ABSTRACT
Consider the following equation in compressible form of mass conservation:
k
0, 1 for 2-D stagnation, forced-convection, free-convection, 2-D jets, and k
1 for axisymmetric stagnation flows. Using Equations 11.26a to 11.26f (in the text), show that Equation A
becomes
Problem 11.2:
Consider energy, species and Shvab-Zeldovich represented by property “b” 2-D stagnation, forced, free convection, and 2-D jet, where S
(x, y) is the source term for the conserved scalar variable b. For example, if b
Y
, then the source term, S
kg/m
sec, and b
v
, S
(kg/m
)m/sec
kg/(m
sec
) or N/m
, momentum source or force in N per unit volume. Using the above equation and Equations 11.26a to 11.26f transform b(x, y) to the incompressible coordinate form b(x
′
, y
′
), i.e.,
Problem 11.3:
and property b as
ρv xy k( )
∂ ∂+ = +( )
(ii) the normalizations given in Equations 11.44 to 11.49 (in the text);
show that for any generic property b, Equation B becomes
Problem 11.4: Consider the generalized momentum equations presented in Problem 11.3. Deduce the momentum source term for (a) free convection, with Sv(x, y) = g (r∞ − r); (b) 2-D stagnation flow, k = 0, n = 1; and (c) axisymmetric stagnation flows, k = 1, n = 1.
