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Variational formulation on Joule heating in combined electroosmotic and pressure driven microflows

Sadeghi, A ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ijheatmasstransfer.2013.01.065
  3. Publisher: 2013
  4. Abstract:
  5. The present study attempts to analyze the extended Graetz problem in combined electroosmotic and pressure driven flows in rectangular microchannels, by employing a variational formulation. Both the Joule heating and axial conduction effects are taken into consideration. Since assuming a uniform inlet temperature profile is not consistent with the existence of these effects, a step change in wall temperature is considered to represent physically conceivable thermal entrance conditions. The method of analysis considered here is primarily analytical, in which series solutions are presented for the electrical potential, velocity, and temperature. For general treatment of the eigenvalue problem associated with the solution of the thermal field, an approximate solution methodology based on the variational calculus is employed. An analytical solution is also presented by considering thin electrical double layer limits. The results reveal non-monotonic behaviors of the Nusselt number such as the occurrence of singularities in the local Nusselt number values when the fluid is being heated from the wall. Moreover, the effect of increasing the channel aspect ratio is found to be increasing both the temperature difference between the wall and the bulk flow and the Nusselt number. In addition, higher wall heat fluxes are obtained in the entrance region by increasing the Peclet number
  6. Keywords:
  7. Microchannel ; Approximate solution ; Axial conduction effects ; Bulk flow ; Channel aspect ratios ; EDL ; Eigenvalue problem ; Electrical double layers ; Electrical potential ; Electroosmotic ; Electroosmotic flow ; Entrance region ; Graetz problem ; Inlet temperature ; Local Nusselt number ; Method of analysis ; Microflows ; Pressure-driven ; Pressure-driven flows ; Rectangular microchannels ; Series solutions ; Step changes ; Temperature differences ; Thermal entrance ; Thermal field ; Variational formulation ; Wall heat flux ; Wall temperatures ; Aspect ratio ; Eigenvalues and eigenfunctions ; Electric properties ; Joule heating ; Microchannels ; Nusselt number ; Variational techniques ; Electroosmosis
  8. Source: International Journal of Heat and Mass Transfer ; Volume 61, Issue 1 , June , 2013 , Pages 254-265 ; 00179310 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0017931013000963