Page 291 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

SOME EXAMPLES OF FLUID FLOW AND HEAT TRANSFER PROBLEMS
2.5 3 Re = 100 283
Re = 200
Local Nusselt number 1.5 1
Re = 300
Re = 500
2

0.5
0
5 10 15 20 25 30 35 40
Horizontal distance

Figure 9.23 Forced convection heat transfer downstream of a backward-facing step. Local
Nusselt number distribution on the hot wall for different Reynolds numbers

Figure 9.22 shows the temperature contours for all the different Reynolds numbers
considered. Previous studies indicate that the maximum heat transfer occurred close to
the reattachment length. The incompressible flow is attached to the wall from the inlet
until it reaches the step. The flow is detached from the bottom wall and recirculation
develops downstream of the step as shown previously for the non-isothermal case. The
flow reattaches itself to the bottom wall after the recirculation in the downstream portion
of the step. The location at which the reattachment takes place varies with the Reynolds
number. The higher the Reynolds number, the farther will be the reattachment point from
the step. The reattachment distances from the step are given in Figure 9.22. These values
are in close agreement with reported results (Kondoh et al. 1993).
The thermal action predominantly takes place downstream of the step in the bottom
portion of the channel. It may be observed that as the flow approaches the reattachment
point, the thermal boundary layer shrinks indicating a stronger temperature gradient in the
vicinity of the reattachment point and thus a higher heat transfer rate taking place close to
this point. This is clearly demonstrated in Figure 9.23 in which the local Nusselt number
is plotted along the hot wall downstream of the step. The local Nusselt number starts with
an almost zero value at the corner close to the step and increases smoothly to a maximum
value close to the reattachment point and then drops. It appears that the peak Nusselt
number value is calculated close to, but just after, the reattachment point. After reaching
the peak value, the local Nusselt number drops as the flow approaches the exit.

9.4 Thermal Conduction in an Electronic Package

Electronic packages (EP) are the integrated circuit (IC) carriers called components that are
used in the boards of all electronic systems. EP protect IC chips from a hostile environment,
communicate with other circuit boards and enhance the heat dissipation during operation.
In this section, an investigation has been carried out to find the thermal performance
of an electronic package, which is represented normally by the thermal resistance between