Thermally developing mixed electroosmotically and pressure-driven flow in a triangular micro-duct with a step change wall temperature is investigated. Both axial conduction (Graetz problem extended) and Joule heating effects are taken into consideration. A new higher order accurate method is proposed. The proposed method is based on pseudo spectral Galerkin approach and the eigenfunctions of the Helmholtz equation for a triangular geometry. Convergence of the method is investigated and the effect of the Péclet (Pe) number, Joule heating and Debye–Hückel parameter on the temperature distribution and Nusselt number (Nu) are discussed in detail.

中文翻译：

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三角形微管中压力驱动和电渗流组合的扩展Graetz问题的伪谱解

研究了在具有梯度变化壁温的三角形微管道中热电渗流和压力驱动流的混合流动。同时考虑了轴向传导（扩展了Graetz问题）和焦耳热效应。提出了一种新的高阶精度方法。所提出的方法是基于伪谱Galerkin方法和三角几何Helmholtz方程的本征函数。研究了该方法的收敛性，并详细讨论了佩克利（Pe）数，焦耳热和Debye-Hückel参数对温度分布和努塞尔数（Nu）的影响。