Mathematical modeling of magneto pulsatile blood flow through a porous medium with a heat source

• Autorzy: Sharma B. K. , Sharma M. , Gaur R. K. , Mishra A.

Identyfikatory

DOI

10.1515/ijame-2015-0025

• Języki publikacji: EN

Abstrakty

EN

In the present study a mathematical model for the hydro-magnetic non-Newtonian blood flow in the non-Darcy porous medium with a heat source and Joule effect is proposed. A uniform magnetic field acta perpendicular to the porous surface. The governing non-linear partial differential equations have been solved numerically by applying the explicit finite difference Method (FDM). The effects of various parameters such as the Reynolds number, hydro-magnetic parameter, Forchheimer parameter, Darcian parameter, Prandtl number, Eckert number, heat source parameter, Schmidt number on the velocity, temperature and concentration have been examined with the help of graphs. The present study finds its applications in surgical operations, industrial material processing and various heat transfer operations.

Słowa kluczowe

EN

heat source; blood flow; porous medium; MHD

PL

źródło ciepła; przepływ krwi; materiały porowate; magnetohydrodynamika

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2015
• Tom: Vol. 20, no. 2
• Strony: 385--396
• Opis fizyczny: Bibliogr. 31 poz., tab., wykr.

Twórcy

autor

Sharma B. K.

• Department of Mathematics Birla Institute of Technology and Science Pilani, Rajasthan, INDIA

autor

Sharma M.

• Department of Biotechnology, FASC Mody University of Science and Technology Lakshmangarh, Rajasthan, INDIA

autor

Gaur R. K.

• Department of Biotechnology, FASC Mody University of Science and Technology Lakshmangarh, Rajasthan, INDIA

autor

Mishra A.

• Department of Aerospace Engineering Indian Institute of Science Bangalore, INDIA

Bibliografia

• [1] Baish J.W. (1990): Heat transport by countercurrent blood vessels in the presence of an arbitrary pressure gradient. – ASME J Biomech. Eng., 112:207.
• [2] Bhargava R., Rawat S., Takhar H.S. and Bég O.A. (2007): Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel. – Meccanica, vol.42, pp.247-262.
• [3] Chamkha Ali J. (2004): Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption. – Int. J. Engg. Sci., vol.42, pp.217-230.
• [4] Cokelet G.R. (1972): The rheology of human blood. In: Fung YC (ed) Biomechanics-its foundations and objectives. – New York: Prentice Hall.
• [5] Consiglieri L., Santos I. and Haemmerich D (2003): Theoretical analysis of the heat convection coefficient in large vessels and the significance for thermal ablative therapies. – Phys. Med. Biol., vol.48, pp.4125-4134.
• [6] Davalos R.V., Rubinsky B. and Mir L.M. (2003): Theoretical analysis of the thermal effects during in vivo tissue electroporation. – Bioelectrochem J., vol.61, pp.99–107.
• [7] Dybbs A. and Edwards R.V. (1984): A new look at porous media fluid mechanics: Darcy to Turbulent. In: Bear J., Corapcioglu M.Y. (eds) Fundamentals of Transport Phenomena in Porous Media NATO ASI series E: Applied Sciences, vol.82, pp.199-256.
• [8] Hoffman J.D. (1992): Numerical Methods for Engineers and Scientists. – New York: McGraw-Hill.
• [9] Kandasamy R., Periasamy K. and Prashu Sivagnana K.K. (2005): Effects of chemical reaction, heat and mass transfer along wedge with heat source and concentration in the presence of suction or injection. – Int. J. Heat Mass Transfer, vol.48, pp.1388-1394.
• [10] Khaled A.R.A. and Vafai K. (2003): The role of porous media in modeling flow and heat transfer in biological tissues. – Int. J. Heat and Mass Transfer, vol.46, pp.4989-5003.
• [11] Louckopoulos V.C. and Tzirtzilakis E.E. (2004): Biomagnetic channel flow in spatially varying magnetic field. – Int. J. Eng. Sci., vol.42, pp.571-590.
• [12] McLellan K., Petrofsky J.S., Bains G., Zimmerman G., Prowse M. and Lee S. (2009): The effects of skin moisture and subcutaneous fat thickness on the ability of the skin to dissipate heat in young and old subjects, with and without diabetes, at three environmental room temperatures. – Med. Eng. Phys., vol.31, No.2, pp.165-172. doi:10.1016/j.medengphy.2008.08.004.
• [13] Ogulu A. and Amos E. (2007): Modeling pulsatile blood flow within a homogeneous porous bed in the presence of a uniform magnetic field and time-dependent suction. – Int. Comm. Heat Mass Transfer, vol.34, pp.989-995.
• [14] Pennes H.H. (1948): Analysis of tissue and arterial blood temperatures in the resting human forearm. – J. Appl. Physiol., vol.1, No.22, pp.93–122.
• [15] Petrofsky J.S., Bains G., Raju C., Lohman E., Berk L., Prowse M., Gunda S., Madani P. and Batt J. (2009): The effect of the moisture content of a local heat source on the blood flow response of the skin. – Archives of Dermatological Research, vol.301, No.8, pp.581-585.
• [16] Pop I. and Ingham D.B. (2001): Convective Heat Transfer: Mathematical and Numerical Modelling of Viscous Fluids and Porous Media, Pergamon, Oxford.
• [17] Preziosi L. and Farina A. (2002): On Darcy’s law for growing porous media. – Int. J. Non-Linear Mech., vol.37, pp.485-491.
• [18] Rawat S., Bhargava R., Anwar Bég O., Bhargava P. and Hughes Ben R. (2009): Pulsatile dissipative magneto-biorheological fluid flow and heat transfer in a non-Darcy porous medium channel: finite element modeling. – Emirates Journal for Engineering Research, vol.14, No.2, pp.77-90.
• [19] Sharma B.K., Agarwal M. and Chaudhary R.C. (2007): MHD fluctuating free convective flow with radiation embedded in porous medium having variable permeability and heat source/sink. – Journal of Technical Physics, vol.47, No.1, pp.47-58.
• [20] Sharma B.K., Agarwal M. and Chaudhary R.C. (2007): Effects of injection/suction on three-dimensional Couette flow with heat source/sink. – Ind. J. of Theoretical Physics, vol.55, No.1, pp.27-37.
• [21] Sharma B.K., Chaudhary R.C. and Agarwal M. (2008): Radiation effect on steady free convective flow along a uniform moving porous vertical plate in presence of heat source/sink and transverse magnetic field. – Bull. Cal. Math. Soc., vol.100, pp.529-538.
• [22] Sharma B.K., Gupta S., Krishna V.V. and Bhargavi R.J. (2014): Soret and Dufour effects on an unsteady MHD mixed convective flow past an infinite vertical plate with Ohmic dissipation and heat source. – Afrika Matematika, vol.25, pp.799-821, DOI 10.1007/s13370-013-0154-6.
• [23] Sharma B.K., Jha A.K. and Chaudhary R.C. (2007): Hall effect on MHD free convective flow of a viscous fluid past an infinite vertical porous plate with Heat source/sink effect. – Romania Journal of Physics, vol.52, No.5-6, pp.487-504.
• [24] Sharma B.K., Mishra A. and Gupta S. (2013): Heat and mass transfer in magneto-biofluid flow through a non-Darcian porous medium with Joule effect. – J. Eng. Phys. and Thermo Phys., vol.86, No.4, pp.716-725.
• [25] Sharma B.K., Sharma P.K. and Chand T. (2011): Effect of radiation on temperature distribution in three-dimensional Couette flow with heat source/sink. – International Journal of Applied Mechanics and Engineering, vol.16, No.2, pp.531-542.
• [26] Shrivastava D., McKay B. and Romer R.B. (2005): An analytical study of heat transfer in finite tissue with two blood vessels and uniform Dirichlet boundary conditions. – ASME J. Heat Transfer, vol.127, No.2, 179–188.
• [27] Skalak R. and Chien S. (1982): Rheology of blood cells as soft tissues. – Biorheology, vol.19, pp.453–461.
• [28] Sorek S. and Sideman S. (1986): A porous medium approach for modelling heart mechanics, B l-D case. – Math. Biosci., vol.81, pp.14-32.
• [29] Takeuchi T., Mizuno T., Higashi T., Yamagishi A. and Date M. (1995): Orientation of red blood cells in high magnetic field. – J. Magn. Magn. Mater., vol.140, pp.1462–1463.
• [30] Tzirtzilakis E.E. and Tanoudis G.B. (2003): Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer. – Int. J. Numer. Methods Heat Fluid Flow, vol.13, No.7, pp.830-848.
• [31] Vankan W.J., Huyghe J.M., Janssen J.D., Huson A., Hacking W.J.G. and Schrenner W. (1997): Finite element analysis of blood flow through biological tissue. – Int. J. Eng. Sci., vol.35, pp.375-385.