Prediction of new vortices in single-phase nanofluid due to dipole interaction
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Prediction of new vortices in single‑phase nanofluid due to dipole interaction Shabbir Ahmad1 · Jianchao Cai1 · Kashif Ali2 Received: 1 June 2020 / Accepted: 9 September 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract Magnetic field effects are encountered in many engineering applications which include but are not limited to metal casting, nuclear reactor coolers, and geothermal energy extraction. On the other hand, due to their outstanding thermal performance, nanofluids have been successful in obtaining acceptability as per the new generation of heat transfer fluids in automotive cooling devices, in heat exchangers, and building heating. Therefore, this research is carried out to understand how the nanofluid flow in a cavity is affected by a magnetic field (due to a dipole placed nearby). The single-phase model is employed for modeling the nanofluid, whereas the governing partial differential equations are solved numerically. The dipole may give rise to the new vortices in the flow near its location while enhancing Nusselt number. The Reynolds number reduces Nusselt number along the lower wall while affecting the strength of vortices near the dipole location. Increasing the strength of the dipole results in distorting the symmetry of streamlines by first enhancing the size of the lower vortex; some vortices near dipole also join and merge. Further, the magnetic field makes the temperature field nonsymmetric and shifts the zone of higher temperature gradient around the location of a dipole. The presence of dipole is more effective for skin friction compared with the Nusselt number. Keywords Nanofluids · Spatially varying magnetic field · Stream-vorticity formulation · Dipole List of symbols Cf Skin friction (−) Cfl , Cfu Skin friction at the lower and upper plates, respectively cp Specific heat at constant pressure (J kg−1) Ec Eckert number (−) H Magnetic field (T) H̄ Intensity of magnetic field (T) k Thermal conductivity (W m−1 K−1) kf Thermal conductivity of fluid knf Thermal conductivity of nanofluid ks Thermal conductivity of solid L Length (m) M Magnetization (A m−1) * Jianchao Cai [email protected] 1
Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, People’s Republic of China
Department of Basic Sciences and Humanities, Muhammad Nawaz Sharif University of Engineering and Technology, Multan, Pakistan
2
̄ Magnetization property (A m−1) M Mn Magnetic number (−) Nu Nusselt number (−) Nul , Nuu Nusselt number for lower and upper channel plates, respectively P Dimensional pressure (Pa) Pr Prandtl number (−) q̄ Heat flux (W m−2) Re Reynolds number (−) T Temperature (K) ΔT Temperature difference (K) Tc , Th Constant temperature of lower and upper plates (K) T̄ c Curie temperature (K) t Dimensional time (s) t′ Dimensionless time (−) U , V Dimensional components of velocity (m s−1) u, v Dimensionless components of velocity (−) X, Y Dimensional coordinates along and normal to the plates (m) x, y Dimensionless coordinates along and n
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