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Influence of applied magnetic field on nonlinear mixed convective nanoliquid flow past a permeable rough cone

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Abstract

The concept of magnetohydrodynamic nonlinear mixed convective nanoliquid flow over a vertical rough cone finds applications in science and engineering fields, especially in aerospace and thermal engineering as well as in other designing and manufacturing processes. In the present investigation, the cone surface roughness, which arises during the manufacturing processes, is modelled using sine wave forms. A uniform magnetic field is applied to analyse its impact on the transport characteristics of the flow. The study of such flow problems involving physical parameters such as nonlinear convection, permeable roughness, nanoparticles and external magnetic field is an innovative approach. The flow problem is modelled using nonlinear coupled partial differential equations which are transformed into dimensionless form by using Mangler’s non-similar transformations. The resulting equations are solved by utilizing the quasilinearization technique in combination with the implicit finite difference scheme. Effects of the different physical parameters on profiles and gradients are analysed by the graphical representations. Findings show that the higher values of the nonlinear mixed convection parameter will increase nanofluid velocity and magnitude of the coefficient of surface friction. Prominent sinusoidal oscillations are found in the surface gradients away from the apex of the cone due to the surface roughness effects.

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Abbreviations

A :

Suction/injection

B 0 :

Magnetic field strength

C f :

Skin friction coefficient

\(C_{{{\text{nf}}}}\) :

Heat capacity of nanofluid (J K−1)

\(C_{pp}\) :

Specific heat capacity of nanoparticles (J K−1)

\(D_{{\text{B}}}\) :

Brownian diffusion coefficient (m2 s−1)

\(D_{{\text{T}}}\) :

Thermophoretic coefficient (m2 s−1)

f :

Dimensionless stream function

F :

Dimensionless velocity

g :

Acceleration due to gravity (m s−2)

G :

Dimensionless temperature

NSh:

Nanoparticle Sherwood number

Nu:

Nusselt number

S :

Dimensionless volume fraction profile

T :

Temperature (K)

\(T_{{\text{w}}} ,T_{\infty }\) :

Temperature at the wall and ambient conditions (K)

u :

x-component of velocity(m s−1)

U 0 :

Reference velocity (m s−1)

U w :

Wall velocity (m s−1)

\(U_{\infty }\) :

Free stream velocity constant (m s−1)

v :

y-component of velocity (m s−1)

x :

Distance along x coordinate (m)

y :

Distance along y-coordinate (m)

\(g\) :

Acceleration due to gravity (m s−2)

\(\sigma\) :

Electrical conductivity of the fluid (S m−1)

\(\rho\) :

Density of fluid (Kg m−3)

\(\psi\) :

Dimensionless stream function

\(\nu\) :

Kinematic viscosity (m2 s−1)

\(\phi\) :

Nanoparticle volume fraction

\(\gamma\) :

Nonlinear mixed convection parameter

\(\beta_{1}\) :

Nonlinear volumetric coefficient of thermal expansion of nanofluid (K−1)

\(\alpha\) :

Small parameter

\(\rho_{{\text{f}}}\) :

Density of base fluid (Kg m−3)

\(\rho_{{\text{p}}}\) :

Nanoparticle mass density (Kg m−3)

\(\beta_{0}\) :

The volumetric coefficient of thermal expansion of nanofluid (K−1)

\(\alpha_{m}\) :

Thermal diffusivity

\(\phi_{{\text{w}}}\) :

Nanoparticle volume fraction at the wall

\(\phi_{\infty }\) :

Ambient nanoparticle volume fraction

\(\xi ,\,\eta\) :

Transformed variables

\(\xi ,\,\eta\) :

Partial derivatives with respect to these variables

0:

Condition at the wall

\(\infty\) :

Free stream, respectively

w:

Conditions at the surface wall

nf:

Nanofluid

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Authors and Affiliations

  1. Department of Mathematics, Karnatak University, Pavate Nagar, Dharwad, 580003, India

    P. M. Patil & Madhavarao Kulkarni

  2. Department of Physics, Karnatak University, Pavate Nagar, Dharwad, 580003, India

    J. R. Tonannavar

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  1. P. M. Patil
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  2. Madhavarao Kulkarni
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  3. J. R. Tonannavar
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Patil, P.M., Kulkarni, M. & Tonannavar, J.R. Influence of applied magnetic field on nonlinear mixed convective nanoliquid flow past a permeable rough cone. Indian J Phys 96, 1453–1464 (2022). https://doi.org/10.1007/s12648-021-02073-6

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