Combined Free and Forced Convection

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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
Open content licensed under CC BY-NC-SA



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).


[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.

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