Influence of Shape of Nanoparticles on Nanofluid Hydrothermal Behavior

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 978-1-5225-7595-5.ch006.m01 and others are stationary. The lower wall has constant temperature 978-1-5225-7595-5.ch006.m02 and the temperature of other walls is 978-1-5225-7595-5.ch006.m03. 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:

978-1-5225-7595-5.ch006.m04
(1)
978-1-5225-7595-5.ch006.m05
(2)
978-1-5225-7595-5.ch006.m06
(3)
978-1-5225-7595-5.ch006.m07
(4)

978-1-5225-7595-5.ch006.m08978-1-5225-7595-5.ch006.m09and 978-1-5225-7595-5.ch006.m10 are defined as:

978-1-5225-7595-5.ch006.m11
(5)
978-1-5225-7595-5.ch006.m12
(6)
978-1-5225-7595-5.ch006.m13
(7)

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

978-1-5225-7595-5.ch006.m14
(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

978-1-5225-7595-5.ch006.m15
(9) in which 978-1-5225-7595-5.ch006.m16 and 978-1-5225-7595-5.ch006.m17are 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:

978-1-5225-7595-5.ch006.m18
(10)

Introducing dimensionless quantities:

978-1-5225-7595-5.ch006.m19
(11)

The final formulae are:

978-1-5225-7595-5.ch006.m20
(12)
978-1-5225-7595-5.ch006.m21
(13)
978-1-5225-7595-5.ch006.m22
(14) where dimensionless and constants parameters are illustrated as:
978-1-5225-7595-5.ch006.m23
(15) and boundary conditions are:

978-1-5225-7595-5.ch006.m24 on bottom wall 978-1-5225-7595-5.ch006.m25 on other walls 978-1-5225-7595-5.ch006.m26 on all walls(16)

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

978-1-5225-7595-5.ch006.m27
(17)
978-1-5225-7595-5.ch006.m28
(18)

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