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Heat transfer exaggeration and entropy analysis in magneto-hybrid nanofluid flow over a vertical cone: a numerical study

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Abstract

Entropy analysis is closely scrutinized for unsteady mixed convection in magneto-hybrid nanofluid (Cu–Fe\(_3\)O\(_4\)–water) flow over an inverted cone surrounded by a porous medium. The mathematical model comprises nonlinear, coupled partial differential equations. The numerical solutions of constitutive equations assisted by related initial boundary conditions are obtained by an effective finite difference method. The specified ranges for active parameters are: \(0\le \varphi _\mathrm{hnf}\le 0.04\), \(0\le M\le 5\), \(0.5\le K\le 3.5\), \(0.6\le \hbox {Gr}\le 1\) and \(0.1\le \hbox {Br}\Omega ^{-1} \le 0.4\). The impact of various parameters arising in the constitutive flow model on the virtual flow parameters is analyzed carefully, and the outcomes are illustrated graphically. Also, steady-state entropy production and Bejan lines are plotted for various active parameters. In addition, the physical quantities, i.e., heat transfer and momentum coefficient, are scrutinized for various parameters and the outcomes are displayed in the tabulated form. It is witnessed that heat transfer rates improved incredibly with growing estimates of hybrid nanoparticles volume fraction. The Nusselt number enhancement of Cu–Fe\(_3\)O\(_4\)–water hybrid nanofluid are 0.53%, 0.76%, 0.95% and 1.1% corresponding to volume concentration of 1%:4% with a difference of 1%, respectively. The theoretical measurement of skin friction showed a maximum enhancement of 0.25% at a volume concentration of 1% compared with Fe\(_3\)O\(_4\)–water nanofluid. Moreover, the momentum and heat transport coefficients are compared with those of natural convection and the result showed that heat transfer coefficient attains higher rates in mixed convectional flow compared with natural convection.

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Abbreviations

(U, V):

Velocity components in (x, y) direction

(x, y):

Cartesian coordinates

B :

Magnetic field

Be:

Bejan number

Br:

Brinkman number

\(C_\mathrm{p}\) :

Specific heat capacity

g :

Gravitational acceleration

Gr:

Thermal Grashof number

K :

Dimensionless porosity parameter

k :

Thermal conductivity

\(k_{0}\) :

Permeability of porous medium

L :

Reference length

M :

Dimensionless magnetic parameter

\(\hbox {Nu}_\mathrm{x}\) :

Local Nusselt number

q :

Heat flux

r :

Radius of the cone

\(S_{0}\) :

Characteristic entropy generation

\(S_\mathrm{GEN}\) :

Dimensionless entropy generation

\(S_\mathrm{gen}\) :

Volumetric entropy generation

T :

Temperature

t :

Time

Pr:

Prandtl number

\(\alpha\) :

Half angle of the cone

\(\beta\) :

Volumetric thermal expansion

\(\Delta\) :

Grid/step size

\(\mu\) :

Dynamic viscosity

\(\nabla\) :

Gradient operator

\(\nu\) :

Kinematic viscosity

\(\rho\) :

Density

\(\sigma\) :

Electrical conductivity

\(\tau _\mathrm{x}\) :

Local skin friction

\(\varphi\) :

Nanoparticles volume fraction

\(\hbox {Br}\Omega ^{-1}\) :

Group parameter

*:

Non-dimensional

f:

Base fluid

hnf:

Hybrid nanofluid

i:

Grid point in the x direction

j:

Grid point in the y direction

k:

Time level

nf:

Nanofluid

s:

Nanoparticles

w:

Wall

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Authors and Affiliations

  1. Department of Mathematics, Sardar Bahadur Khan Women’s University, Quetta, Pakistan

    Hanifa Hanif

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Ilyas Khan

  3. Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia

    Hanifa Hanif & Sharidan Shafie

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Hanif, H., Khan, I. & Shafie, S. Heat transfer exaggeration and entropy analysis in magneto-hybrid nanofluid flow over a vertical cone: a numerical study. J Therm Anal Calorim 141, 2001–2017 (2020). https://doi.org/10.1007/s10973-020-09256-z

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