Effects of variable fluid properties and mixed convection on biomagnetic fluid flow and heat transfer over a stretching sheet in the presence of magnetic dipole

• Autorzy: Murtaza M. G. , Alam Jahangir , Tzirtzilakis E. E. , Shamshuddin Md. , Ferdows M.
• Języki publikacji: EN

Abstrakty

EN

This investigations covers the numerical analysis of a steady biomagnetic fluid flow (BFD) that passed through a two dimensional stretching sheet under the influence of magnetic dipole. The effect of fluid variable viscosity and thermal conductivity are also taken into consideration as assumed to vary as linear function of temperature. Our model mathematically formulated for BFD namely blood which consist of principles of magnetohydrodynamic (MHD) and ferrohydrodynamic (FHD), where blood treated as an electrically conducting fluid as well as polarization. Using similarity transformations, the governing system of partial differential equations are transferred into system of ordinary differential equations (ODE). The resulting coupled non linear ODE is numerically solved by employing bvp4c function technique available in MATLAB software. The effects of pertinent parameters namely ferromagnetic interaction parameter, magnetic field parameter, mixed convection parameter, viscosity variation parameter, Prandtl number, thermal conductivity parameter etc are plotted and discussed adequately for velocity and temperature profile as well as skin friction coefficient and rate of heat transfer. The results revels that velocity profile decreases as enhanced values of ferromagnetic number whereas temperature profile increased. Also found that skin friction coefficient reduces and rate of heat transfer increases by increasing values of thermal conductivity parameter and viscosity variation parameter. For numerical validation a comparisons has been made for some specific values with previous investigators. We hope that the present analysis will present in bio-medical and bio-engineering sciences.

Słowa kluczowe

EN

stretching sheet; biomagnetic fluid; magnetohydrodynamic; ferrohydrodynamic; magnetic dipole; magnetization; variable viscosity; thermal conductivity

PL

rozciąganie arkusza; płyn biomagnetyczny; magnetohydrodynamika; ferrohydrodynamika; dipol magnetyczny; namagnesowanie; zmienna lepkość; przewodność cieplna

• Wydawca: Institute of Heat Engineering, Warsaw University of Technology
• Czasopismo: Journal of Power Technologies
• Rocznik: 2023
• Tom: Vol. 103, nr 4
• Strony: 193--208
• Opis fizyczny: Bibliogr. 42 poz., rys., tab., wykr.

Twórcy

autor

Murtaza M. G.

• Department of Mathematics, Comilla University, Cumilla-3506, Bangladesh

autor

Alam Jahangir

• Research Group of Fluid Flow Modeling and Simulation, Department of Applied Mathematics, University of Dhaka, Dhaka-1000, Bangladesh

autor

Tzirtzilakis E. E.

• Fluid Mechanics and Turbomachinary Laboratory, Department of Mechanical Engineering, University of the Peloponnese, Tripoli, Greece

autor

Shamshuddin Md.

• Department of Mathematics, Vaagdevi College of Engineering (Autonomous), Warangal, Telangana State, India

autor

Ferdows M.

• Research Group of Fluid Flow Modeling and Simulation, Department of Applied Mathematics, University of Dhaka, Dhaka-1000, Bangladesh

Bibliografia

• [1] Haik, Y., Chen, C.J. and Pai, V., Development of biomagnetic fluid dynamics, Proceedings of the IX international Symposium on Transport Properties in Thermal fluid engineering, Singapore, Pacific center of thermal fluid engineering, 1996; 25: 121-126.
• [2] Tzirtzilakis, E. E., A Mathematical model for blood flow in magnetic field, Physics of fluids, 2005; 17: 077103-1-14.
• [3] Tzirtzilakis, E. E. and Kafoussias, N. G., Biomagnetic fluid flow over astretching sheet with nonlinear temperature dependent magnetization, Z. Angew. Math. Phys.(ZAMP), 2003;8:54-65.
• [4] Rahman, R., Ellahi, Su., Nadeem, M.M., Gulzar, S. and Vafi, k., A mathematical study of non Newtonian micropolar fluid in a arterial blood flow through composite sterosis, Applied Mathematics and information sciences, 2014; 8:1567-1573.
• [5] Prallhad, R.N. and Schutz, D.H, Modeling of arterial stenosis and its applications to blood diseases, Mathematical Biosciences, 2014; 190: 203-220
• [6] Sakiadis, B. C., Boundary layer behaviour on continuous solid surfaces, AICHE Journal, 1961; 7: 26–28.
• [7] Sakiadis, B. C., Boundary layer behaviour on continuous solid surfaces: II, the boundary layer on a continuous flat surface, AICHE Journal. 1961; 17: 221–225.
• [8] Crane, L. J., Flow past a stretching plate, Zeitschrift fur Angewandte Mathematikund Physik, 1970; 21: 645– 647.
• [9] Sharidan, S, Mahmood, T., Pop, I., Similarity solutions for the unsteady boundary layer flow and heat transfer due to a stretching sheet, Int J Appl Mech Eng.,2006; 11: 647–54.
• [10] Carragher, P.,.Crane, LJ., Heat transfer on continuous stretching surface, ZAMM ,1982; 62: 564–5.
• [11] Grubka, L. J. and Bobba, K. M.., Heat Transfer Characteristics of a Continuous Stretching Surface With Variable Temperature, ASME J. Heat Transfer,1985;107: 248–250.
• [12] Brady, J. F. and Acrivos, A., Steady flow in a channel or tube with an accelerating surface velocity. An exact solution to the Navier-Stokes equations with reverse flow, Journal of Fluid Mechanics, 1981; 112: 127-150.
• [13] Salem, AM., Variable viscosity and thermal conductivity effects on MHD flow and heat transfer in viscoelastic fluid over a stretching sheet, Phys Lett A, 2007; 369: 315–22.
• [14] Anjali Devil, SP., Ganga, B., Effects of viscous and Joules dissipation on MHD flow, heat and mass transfer past a stretching porous media, Nonlinear Anal Model Control, 2009; 14: 303–14.
• [15] Mukhopadhyay, S., Layek, GC., Effect of thermal radiation and variable fluid viscosity on free convective and heat transfer past a porous stretching surface, Int. J Heat Mass Transfer, 2008;2167-78.
• [16] Malik, MY., Hussain, A. and Nadeem, S., Boundary layer flow of an Eyring-Powell model fluid due to a stretching cylinder with variable viscosity, Scientia Iranica , 2013; 20: 313–321.
• [17] Singh, V and Agarwal, S., Flow and heat transfer of Maxwell fluid with variable viscosity and thermal conductivity over an exponentially stretching sheet, American journal of fluid dynamics, 2013; 3: 87-95.
• [18] Ahmmed, S. F., Das, M. K., Ali, L. E, Analytical Study on Unsteady MHD Free Convection and Mass Transfer Flow Past a Vertical Porous Plate, American Journal of Applied Mathematics, 2015;3: 64-74.
• [19] Ali, N., Khan, SU. and Abbas, Z, Hydromagnetic Flow and Heat Transfer of a Jeffrey Fluid over an Oscillatory Stretching Surface, Z. Naturforsch., 2015; 70: 567–576.
• [20] Gul, T., Islam, S., Shah, RA., Khalid, A., Khan, I., Shafie, S., Unsteady MHD Thin Film Flow of an Oldroyd-B Fluid over an Oscillating Inclined Belt, PloS ONE, (2015).
• [21] Mahmoud, M. A. A., Variable Viscosity Effects of Hydromagnetic Boundary Layer Flow Along a Continuously Moving Vertical Plate in the Presence of Radiation, Appl. Math. Sci., 2007; 1: 799-814.
• [22] Subhas Abel, M., Siddheshwar, PG. and Mahesha, N., Effects of thermal buoyancy and variable thermal conductivity on the MHD flow and heat transfer in a power-law fluid past a vertical stretching sheet in the presence of a non-uniform heat source, International Journal of Non-Linear Mechanics, 2009; 44: 1–12 .
• [23] Makinde, OD., Khan, WA. and Khan, ZH., Buoyancy effects on MHD stagnation point flow and heat transfer of a nano fluid past a convectively heated stretching/shrinking sheet, International journal of heat and mass transfer, 2013; 62: 526-533.
• [24] Abo-Eldahaband, E. M., Elbarbary, E. M. E., Hall current effect on magneto hydrodynamic free convection flow past a semi-infinite vertical plate with mass transfer, Int. J. of Eng. Sci., 2001; 39: 1641-1652.
• [25] Rana, M. A., Siddiqui, A. M. and Ahmed, N., Hall effect on Hartmann flow and heat transfer of a Burger’s fluid, Phys. Letters A, 2008; 372: 562-568.
• [26] Alinejad, J. and Samarbakhsh, S., Viscous flow over non linearly stretching sheet with effects of viscous dissipation, Journal of applied mathematics,2012;2012:1-10. doi:10.1155/2012/587834.
• [27] Gireesha, BJ., Ramesh, GK. and Bagewadi, CS., Heat transfer in MHD flow of a dusty fluid over a stretching sheet with viscous dissipation, Advances in Applied Science Research, 2012; 3: 2392-2401.
• [28] Hazarika, G.C. and Santana Hazarika, Effects of variable viscosity and thermal conductivity on Magneto hydrodynamics mixed convective flow over a stretching surface with radiation, IJSRET, 2015;4
• [29] Tzirtzilakis, E. E., A simple numerical methodology for BFD problems using stream function vortices formulation, Communications in numer. Methods in Engineering, 2000; 2: 1-6.
• [30] Anderson, H.I. and Valens, O.A., Flow of a heated Ferro fluid over a stretching sheet in the presence of amagnetic dipole, Acta Mechanical, 1998; 28: 39-47.
• [31] Lai, F.C., Kulacki, F.A., The effect of variable viscosity on conductive heat transfer along a vertical surface in a saturated porous medium, Int. J. Heat Mass Transfer,1990; 33: 1028-1031.
• [32] Salawu, S. O., Dada, M. S., The radiative heat transfer of variable viscosity and thermal conductivity effects on inclined magnetic field with dissipation in a non-Darcy medium, Journal of Nigerian Mathematical Society, 2016;35:93–106 .
• [33] Ioan Pop, Rama Subba Reddy Gorla and Majid Rashidi, The effect of variable viscosity on flow and heat transfer to a contiuous moving flat plate, Int. J. Engng Sci., 1992; 30: 1-6. [34] Valvano, JW., Nho, S., Anderson, GT., Analysis of the Weinbaum-Jiji model of blood flow in the canine kidney cortexfor self-heated thermistorsrom, J Biomech Eng. 1994; 116:201-207.
• [35] Murtaza, M. G., Tzirtzilakis, E. E. and Ferdows, M., Duality of Biomagnetic fluid flow and heat Transfer over a quadratic stretched sheet, J. of Power Technologies, 2021; 101(3):154-162
• [36] Reddy, S.R.R., Bala Anki Reddy, Suneetha, S. P., Magnetohydro dynamic flow of blood in a permeable inclined stretching surface with viscous dissipation, no-uniform heat source/sink and chemical reaction, Frontiers in Heat and Mass Transfer(FHMT), 2018; 10.
• [37] Misra, J. C., Shit, G. C., Biomagnetic viscoelastic fluid flow over a stretching sheet, Applied Mathematics and Computation, 2009; 210: 350-361.
• [38] Tzirtzilakis, E.E., Tanoudis, G.B., Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer, Int. J. Numer. Methods Heat Fluid flow, 2003; 13: 830–848.
• [39]Nikiforov, V.N., Magnetic induction hyperthermia, Russian Physics Journal, 2007; 50:913-924.
• [40] Murtaza, M. G., Tzirtzilakis, E. E. and Ferdows, M., Three-Dimensional Biomagnetic Flow and Heat Transfer over a Stretching Surface with Variable Fluid Properties, Advanced in mechanics and Mathematics, 2019; 41: 403-414.
• [41] Prasad, K .V., Vajravelu, K . and Datti, P.S., Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties, International Journal of non-linear Mechanics, 2010; 45: 320-330.
• [42] Loukopoulos, V. C., Tzirtzilakis, E. E., Biomagnetic channel flow in spatially varying Magnetic field. International Journal of Engineering Science, 2004; 42: 571-590.