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Fully developed entropy-optimized MHD nanofluid flow by a variably thickened rotating surface

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Abstract

Entropy generation analysis for three-dimensional (3D) magnetohydrodynamic (MHD) flow of viscous fluid through a rotating disk is addressed in this article. Entropy generation is explored as a function of temperature and velocity. The modeling of the considered problem is performed through Buongiorno model. Conservation of energy comprises dissipation, convective heat transport and Joule heating. Flow under consideration is because of nonlinear stretching velocity of disk. Transformations used lead to the reduction of partial differential equations into ordinary differential equations. Total entropy generation rate is scrutinized. Non-linear computations have been carried out. Domain of convergence for the obtained solutions is identified. Radial, axial and tangential velocities are interpreted. Entropy equation is studied in the presence of dissipation, Brownian diffusion and thermophoresis effects. Velocity and temperature gradients are discussed graphically. Meaningful results are summed up in the concluding section.

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Data availability

The data that support the findings of this study are available within the article, the data are made by the authors themselves and do not involve references of others.

Abbreviations

u, V, w :

Velocity components

\(r,\vartheta ,z\) :

Space coordinates

T :

Fluid temperature

T ∞ :

Ambient temperature

T f :

Convective fluid temperature

C:

Fluid concentration

C ∞ :

Ambient concentration

u :

Stretching velocity in r direction

B 0 :

Strength of magnetic field

ρ :

Fluid density

c p :

Specific heat

qr:

Radiative heat flux

ℎ:

Convective heat transfer coefficient

D :

Brownian diffusion coefficient

D :

Thermophoresis diffusion coefficient

F :

Dimensionless velocity

M:

Magnetic parameter

A:

Ratio of velocities

Rd:

Radiation parameter

Pr:

Prandtl number

N b :

Brownian motion parameter

N T :

Thermophoresis parameter

S c :

Schmidt number

β :

Biot number

Nu x :

Local Nusselt number

Re x :

Local Reynolds number

k∗:

Coefficient of mean absorption

a, c :

Positive constants

τ :

Surface shear stress

σ∗:

Stefan–Boltzmann constant parameter

\(\theta\) :

Dimensionless temperature

\(\Phi\) :

Dimensionless concentration

\(\eta\) :

Dimensionless space variable

\(\nu\) :

Kinematic viscosity

μ :

Dynamic viscosity

∞:

Condition at the free stream

w :

Condition at the surface

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad, 44000, Pakistan

    M. Waleed Ahmed Khan & F. Shah

  2. Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan

    M. Ijaz Khan

  3. Department of Mathematics, Huzhou University, Huzhou, 313000, People’s Republic of China

    Yu-Ming Chu

  4. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, People’s Republic of China

    Yu-Ming Chu

  5. Department of Mathematics and Computer Science, Beirut Arab University, Beirut, Lebanon

    Seifedine Kadry

Authors
  1. M. Waleed Ahmed Khan
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  2. F. Shah
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  3. M. Ijaz Khan
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  5. Seifedine Kadry
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Correspondence to Yu-Ming Chu.

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Khan, M.W.A., Shah, F., Khan, M.I. et al. Fully developed entropy-optimized MHD nanofluid flow by a variably thickened rotating surface. Appl. Phys. A 126, 890 (2020). https://doi.org/10.1007/s00339-020-04068-2

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