Page 242 - Finite Element Analysis with ANSYS Workbench

12.1 Basic Equations 233

pressure,  is the total energy,  and  are the normal stresses,
y
x
 xy is the shearing stress, q and q are the heat fluxes in the x-
x
y
and y-directions.

12.1.2 Related Equations

The total energy consists of the internal energy e and
the kinetic energy as,
1
u 
 = e   2 v
2
2
The internal energy e can be written in forms of the temperature T
or the pressure p as,
e = c v T = p ( 1  ) 
where  is ratio of the specific heats at constant pressure and
volume,
 = c p c
v
The pressure p can also be written in form of the total
energy  and velocity components u, v as,


p =     1   1    2  v 2 u  
 2 
The internal energy e is used to determine the enthalpy h from,


h = e =   1   2  v 2 u  
 2 
and the total enthalpy H from,

1    1
u 
u 
H = h   2 v =    2 v
2
2
2 2
The speed of sound a is determined from the pressure and density,
a =  p 
In the above differential equations, the normal stress
components and shearing stress are written on forms of the velocity
components u, v as,