Heat Transfer Today

Educational Software for
Heat and Mass Transfer

Student Projects

Self-similar Boundary Layer Calculations

In this project we implement a 4th order Runge-Kutta integration scheme to solve the Blasius equation for laminar flow over a flat plate.   Since one of the three boundary conditions is given out at the freestream (η = ∞), a shooting method based on the half-interval method is implemented.   Once the solution for the flow is in hand, those results are used in solving the temperature distribution for two cases: (1) With a fixed wall temperature and no viscous dissipation (2) With viscous dissipation included and the wall kept adiabatic.   A tridiagonal system for the temperature distribution arises in both cases.  For the latter scenario, the final temperature distributions look as seen below:

Temperature arising in self-similar, laminar boundary layer flow on a flat plate due to viscous dissipation. Three representative fluids, Mercury ( Pr << 1), Water ( Pr >1 )and Air ( Pr ~ 1 ) are included for comparison. As expected, the computed wall temperatures (adiabatic wall temperatures) are found to be about the square root of the Prandtl number.


Note that a much more versatile and highly interactive forced convection boundary layer virtual laboratory is available as part of the Heat Transfer Today collection as a Visual Studio executable.

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