Loading...

Graetz problem extended to mixed electroosmotically and pressure-driven flow

Sadeghi, A ; Sharif University of Technology | 2012

641 Viewed
  1. Type of Document: Article
  2. DOI: 10.2514/1.T3737
  3. Publisher: 2012
  4. Abstract:
  5. Thermally developing mixed electroosmotically and pressure-driven flow in a parallel plate microchannel with a step change in wall temperature is considered in the framework of an extended Graetz problem. Both Joule heating and viscous dissipation effects are taken into consideration. Expressions for the dimensionless temperature and Nusselt number in the form of infinite series are presented. In general, the associated eigenvalue problem is solved numerically. Nevertheless, an analytical solution is also presented for axial locations close to the entrance. Comparisons are made between the present results and those obtained by approximating the electroosmotic velocity with the Helmholtz-Smoluchowski velocity. It is revealed that, for a pressure-assisted flow with a sufficiently high magnitude of pressure gradient, the Nusselt number is weakly dependent on the dimensionless Debye-Hückel parameter. Accordingly, the approximate solution is valid for such cases. However, unless a sufficiently large value of the dimensionless Debye-Hückel parameter is considered, the incurred error rapidly increases when the pressure gradient is absent or acts adversely. The approximate solution also fails to predict accurate results near the singularity points that occur in the Nusselt numbers when the wall temperature in the downstream is higher than that of upstream
  6. Keywords:
  7. Analytical solutions ; Approximate solution ; Axial locations ; Eigenvalue problem ; Electroosmotic velocity ; Graetz problem ; Infinite series ; Parallel plates ; Pressure-driven flows ; Singularity point ; Step changes ; Viscous dissipation ; Wall temperatures ; Eigenvalues and eigenfunctions ; Pressure gradient ; Nusselt number
  8. Source: Journal of Thermophysics and Heat Transfer ; Volume 26, Issue 1 , 2012 , Pages 123-133 ; 08878722 (ISSN)
  9. URL: http://arc.aiaa.org/doi/abs/10.2514/1.T3737