1. External Convection: Laminar Flat Plate
For a constant property, laminar flow a similarity solution exists for the flow field u(y)
Major flow parameters:
local boundary layer thickness
local skin friction coefficient
average skin friction coefficient

2. External Convection: Laminar Flat Plate
For a constant property, laminar flow a similarity solution exists for the flow field u(y)
Major heat transfer parameters:
local thermal boundary layer thickness
uniform surface temperature, Ts
local Nusselt number
(Pr > 0.6)
average Nusselt number
uniform surface heat flux, q”s
local Nusselt number
(Pr > 0.6)
average Nusselt number

3. External Convection: Turbulent Flat Plate
For turbulent flow, only empirical relations exist
local skin friction coefficient
uniform surface
temperature, Ts
uniform surface
heat flux, q”s
local Nusselt number
(Pr > 0.6)
Average parameters
average skin friction coefficient
average Nusselt number
assuming xc for Rex,c = 5×105
uniform surface
temperature, Ts
For xc= 0 or L >> xc (Rex,L >> Rex,c)
average skin friction coefficient
uniform surface
temperature, Ts
average Nusselt number

4. External Convection: Starting Length
The effect of an unheated starting length (USL) can be represented on the local Nusselt number as:
Parameters a, b, C, & m depend on
thermal boundary condition: uniform surface temperature (UST) or uniform heat flux (UHF)
flow conditions: laminar or turbulent
where
LAMINAR
TURBULENT a
3/4
9/10 b
1/3
1/9 C
0.332
0.453
0.0296
0.0308 m
1/2
4/5

5. External Convection: Starting Length
Uniform Surface Temperature (UST)
Uniform Heat Flux (UHF)
The Nusselt number (and heat transfer coefficient) are functions of the fluid properties (ν,ρ,α,cp,k)
the effect of variable properties may be considered by evaluating all properties at the film temperature
most accurate solutions often require iteration on the film properties
p = 1 (laminar throughout)
p = 4 (turbulent throughout)
numerical integration for laminar/turbulent flow

6. External Convection: Cylinder in Cross Flow
As with flat plate flow, flow conditions determine heat transfer
Flow conditions depend on special features of boundary layer development, including onset at stagnation point, separation, and onset of turbulence
Stagnation point: location of zero velocity and maximum pressure
boundary layer development under a favorable pressure gradient  acceleration of the free stream flow
There is a minimum in the pressure distribution p(x) and toward the rear of the cylinder, the pressure increases.
boundary layer development under an adverse pressure gradient

7. External Convection: Cylinder in Cross Flow
Separation occurs when the momentum of the free stream flow is insufficient to overcome the adverse pressure gradient
the velocity gradient reduces to zero
flow reversal occurs accompanied by a downstream wake
Location of separation depends on boundary layer transition
note:

8. External Convection: Cylinder in Cross Flow
Force (FD) imposed by the flow on the cylinder is composed of two phenomena
friction  boundary layer shear stress
form drag (pressure drag)  pressure differential due to wake
drag
coefficient
Af is the area projected perpendicular to free stream

9. External Convection: Cylinder in Cross Flow
Thermal considerations: uniform surface temperature, Ts
heat transfer a function of the angel of separation θ
empirical correlations are used to determine average Nusselt numbers
Hilpert correlation: Pr ≥ 0.6
also suitable for non-circular cylinders
Churchill and Bernstein: ReDPr > 0.2
ReD C m
0.4-4
0.989
0.330
4-40
0.911
0.385
0.683
0.466
,000
0.193
0.618
40, ,000
0.027
0.805

10. External Convection: Sphere in Cross Flow
Similar flow issues as cylinder in cross flow arise
Thermal considerations: uniform surface temperature, Ts
heat transfer again defined by empirical correlations
Whitaker correlation:
0.71 < Pr < 380
3.5 < ReD < 7.6×104
evaluate fluid properties at T∞ except for μs which is evaluated at Ts

11. External Convection: Impinging Jet
Impinging jet consists of a high speed flow impacting a flat surface
generates large convection coefficients
The flow and heat transfer are affected by a number of factors
shape/size of jet, velocity of jet, distance from plate, …
Significant hydrodynamic features:
mixing and velocity profile development in the free jet
stagnation point and zone
velocity profile development in the wall jet

12. External Convection: Impinging Jet
Local Nusselt number distribution:
Average Nusselt number based on empirical correlations for single nozzles and arrays of nozzles
function of Reynolds number, Pr, distance along wall (r or x), height of jet (H)

13. External Convection: Impinging Jet
Martin correlation: uniform surface temperature, Ts
single round nozzle
single slot nozzle
valid for
valid for