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Comparative Analysis of Five Nanoparticles in the Flow of Viscous Fluid with Nonlinear Radiation and Homogeneous–Heterogeneous Reaction

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Abstract

The current study investigates the flow of viscous nanofluids over the stretching surface with variable thickness in the presence of heterogeneous and homogeneous reactions. Comparison is made for water-based nanofluids with copper (Cu), silver (Ag), copper oxide (CuO), aluminum oxide (Al2O3), and titanium oxide (TiO2) as nanoparticles. The heat transfer phenomenon is characterized by nonlinear thermal radiation. The formulation of the model consists of partial differential equations with convective boundary conditions, which are converted into ordinary differential equations with the help of boundary layer approximation. The convergent series solution is computed with the help of an efficient analytical method, namely the Optimal Homotopy technique. For the validation of the suggested approach, the convergence of the obtained results is illustrated for different values of involved parameters. Moreover, residual errors for the varied number of terms in the derived series solution are displayed graphically. To validate the accuracy of the present results, a comparison with previously published results is presented. The influence of various variables on the velocity profile, the distribution profiles of temperature, and concentration is graphically discussed. Heat transfer rate (or local Nusselt number) and skin friction coefficient are estimated through the Tables. It is observed that temperature rises for higher radiation parameter and the temperature of aluminum oxide nanofluid is more because of its higher thermal conductivity as compared to other four nanoparticles. The study also reveals that with an improvement in the volume fraction of nanoparticles, the degree of the heat transfer rate and the coefficient of skin friction also increases.

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Abbreviations

u, v :

Velocity components

T :

Temperature

b :

Stretched sheet constant

\((\rho c_{p} )_{nf}\) :

Heat capacitance

\(\mu_{f}\) :

Base fluid dynamic viscosity

\(h_{f}\) :

Non-uniform heat transfer coefficient

\(\alpha_{nf}\) :

Thermal diffusivity

\(\rho_{nf}\) :

Effective density of nanofluid

\(T_{\infty }\) :

Ambient temperature

\(K^{ * }\) :

Heterogeneous rate constant

\(K_{r}\) :

Homogeneous rate constant

\(C_{\infty }\) :

Ambient concentration

\(q_{r}\) :

Thermal radiation

\(k_{f}\) :

Mean adsorption coefficient

\(q_{w}\) :

Wall heat flux

\(D_{A}\) :

Coefficient of diffusion specie A

\(D_{B}\) :

Coefficient of diffusion specie B

\(\theta_{w}\) :

Temperature ratio parameter

c p :

Specific heat

x, y :

Cartesian coordinates

w :

Wall notation

U w :

Stretching velocity

\(a_{ \circ } ,\,b_{ \circ } ,\lambda\) :

Dimensionless constant

\(T_{f}\) :

Wall temperature

\(\mu_{nf}\) :

Dynamic viscosity of nanofluid

\(U_{ \circ }\) :

Dimensional constant

\(\rho_{f}\) :

Density of the base fluid

\(B_{t}\) :

Thermal Biot number

n :

Power-law index

Sc:

Schmidt number

a, b :

Reaction rate species

\(k_{nf}\) :

Effective thermal conductivity of nanofluid

\(\alpha\) :

Variable wall thickness

\(E_{c}\) :

Eckert number

R :

Radiation parameter

\(\Pr\) :

Prandtl number

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha 61413, Saudi Arabia for funding this work through research groups program under Grant Number R.G.P-1/36/42.

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Authors and Affiliations

  1. Department of Mathematics, Air University, Islamabad, 44000, Pakistan

    Seemab Bashir

  2. Department of Computer Science, Bahria University, Islamabad, 44000, Pakistan

    Muhammad Ramzan

  3. Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Kingdom of Saudi Arabia

    M. Y. Malik

  4. Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia

    Hammad Alotaibi

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  1. Seemab Bashir
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Contributions

MR supervised and conceived the idea; SB wrote the manuscript; and MYM and HA helped in the revised draft and validation.

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Correspondence to Muhammad Ramzan.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Bashir, S., Ramzan, M., Malik, M.Y. et al. Comparative Analysis of Five Nanoparticles in the Flow of Viscous Fluid with Nonlinear Radiation and Homogeneous–Heterogeneous Reaction. Arab J Sci Eng 47, 8129–8140 (2022). https://doi.org/10.1007/s13369-021-06094-5

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