# A numerical study of 2D electrothermal flow using boundary element method

Qinlong Ren, Cholik Chan, Alberto L. Arvayo

Research output: Contribution to journalArticle

9 Citations (Scopus)

### 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) 2777-2795 19 Applied Mathematical Modelling 39 9 https://doi.org/10.1016/j.apm.2014.11.013 Published - May 1 2015

### Fingerprint

Boundary element method
Boundary Elements
Numerical Study
Joule heating
Joule Heating
Reynolds number
Low Reynolds number
Singular Integrals
Lab-on-a-chip
Laplace equation
Poisson equation
Microfluidics
Heat conduction
Flow of fluids
Temperature distribution
Physics
Continuity Equation
Stokes Equations
Electric fields

### Keywords

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

### ASJC Scopus subject areas

• Applied Mathematics
• Modeling and Simulation

### Cite this

A numerical study of 2D electrothermal flow using boundary element method. / Ren, Qinlong; Chan, Cholik; Arvayo, Alberto L.

In: Applied Mathematical Modelling, Vol. 39, No. 9, 01.05.2015, p. 2777-2795.

Research output: Contribution to journalArticle

Ren, Qinlong ; Chan, Cholik ; Arvayo, Alberto L. / A numerical study of 2D electrothermal flow using boundary element method. In: Applied Mathematical Modelling. 2015 ; Vol. 39, No. 9. pp. 2777-2795.
title = "A numerical study of 2D electrothermal flow using boundary element method",
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.",
keywords = "Boundary element method, Buoyancy force, Coulomb force, Dielectric force, Laplace's equation, Stokes flow",
author = "Qinlong Ren and Cholik Chan and Arvayo, {Alberto L.}",
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T1 - A numerical study of 2D electrothermal flow using boundary element method

AU - Ren, Qinlong

AU - Chan, Cholik

AU - Arvayo, Alberto L.

PY - 2015/5/1

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N2 - 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.

AB - 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.

KW - Boundary element method

KW - Buoyancy force

KW - Coulomb force

KW - Dielectric force

KW - Laplace's equation

KW - Stokes flow

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