Nanofluid Treatment in Existence of Magnetic Field Using Non-Darcy Model for Porous Media

Nanofluid Treatment in Existence of Magnetic Field Using Non-Darcy Model for Porous Media

DOI: 10.4018/978-1-5225-7595-5.ch008

Abstract

In this chapter, the non-Darcy model is employed for porous media filled with nanofluid. Both natural and forced convection heat transfer can be analyzed with this model. The governing equations in forms of vorticity stream function are derived and then they are solved via control volume-based finite element method (CVFEM). The effect of Darcy number on nanofluid flow and heat transfer is examined.
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2. Mhd Nanofluid Free Convective Heat Transfer In A Porous Tilted Enclosure

2.1. Problem Definition

Figure 1 illustrates the important geometric parameters of current geometry. Also sample mesh is presented. The inner and outer cylinders are considered as hot and cold walls, respectively. Horizontal magnetic field has been considered.

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.ch008.m01
(1)
978-1-5225-7595-5.ch008.m02
(2)
978-1-5225-7595-5.ch008.m03
(3)
978-1-5225-7595-5.ch008.m04
(4)

978-1-5225-7595-5.ch008.m05, 978-1-5225-7595-5.ch008.m06 and 978-1-5225-7595-5.ch008.m07 are defined as:

978-1-5225-7595-5.ch008.m08
(5)
978-1-5225-7595-5.ch008.m09
(6)
978-1-5225-7595-5.ch008.m10
(7)
978-1-5225-7595-5.ch008.m11
(8)

978-1-5225-7595-5.ch008.m12 are obtained according to Koo–Kleinstreuer–Li (KKL) model:

978-1-5225-7595-5.ch008.m13
(9)
978-1-5225-7595-5.ch008.m14
(10)

All required coefficients and properties are illustrated in Tables 1 and 2.

Vorticity and stream function should be used to eliminate pressure source terms:

978-1-5225-7595-5.ch008.m15
(11)

Introducing dimensionless quantities:

978-1-5225-7595-5.ch008.m16
(12)

The final formulae are:

978-1-5225-7595-5.ch008.m17
(13)
978-1-5225-7595-5.ch008.m18
(14)
978-1-5225-7595-5.ch008.m19
(15) where dimensionless and constants parameters are defined as:
978-1-5225-7595-5.ch008.m20
(16) and boundary conditions are:

978-1-5225-7595-5.ch008.m21 on inner wall 978-1-5225-7595-5.ch008.m22 on outer wall 978-1-5225-7595-5.ch008.m23 on other walls 978-1-5225-7595-5.ch008.m24 on all walls(17)

Local and average Nusselt over the hot wall can be calculated as:

978-1-5225-7595-5.ch008.m25
(18)
978-1-5225-7595-5.ch008.m26
(19)

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