Combined Free and Forced Convection
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
The Grashof number 
and the square of the Reynolds number 
are plotted as functions of the velocity of air as it passes over a flat plate. The yellow area represents the region where 
and free convection dominates heat transfer. The blue area represents the region where 
and forced convection dominates heat transfer. The dashed purple line represents the air velocity (select with slider), and the Nusselt number 
is displayed above the plot for that velocity. The plate diagram is a representation of the system. You can vary the plate temperature, fluid temperature and plate length with sliders.
Contributed by: Mathew L. Williams (April 2014)
Additional contributions by: Rachael L. Baumann and John L. Falconer
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA
Snapshots
Details
This Demonstration shows parameters that lead to combined forced and free convection over a flat plate. The conventional range where free and forced convection are combined is 
. A combined equation was used to calculate the Nusselt number for all velocities:
,
,
,
where the subscripts 
and 
refer to forced and natural convection, and 
is a constant determined by the critical Reynolds number.
The Reynolds number is:
,
where 
is the velocity of air, 
is plate length and 
is kinematic viscosity of air.
The Grashof and Rayleigh 
numbers are:
,
,
where 
is acceleration due to gravity, 
is the thermal expansion coefficient (approximated as 
), 
is the air temperature, 
is plate temperature and 
is the Prandtl number ( and are approximated by fitting an equation to a range of known values of and at corresponding temperatures for air).
Reference
[1] T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. DeWitt, Introduction to Heat Transfer, 6th ed., Hoboken: John Wiley and Sons, 2011.
Permanent Citation
Heat Transfer in a Bank of Tubes
Benjamin L. Kee
Parallel and Counterflow Heat Exchangers
Rachael L. Baumann
Carnot Cycles with Irreversible Heat Transfer
Rachael L. Baumann
Compressible Flow through a Nozzle/Diffuser
Rachael L. Baumann
Compare Compressors or Turbines with Different Efficiencies
Rachael L. Baumann
Temperature-Entropy Diagram for Water
Adam J. Johnston
Joule-Thomson Expansion
Adam J. Johnston
Effect of Tube Diameter on Plug Flow Reactor
Rachael L. Baumann
Inhibition of Enzyme Reactions in Continuous Stirred-Tank Reactor and Batch Reactor
Rachael L. Baumann
Forces on a Completely Submerged Gate
Rachael L. Baumann
