7 Numerical Solution Examples

7.1 Laminar boundary layer

Shown in Fig. (1) is an animation of stream function (top) and temperature contours (bottom) for a laminarboundary layer. The simulation corresponds to ReL = 104 and Pr = 1. The starting length was Xs = 0.1,and 40 and 80 mesh points were used in the vertical and horizontal directions.

The initial condition has the fluid at rest with zero temperature. At t = 0 the inflow velocity is imposedon the left face and the surface temperature is instantly changed to unity. Understand that these conditionsare contrived; they do not represent some physically realistic initial value problem. Nevertheless, observethat the heat flux is initially uniform throughout the surface, with the exception of the leading edge. It willtake the convective flow one unit of time to traverse the heated surface – this is because the time is scaledwith the convective residence time L/U∞ – and the development of the boundary layers over this time spanis observed.

Figure 1. Stream function and temperature evolution, laminar boundary layer, Re = 104, Pr = 1.

Figure (2) shows the evolution of the local Nusselt number.

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Figure 2. Nux evolution, laminar boundary layer, Re = 104, Pr = 1.

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