This paper presents semi-analytical solutions to the Extended Graetz Problem in micro-channels. The flow driving mechanism is electroosmosis combined with a pressure gradient. The hypothesis of a thin electrical double layer (EDL) is not considered, leading to a more realistic model. The considered problem is that of laminar flow in a rectangular channel. The solution methodology is based on the Generalized Integral Transform Technique. The presented solution yields a closed-form expression for calculating the Nusselt number. The only numerical step required by the solution involves the numerical computation of eigenvalues and eigenvectors, necessary for a matrix exponential evaluation. With the results, the effects of the channel geometry and flow driving mechanisms on the Nusselt number are analyzed.
- Fluids Engineering Division
- Heat Transfer Division
Semi-Analytical Solutions to the Extended Graetz Problem in Rectangular Microchannel Flow Driven by Electroosmosis
Sphaier, LA, & Moreira, DC. "Semi-Analytical Solutions to the Extended Graetz Problem in Rectangular Microchannel Flow Driven by Electroosmosis." Proceedings of the ASME 2013 11th International Conference on Nanochannels, Microchannels, and Minichannels. ASME 2013 11th International Conference on Nanochannels, Microchannels, and Minichannels. Sapporo, Japan. June 16–19, 2013. V001T12A016. ASME. https://doi.org/10.1115/ICNMM2013-73179
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