the left and right sides if that heating option has been selected) is plotted in the righthand window as a function of time. Switching the heating direction or changing the Rayleigh number in the midst of a run produces interesting transients.
Unless one has selected a very large number of grid points (which may happen especially with a low height/width ratio), performance is satisfactory on most current platforms. Very thorough implementation instructions of this algorithm are available and may be downloaded from within the program executable. Development of this algorithm is suitable as a several-week-long project in a graduate-level computational methods or convection heat transfer course.
Video Introduction
A two-minute-long video demontrating the capabilites of HTTPorous may be found here.