# Influence of Shape of Nanoparticles on Nanofluid Hydrothermal Behavior

DOI: 10.4018/978-1-5225-7595-5.ch006

## Abstract

The shape of nanoparticles can change the thermal conductivity of nanofluid. So, the effect of shape factor on nanofluid flow and heat transfer has been reported in this chapter. Governing equations are presented in vorticity stream function formulation. Control volume-based finite element method (CVFEM) is utilized to obtain the results. Results indicate that platelet shape has the highest rate of heat transfer.
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## 2. Forced Convection Of Nanofluid In Presence Of Constant Magnetic Field Considering Shape Effects Of Nanoparticles

### 2.1. Problem Definition

Figure 1 depicts the geometry, boundary condition and sample element. The lower wall has the velocity of and others are stationary. The lower wall has constant temperature and the temperature of other walls is . Horizontal magnetic field has been applied. Nanofluid forced convection heat transfer in a porous semi annulus is investigated.

### 2.2. Governing Equation

2D steady convective flow of nanofluid in a porous media is considered in existence of constant magnetic field. The PDEs equations are:

(1)
(2)
(3)
(4)

and are defined as:

(5)
(6)
(7)

The KKL (Koo-Kleinstreuer-Li) correlation has been utilized for viscosity of nanofluid

(8)

The related coefficient and properties of Cuo-water nanofluid is presented in Table 1 and 2. Maxwell model and Hamilton–Crosser model for irregular particle geometries by introducing a shape factor can be expressed as

(9) in which and are the conductivities of the particle material and the base fluid. In this equation “m” is shaper factor. Table 3 shows the different values of shape factors for various shapes of nanoparticles. Vorticity and stream function should be used to eliminate pressure source terms:

(10)

Introducing dimensionless quantities:

(11)

The final formulae are:

(12)
(13)
(14) where dimensionless and constants parameters are illustrated as:
(15) and boundary conditions are:

on bottom wall on other walls on all walls(16)

Local and average Nusselt over the hot wall can calculate as:

(17)
(18)

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