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Simultaneous impacts of MHD and variable wall temperature on transient mixed Casson nanofluid flow in the stagnation point of rotating sphere

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Abstract

A numerical analysis is provided to scrutinize time-dependent magnetohydrodynamics (MHD) free and forced convection of an electrically conducting non-Newtonian Casson nanofluid flow in the forward stagnation point region of an impulsively rotating sphere with variable wall temperature. A single-phase flow of nanofluid model is reflected with a number of experimental formulae for both effective viscosity and thermal conductivity of nanofluid. Exceedingly nonlinear governing partial differential equations (PDEs) subject to their compatible boundary conditions are mutated into a system of nonlinear ordinary differential equations (ODEs). The derived nonlinear system is solved numerically with implementation of an implicit finite difference procedure merging with a technique of quasi-linearization. The controlled parameter impacts are clarified by a parametric study of the entire flow regime. It is depicted that from all the exhibited nanoparticles, Cu possesses the best convection. The surface heat transfer and surface shear stresses in the x- and z-directions are boosted with maximizing the values of nanoparticle solid volume fraction φ and rotation λ. Besides, as both the surface temperature exponent n and the Casson parameter γ upgrade, an enhancement of the Nusselt number is given.

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Abbreviations

a :

gradient of velocity at the edge (s−1)

B 0 :

magnetic field (T)

C f x :

shear stress in x-direction

C f z :

shear stress in z-direction

c p :

specific heat (J·kg−1·K−1)

F :

non-dimensional stream function

g :

acceleration due to gravity (m·s−2)

Gr :

Grashof number

k :

thermal conductivity, (W·m−1·K−1)

M g :

parameter of magnetic field

Pr :

Prandtl number

R :

radius of the sphere (m)

Re :

Reynolds number

S :

velocity components in y-direction (m·s−1)

Sc :

Schmidt number

t :

time (s)

T :

dimensional temperature (K)

(u, v, w):

velocity components (m·s−1)

U :

ambient velocity (m·s−1)

(x, y, z):

Cartesian coordinates (m)

β :

coefficient of thermal expansion (K−1)

μ :

dynamic viscosity (kg·m−1·s−1)

λ :

rotation parameter

σ :

electrical conductivity (S·m−1)

ρ :

fluid density (kg·m−3)

θ :

dimensionless temperature

Ω:

angular velocity (s−1)

v :

kinematic viscosity (m2·s−1)

γ*:

mixed convection parameter

γ:

Casson parameter

φ :

nanoparticle solid volume fraction

w:

conditions at the surface

∞:

conditions in the free stream

p:

solid material

nf:

nanofluid particle

f:

fluid

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Acknowledgements

The authors would like to express their gratitude to the reviewers for their constructive and precise suggestions.

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  1. Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt

    A. Mahdy

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Mahdy, A. Simultaneous impacts of MHD and variable wall temperature on transient mixed Casson nanofluid flow in the stagnation point of rotating sphere. Appl. Math. Mech.-Engl. Ed. 39, 1327–1340 (2018). https://doi.org/10.1007/s10483-018-2365-9

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  • DOI: https://doi.org/10.1007/s10483-018-2365-9

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