Page 235 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

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CONVECTION HEAT TRANSFER
7.11.3 Mixed convection heat transfer
A mixed convection heat transfer mode has features of both forced and natural convection.
The mixed convection solution to a heat transfer problem is necessary if the Reynolds num-
ber is small and the importance of the buoyancy contribution is significant. The equations
solved are those of forced convection with the addition of a source term (Equation 7.70)
in the gravitational direction. If the direction of gravity is not aligned with either of the
coordinate directions (x 1 and x 2 ), then appropriate components of the source term need to
be added to the momentum equations. The effect of mixed convection can be measured by
calculating the source term of Equation 7.70. If this term is close to zero, then the buoyancy
effects can be ignored and a forced convection solution is sufficient. However, if the value
of the source term is far from being zero (either in the negative or positive sense), then a
mixed convection solution is essential.
Here we consider a simple mixed convection problem in a rectangular vertical channel
as shown in Figure 7.29. In order to compare the results with the analytical solution for

Flow reversal
p = 0

Cold wall Hot wall
u 1 = u 2 = 0 g u 1 = u 2 = 0 3
T c = 0 T h = 1

x 2

x 1

Cold fluid in
u 2 = 1
u 1 = 0
T a = 0

1
Figure 7.29 Mixed convection in a vertical channel. Geometry and boundary conditions