##### Boundary Layer

##### Description

This simulation shows laminar flow over an isothermal, flat plate where the plate temperature \( T_{s} \) is greater than the free stream fluid temperature \( T_{\infty} \). The user has the ability to study hydrodynamic effects or thermal effects by selecting the radio button in the top right corner of the window. When “velocity” is selected, the velocity boundary layer thickness \( \delta \) is highlighted and plotted with normalized position along the length of the plate \( x/x_{crit} \). Here, \( x_{crit} \) is the critical location for transition from laminar flow to turbulent flow. Additionally, the velocity profile inside the boundary layer (x-component of velocity \( u \) with height above the plate \( y \)) is highlighted and plotted at the position of the slider bar. The slope of the velocity profile at the surface of the plate \( \frac{ \partial u }{ \partial y } |_{y=0} \) as a function of \( x/x_{crit} \) is highlighted and plotted in the lower left plot. The non-dimensional quantity local coefficient of friction \( C_{f,x} \) as a function of \( x/x_{crit} \) is highlighted and plotted in the lower middle plot. The lower right plot shows the local convection coefficient as a function of position for a specific fluid and flow velocity.

When “temperature” is selected, the thermal boundary layer thickness \( \delta t \) is highlighted and plotted with \( x/x_{crit} \). The temperature profile inside the boundary layer (fluid temperature \( T \) with height above the plate \( y \)) is highlighted and plotted at the position of the slider bar. The slope of the temperature profile at the surface of the plate \( \frac{ \partial T }{ \partial y } |_{y=0} \) as a function of \( x/x_{crit} \) is highlighted and plotted in the lower left plot. The nondimensional quantity local Nusselt number \( Nu_{x} \) as a function of \( x/x_{crit} \) is highlighted and plotted in the lower middle plot. The local convection coefficient \( h_{x} \) as a function of \( x/x_{crit} \) is shown in the lower right plot (solid black line) for a specific fluid. The average convection coefficient between the leading edge and the position of the slider bar \( h_{0 – x} \) is related to the integral of \( h_{x} \) and is indicated in the plot window. Change the Prandtl number \( Pr \) of the fluid with the drop-down menu and observe how it affects \( \delta t \), \( \frac{ \partial T }{ \partial y } |_{y=0} \), \( Nu_{x} \), \( h_{x} \), and \( h_{0 – x} \).