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Numerical investigation on effects of entropy generation and dispersion of hybrid nanoparticles on thermal and mass transfer in MHD Maxwell fluid

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Abstract

In this article, the Maxwell hybrid nanofluid flow passing over a pipe is discussed. We considered the base fluid as engine oil, while the hybrid nanofluids are copper and aluminum oxide. Irreversibility analysis and entropy generation have been examined, and the effects on physical parameters have also been examined. The mathematical model of this problem (nonlinear coupled equations) in cylindrical coordinates is solved by FEM. Began number and entropy generation are sketched for different values of parameters, and the effects of these parameters are discussed. The Deborah number is the measure of the elasticity of the fluid, and elasticity is the characteristics of the fluid due to which fluid avoids or tries to avoid momentum changes. Therefore, Deborah number has shown a decreasing behavior on the motion of the particles of both mono–nanoengine oil and hybrid nanoengine oil. Entropy generation is boosted when curvature is raised.

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Abbreviations

De:

Deborah number

\(\Pr\) :

Prandtl number

Ec:

Eckert number

Ha:

Hartmann number

\({\text {Re}}\) :

Reynolds number

Sc:

Schmidt number

Br:

Brikmann number

u, v :

Velocity components

T :

Fluid temperature

C :

Fluid concentration

n :

Temperature exponent or index

\(E_\mathrm{{G}}\) :

Entropy generation parameter

\(c_\mathrm{{p}}\) :

Specific heat

\(T_\mathrm{{w}}\) :

Surface temperature

\(T_{\infty }\) :

Ambient temperature

\(C_\mathrm{{w}}\) :

Surface concentration

\(C_{\infty }\) :

Ambient concentration

\(B_{0}\) :

Magnitude of magnetic induction

c, l :

Constants

\(D^{*}\) :

Mass conductance

D :

Radius of cylinder

\(\lambda _{1}\) :

Fluid relaxation time

\(\tilde{K}\) :

Thermal conductivity

\(U_\mathrm{{w}}\) :

Stretching velocity

\(\theta\) :

Dimensionless temperature

\(\alpha\) :

Curvature parameter

\(\rho\) :

Density

\(\tilde{\sigma }\) :

Electrical conductivity

\(\nu\) :

Kinetic viscosity of fluid

\(\phi\) :

Dimensionless concentration

\(\mu\) :

Shear rate viscosity

\(\eta\) :

Similarity variable

\(\varphi\) :

Volume fraction

f:

Fluid

hnf:

Hybrid nanofluid

\(\mathrm{{s}}_{1} , \mathrm{{s}}_{2}\) :

Solid nanoparticles

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  1. Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, 44000, Pakistan

    M. Nawaz & U. Arif

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Nawaz, M., Arif, U. Numerical investigation on effects of entropy generation and dispersion of hybrid nanoparticles on thermal and mass transfer in MHD Maxwell fluid. J Therm Anal Calorim 147, 13551–13560 (2022). https://doi.org/10.1007/s10973-022-11489-z

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