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Significance of homogeneous–heterogeneous reactions in Darcy–Forchheimer three-dimensional rotating flow of carbon nanotubes

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Abstract

Three-dimensional rotating flow of water-based carbon nanotubes is investigated in the presence of Darcy–Forchheimer porous space and homogeneous–heterogeneous reactions. Variable surface temperature condition is employed. Exponentially stretchable sheet induces the flow. Xue model has been implemented for nanoliquid transport mechanism. Suitable transformations lead to strong nonlinear ordinary differential system. An optimal homotopic algorithm is used to tackle the governing nonlinear system. Results for single-wall carbon nanotubes and multi-wall carbon nanotubes have been studied. Plots are displayed just to explore the role of flow parameters on solutions. Skin friction coefficients and heat transfer rate have been plotted and discussed. Our findings indicate that the skin friction coefficients and local Nusselt number are enhanced for larger values of nanoparticles volume fraction.

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Abbreviations

u, v, w :

Velocity components

μ f :

Fluid dynamic viscosity

ν f :

Kinematic fluid viscosity

k f :

Basefluid thermal conductivity

α f :

Thermal diffusivity of base fluid

T w :

Surface temperature

\(u_{\text{w}} (x)\) :

Surface stretching velocity

u 0 :

Reference velocity

F :

Non-uniform inertia coefficient

C b :

Drag coefficient

λ :

Local porosity parameter

Sc :

Schmidt number

ϕ :

Nanoparticles volume fraction

θ :

Dimensionless temperature

Pr :

Prandtl number

k c, k s :

Rate constants

k 1 :

Homogeneous reaction parameter

Re x :

Local Reynolds number

C fx, C fy :

Skin friction coefficients

x, y, z :

Space coordinates

ρ f :

Fluid density

ν nf :

Kinematic nanofluid viscosity

k nf :

Nanofluid thermal conductivity

α nf :

Thermal diffusivity of nanofluid

T ∞ :

Ambient fluid temperature

k CNT :

CNTs thermal conductivity

k*:

Permeability of porous medium

D A, D B :

Diffusion coefficients

Ω :

Local rotation parameter

Fr :

Forchheimer number

ζ :

Dimensionless variable

f′, g :

Dimensionless velocities

r :

Dimensionless concentration

α :

Ratio number

A, B :

Chemical species

k 2 :

Heterogeneous reaction parameter

\(H_{\text{j}}^{**}\) :

Arbitrary constants

Nu x :

Local Nusselt number

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    Tasawar Hayat & Arsalan Aziz

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Tasawar Hayat & Ahmed Alsaedi

  3. Department of Mathematics, Government College Women University, Sialkot, 51310, Pakistan

    Taseer Muhammad

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  1. Tasawar Hayat
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Hayat, T., Aziz, A., Muhammad, T. et al. Significance of homogeneous–heterogeneous reactions in Darcy–Forchheimer three-dimensional rotating flow of carbon nanotubes. J Therm Anal Calorim 139, 183–195 (2020). https://doi.org/10.1007/s10973-019-08316-3

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