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situations, it is customary to compare the results with analytical, or experimental, data if
available. The past experience of the user also helps in obtaining an accurate solution for
complicated problems. CONVECTION HEAT TRANSFER
7.10 Laminar Isothermal Flow

In this section, an example of a steady state isothermal flow problem is discussed. The
isothermal solution procedure is obtained by neglecting the temperature, or energy, equation
from the governing set of equations. In other words, Step 4 of the scheme is neglected
thereby assuming isothermal flow. The problem selected is a simple two-dimensional devel-
oping flow in a rectangular channel as shown in Figure 7.17.

7.10.1 Geometry, boundary and initial conditions

The ‘CBS flow’ code is used to solve this problem. The steps employed are as discussed
in Section 7.5. However, the ‘CBS flow’ code is written using a non-dimensional form of
the governing equations. Therefore, the steps of the scheme have to undergo appropriate
changes. The non-dimensional scaling discussed in Section 7.3.1 should be reflected in
the geometry. The non-dimensional geometry used is shown in Figure 7.17. The defined
inlet Reynolds number is based on the inlet height and is therefore equal to unity in the
non-dimensional form. The length of the channel was assumed to be 15 times the height.
On the basis of the characteristic analysis discussed in many books, (Hirsch 1989), a
subsonic, incompressible two-dimensional isothermal flow problem requires two boundary
conditions at the inlet and one boundary condition at the exit. It is normal practice to
impose the velocity components at the inlet and pressure at the exit. In order that pressure
may be imposed at the exit, it is necessary that the flow does not undergo any appreciable
variation close to the exit. In other words, the channel length should be much greater than
the height.
The boundary conditions may be summarized as follows:

Inlet: Uniform velocity component u 1 of a non-dimensional value of unity and the velocity
component u 2 equal to zero.
Exit: A constant non-dimensional pressure value is assumed. Here, the value is prescribed
as being zero.

Inlet: u 1 = 1, u 2 = 0
Solid wall
Exit:
1 u 1 = u 2 = 0 p = 0
Solid wall
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Figure 7.17 Flow through a two-dimensional rectangular channel. Geometry and boundary
conditions