### Abstract

The electrothermal flow phenomena can be applied to many microfluidic devices such as lab-on-a-chip. As a result of the small length scale in these devices, the fluid flow is characterized by a low Reynolds number thus allowing the governing equations to become linear. In this paper, a 2D numerical modeling of the electrothermal flow using boundary element method (BEM) is presented. BEM is an advantageous option for simulating the electrothermal flow. In an electrothermal flow, the volumetric body force depends on the electric field and temperature gradient. The physics is mathematically modeled by (i) Laplace's equation for the electrical potential, (ii) Poisson's equation for the heat conduction with Joule heating, and (iii) continuity and Stokes equations for the low Reynolds number flow. When using BEM to solve the equations, it is well known that a singular integral arises when the source point approaches the field point. Accurate evaluation of the singular integral is important to obtain an accurate simulation. To this end, all the singular and non-singular integrals are evaluated analytically. Consequently, an accurate algorithm is obtained. The formulation and implementation of BEM to model the electrothermal flow and the resulting electrical potential, temperature field, Joule heating and velocity field are presented in this paper.

Original language | English (US) |
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Pages (from-to) | 2777-2795 |

Number of pages | 19 |

Journal | Applied Mathematical Modelling |

Volume | 39 |

Issue number | 9 |

DOIs | |

State | Published - May 1 2015 |

### Keywords

- Boundary element method
- Buoyancy force
- Coulomb force
- Dielectric force
- Laplace's equation
- Stokes flow

### ASJC Scopus subject areas

- Modeling and Simulation
- Applied Mathematics

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## Cite this

*Applied Mathematical Modelling*,

*39*(9), 2777-2795. https://doi.org/10.1016/j.apm.2014.11.013