Fluid Mechanics

TEHD in cylindrical annuli: laboratory results

Consider a fluid-filled cylindrical enclosure with an inner heated cylinder of radius ri maintained at temperature Ti and an outer cooled cylinder of radius ro maintained at temperature To. The annulus is of height H with adiabatic top and bottom boundaries. The temperature difference DT = To-Ti induces natural convection in the gap width d = ro-ri at infinitesimal small increments of DT. This base flow experiences transition to instabilities depending on the radius ratio h= ri/ro, aspect ratio G = H/d, physical properties of the fluids (weighted with the Prandtl number) and on the driving force (weighted with the Rayleigh number). In this work here, we study the dielectrophoretic effect as heat transfer augmentation force via the performance of an alternating (a.c.) electric field superposing natural convection in the annulus experimentally. This procedure allows introducing an electric Rayleigh number for the system. Even though that dielectrophoretic effect has been neglected in comparison to dielectric (Coulomb) forces, that are driven by direct current (d.c.) electric fields, we are able to describe clear distortions of the base flow via flow visualization (shadowgraph). In addition, we quantify heat transfer via heating power measurements resulting in the determination of a Nusselt number for the inner cylinder. As already observed by Chandra and Smylie [1] and also described in [2] we observe a minimum of the Nu-numbers in the lower parameter domain of Rae. Up to now, an explanation for this damping of the heat transfer by the superposed electric field is missing. This behavior cannot be seen in the horizontal cell configuration case.


  1. Chandra, B. and Smylie, D. E. (1972). A laboratory model of thermal convection under a central force field. Geophysical Fluid Dynamics, vol. 3, pp. 211- 224.
  2. Dahley, N., Crumeyrolle, O., Futterer, B., Egbers, Ch., & Mutabazi, I. (2011). Parabolic flight experiment "Convection in a Cylinder" - Convection patterns in varying buoyancy forces. J.Phys.: Conf. Ser., vol. 318, p. 082003 (8pp).
  3. Dahley, N., Futterer, B., & Egbers, Ch., (2011). Control of convection by different buoyancy forces. 3rd Micro and Nano Flow Conference, Thessaloniki, Greece, 2011, Brunel, University Press, 2011, Hrsg.: T. Karayiannis, M. Collins, ISBN: 978-1-902316-98-7.
  4. Futterer, B., Dahley, B., & Egbers, C. (2013). Thermal electro-hydrodynamic heat transfer augmentation in vertical annuli exerting dielectrophoretic forces through a.c. electric field. Int. J. Heat Mass Transfer.