Influence of Melting Surface on Nanofluid Convective Heat Transfer

Influence of Melting Surface on Nanofluid Convective Heat Transfer

DOI: 10.4018/978-1-5225-7595-5.ch010

Abstract

In this chapter, the effect of melting surface heat transfer on magnetohydrodynamic nanofluid free convection is analyzed by means of control volume-based finite element method (CVFEM). KKL model is taken into account to obtain viscosity and thermal conductivity of CuO-water nanofluid. The roles of melting parameter, nanofluid volume fraction, Hartmann and Rayleigh numbers are illustrated.
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2. Melting Heat Transfer Influence On Nanofluid Flow Inside A Cavity In Existence Of Magnetic Field

2.1. Problem Definition

Figure 1 depicts the geometry, boundary condition and sample element. The bottom wall is hot wall 978-1-5225-7595-5.ch010.m01 and the top one is melting surface 978-1-5225-7595-5.ch010.m02. Other walls are adiabatic. Horizontal magnetic field has been applied. The enclosure is field with nanofluid.

2.2. Governing Equation

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

978-1-5225-7595-5.ch010.m03
(1)
978-1-5225-7595-5.ch010.m04
(2)
978-1-5225-7595-5.ch010.m05
(3)
978-1-5225-7595-5.ch010.m06
(4)

978-1-5225-7595-5.ch010.m07, 978-1-5225-7595-5.ch010.m08 and 978-1-5225-7595-5.ch010.m09 are calculated as:

978-1-5225-7595-5.ch010.m10
(5)
978-1-5225-7595-5.ch010.m11
(6)
978-1-5225-7595-5.ch010.m12
(7)
978-1-5225-7595-5.ch010.m13
(8)

978-1-5225-7595-5.ch010.m14 are calculated via KKL model:

978-1-5225-7595-5.ch010.m15
(9)
978-1-5225-7595-5.ch010.m16
(10)

Properties and needed parameters are provided Tables 1 and 2.

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

978-1-5225-7595-5.ch010.m17
(11)

Introducing dimensionless quantities:

978-1-5225-7595-5.ch010.m18
(12)

The final formulae are:

978-1-5225-7595-5.ch010.m19
(13)
978-1-5225-7595-5.ch010.m20
(14)
978-1-5225-7595-5.ch010.m21
(15)

Boundary conditions are:978-1-5225-7595-5.ch010.m22 on top wall978-1-5225-7595-5.ch010.m23 on bottom wall978-1-5225-7595-5.ch010.m24 on other walls978-1-5225-7595-5.ch010.m25 Right, left and bottom walls(16) and in melting surface, we have:

978-1-5225-7595-5.ch010.m26
(17) where dimensionless and constants parameters are illustrated as:

978-1-5225-7595-5.ch010.m27
(18)

It should be mentioned that 978-1-5225-7595-5.ch010.m28 is related to Stefan numbers.

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

978-1-5225-7595-5.ch010.m29
(19)
978-1-5225-7595-5.ch010.m30
(20)

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