External Flow External flow system Boundary layers develop

External Flow External flow system Boundary layers develop freely, without constraints imposed by adjacent surfaces (low speed, forced convection with no phase change occurring within the fluid) Primary objective Determination of convection coefficients ( h, hm ) for different flow geometries

The Flat Plate in Parallel Flow Steady, incompressible, laminar flow over an immersed plate at temperature Ts with constant fluid properties and negligible viscous dissipation and dp/dx=0. y x T T=Ts Edge of momentum boundary layer Edge of thermal boundary layer

Blasius Solution (similarity solution) Governing Equations Boundary Conditions Method

Blasius Solution Momentum

Energy For Pr > 0. 6, the nondimensional surface gradient at the surface is found to be proportional to Pr 1/3.

Solution

Solving equation 7. 21 for the temperature profile for different Prandtl number and using the definition of thermal boundary layer,

Species For Sc > 0. 6, the nondimensional surface gradient at the surface is found to be proportional to Sc 1/3

Solution

By the concentration profile for different Sc number and the definition of the concentration boundary layer,

Turbulent flow

Mixed Boundary Layer Conditions

What if there is unheated starting length (USL)? For both UST and USF, the effect of the USL on the local Nusselt number may be represented as follows: Laminar : a=3/4, b=1/3, C=0. 332, m=0. 5 Turbulent: a=9/10, b=1/9, C=0. 0296, m=0. 8

The Cylinder in Cross Flow • Conditions depend on special features of boundary layer development, including onset at a stagnation point and separation, as well as transition to turbulence. – Stagnation point: Location of zero velocity and maximum pressure. – Followed by boundary layer development under a favorable pressure gradient (dp/dx<0) and hence acceleration of the free stream flow(du∞/dx>0) – As the rear of the cylinder is approached, the pressure must begin to increase. Hence, there is a minimum in the pressure distribution, p(x), after which boundary layer development occurs under the influence of an adverse pressure gradient ( dp/dx > 0, du∞/dx < 0 )

– Separation occurs when the velocity gradient (du/dy at y=0) reduces to zero and is accompanied by flow reversal and a downstream wake. Cylinder in Cross Flow (cont. ) – Location of separation depends on boundary layer transition.

Convection Heat and Mass Transfer Local Nusselt number for airflow normal To a circular cylinder (W. H. Giedt, 1949) Read pp 409