Magneto-thermo analysis of oscillatory flow around a non-conducting horizontal circular cylinder
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Magneto‑thermo analysis of oscillatory flow around a non‑conducting horizontal circular cylinder Zia Ullah1 · Muhammad Ashraf1 · A. M. Rashad2 Received: 15 September 2019 / Accepted: 13 March 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract The present study is based on oscillatory mixed-convection flow of electrically conducting fluid around a non-conducting horizontal circular cylinder. By following the statement of the problem, a mathematical model is constituted, and then, the formulated model is transformed into convenient form for integration by using primitive-variable formulation. The behavior of oscillatory skin friction, heat transfer and magnetic flux for pertinent parameters involved in the flow model such as mixedconvection parameter 𝜆 , magnetic force parameter 𝜉 , the magnetic Prandtl number 𝛾 and the Prandtl number Pr is discussed numerically. For this purpose, first velocity profile, temperature distribution and magnetic-field profile at various positions 𝛼 = 𝜋∕6, 𝜋∕3 and 𝜋 of the non-conducting horizontal circular cylinder for steady state are secured and then are used to calculate oscillatory skin friction, heat transfer and current density. It is predicted that oscillatory behavior of skin friction, heat transfer and current density is increased at position 𝛼 = 𝜋∕4 for increasing values of the various physical pertinent parameters. It is pertinent to mention here that the convective heat transfer is practically associated with oscillatory flow behavior. Keywords Magneto-convection · Oscillatory flow · Horizontal cylinder · Skin friction · Heat transfer · Current density List of symbols u, v Velocity along xy-direction (m s −1) Hx , Hy Magnetic field along xy-direction (Tesla) 𝜇 Dynamic viscosity (kg m −1 s −1) 𝜈 Kinematic viscosity (m 2 s −1) 𝜌 Density (kg m −3), 𝜏 Shear stress (P a) g Gravitational acceleration (m s −2) 𝛽 Thermal expansion coefficient (K −1) 𝜈m Magnetic permeability (H m −1) 𝛼 Thermal diffusivity (m 2 s −1) T Temperature (K) Cp Specific heat (J kg −1 K −1) T∞ Ambient fluid temperature (K) ReL Reynolds number GrL Grashof number Greek letters 𝜉 Magnetic force parameter 𝜆 Mixed-convection parameter * Muhammad Ashraf [email protected] 1
Department of Mathematics, Faculty of Science, University of Sargodha, Sargodha, Pakistan
Department of Mathematics, Faculty of Science, Aswan University, Aswan 81528, Egypt
2
𝜃 Dimensionless temperature 𝛾 Magnetic Prandtl number Pr Prandtl number 𝜎 Electrical conductivity
Introduction The phenomenon of hydromagnetic mixed-convection flow around and along different geometries is very important organ of engineering and physical sciences due to its diverse applications in industry and other ranges of life. Mixed-convection oscillatory flow associated with heat transfer characteristics in cylindrical structures has important practical applications in engineering processes of industrial level such as chimney stacks, designing of heat-exchanger tubes, hot rolling, cooling towers, liquid rocket, nuclear reacto
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