3 - General Equation

Below are listed the equations solved by CFD Studio:
  •  Energy conservation equation;
  •  Momentum conservation equation;
  •  Mass conservation equation;
These equations are combined in this general equation:




(3.1)
Then:







(3.2)
 
(3.3)

The contravariant velocities perpendicular to the constant lines x e h, respectively, and:
 




(3.4)
 
(3.5)
 
(3.6)
 
(3.7)

They are transformation metrics and the Jacobian matrix that we shall study in chapter (12).

In order to get the conservation equations from the general equation, we must evaluate f, Gf and Pf as shown on table 3.1.
  Conservation
equation
 f Gf Pf
  Global mass

 1 0 0
  Momentum in x axis
 u m
  Momentum in y axis
v m

  Energy T k / cp 0

Table 3.1 - Values of f, Gf and Sf

It is important to notice that (3.1) is arranged in such a way to solve also axisymmetric problems concerning the South face.

Deductions of conservation equations may be found in [3], and the change of coordinates from (x, y) to (x, h) of conservation general equation is explained in details in [1].

We should remark that we will solve (3.1) using the following simplification hypothesis: laminar and incompressible flow, fluid and constant thermo physical properties.
 
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