Fully developed entropy-optimized MHD nanofluid flow by a variably thickened rotating surface
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Fully developed entropy‑optimized MHD nanofluid flow by a variably thickened rotating surface M. Waleed Ahmed Khan1 · F. Shah1 · M. Ijaz Khan2 · Yu‑Ming Chu3,4 · Seifedine Kadry5 Received: 16 January 2020 / Accepted: 12 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keyword Viscous fluid · Entropy generation · Mixed convection · Buongiorno nanofluid model · Joule heating and viscous dissipation · Convective boundary conditions List of symbols u, V, w Velocity components r, 𝜗, z Space coordinates T Fluid temperature T∞ Ambient temperature Tf Convective fluid temperature C Fluid concentration C∞ Ambient concentration u Stretching velocity in r direction B0 Strength of magnetic field ρ Fluid density * Yu‑Ming Chu [email protected] 1
Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad 44000, Pakistan
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Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan
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Department of Mathematics, Huzhou University, Huzhou 313000, People’s Republic of China
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Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, People’s Republic of China
5
Department of Mathematics and Computer Science, Beirut Arab University, Beirut, Lebanon
cp 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 Nb Brownian motion parameter NT Thermophoresis parameter Sc Schmidt number β Biot number Nux Local Nusselt number Rex Local Reynolds number k* Coefficient of mean absorption a, c Positive constants Greek symbols τ Surface shear stress σ* Stefan–Boltzmann constant parameter 𝜃 Dimensionless temperature Φ Dimensionless concentration 𝜂 Dimensionless space variable
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