Page 289 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

SOME EXAMPLES OF FLUID FLOW AND HEAT TRANSFER PROBLEMS
equations in the gravitational direction. In this section, we will consider a forced heat
convection problem in the downstream portion of a backward-facing step. For coupled
natural and mixed convection problems, the readers are referred to Chapter 7. 281
9.3.1 Backward-facing step
The problem definition is similar to the isothermal flow past a backward-facing step as
discussed in the previous section, the difference being that additional boundary conditions
are prescribed for the temperature field. The boundary conditions discussed in reference
(Kondoh et al. 1993) will be adopted. The solid downstream bottom wall was assumed to
be at a higher temperature than the fluid (results presented here are for air with Pr = 0.71)
entering the channel. All other solid walls were assumed to be insulated. All other boundary
conditions for the velocity and pressure values are the same as the ones discussed for the
isothermal problem in the previous section and are repeated in Figure 9.19.
Three different meshes have been employed to make sure that the solutions presented
are accurate. The first mesh used was mesh (a) in Figure 9.9. The second and third meshes
are finer than the first mesh and are shown in Figure 9.20.
A maximum Reynolds number of 500 was studied. All three meshes were employed to
study the heat transfer at this Reynolds number. The local Nusselt number distribution on
the hot wall downstream of the step is shown in Figure 9.21. As seen, the Nusselt number

Parabolic u and u = 0, T = 0
2
1
2L p = 0
u = u = 0
1
2
T = 1
L
4L 36L
Figure 9.19 Forced convection heat transfer downstream of a backward-facing step.
Geometry and boundary conditions

(a) Mesh2, nodes:8131, elements:15,410

(b) Mesh3, nodes:11,659, elements:22,257

Figure 9.20 Forced convection heat transfer downstream of a backward-facing step.
Unstructured meshes