# Influence of Electric Field on Nanofluid Forced Convection Heat Transfer

DOI: 10.4018/978-1-5225-7595-5.ch007

## Abstract

In this chapter, the effect of electric field on forced convection heat transfer of nanofluid is presented. The governing equations are derived and presented in vorticity stream function formulation. Control volume-based finite element method (CVFEM) is employed to solve the final equations. Results indicate that the flow style depends on supplied voltage, and this effect is more sensible for low Reynolds number.
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## 2. Ehd Nanofluid Force Convective Heat Transfer Considering Electric Field Dependent Viscosity

### 2.1. Problem Definition

Geometry and boundary conditions are shown in Figure 1. All walls are stationary except the lower one. The lid wall is hot wall and the others are cold. Distribution of electric density is depicted in Figure 2.

### 2.2. Governing Equation

Electric field equations should be combined with hydrothermal equations. Electric field equations are:

(1)
(2)
(3)

Charge distribution can be modeled in two ways: mobility and conductivity models. The equation of electric current density is:

(4)

Using the above equations leads to the following equation:

(5)

Diffusion term is small, Equation (4) can be changed to:

(6)

In existence of electric field, Coulomb forces should be added to momentum equations:

(7)

and are defined as:

(8)
(9)
(10)
(11)
(12)

Table 1 illustrate the properties of the base fluid and nanoparticles. Effect of electric field on viscosity of nanofluid has been taken into account:

(13)

Table 2 shows the coefficient values of this equation. Non-dimensional parameters are presented as follow:

(14) where and are and , respectively. By eliminating the over bar, the equations are:

(15)

Stream function and vorticity can be defined as:

(16)

Stream function can satisfy the continuity equation. Vorticity equation can be derived by eliminating pressure sources.

and along the lid wall can be obtained as:

(17)
(18)

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