**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30121

##### Similarity Solutions of Nonlinear Stretched Biomagnetic Flow and Heat Transfer with Signum Function and Temperature Power Law Geometries

**Authors:**
M. G. Murtaza,
E. E. Tzirtzilakis,
M. Ferdows

**Abstract:**

Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformations. Numerical solutions for the governing momentum and energy equations are obtained by efficient numerical techniques based on the common finite difference method with central differencing, on a tridiagonal matrix manipulation and on an iterative procedure. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.

**Keywords:**
Biomagnetic fluid,
FHD,
nonlinear stretching sheet,
slip parameter.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1315703

**References:**

[1] Y. Haik, V. Pai, and CJ. Chen, “Development of magnetic device for cell separation,” J. Magnetic Materials, Vol. 194, pp. 254-261, 1999.

[2] J. C. Misra, A. Sinha, and G. C. Shit, “Flow of a biomagnetic viscoelastic fluid: application to estimate of blood flow in arteries during electromagnetic hyperthermia, a therapeutic procedure for cancer treatment,” App. Math. Mech. Engl, vol.31, pp. 1405-1420, 2010.

[3] Y. Haik, Chen and V. Pai, “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, June 25-28, 121-126,1996.

[4] E. E. Tzirtzilakis, “A Mathematical model for blood flow in magnetic field,” Physics of Fluids, Vol. 17(7), pp. 077103-1-14, 2005.

[5] E. E. Tzirtzilakis and G. B. Tanoudis, “Numerical study of Biomagnetic fluid flow over a stretching sheet with heat transfer,” Int. J. Numer. Methods Heat Fluid flow, vol. 13(7), pp. 830-848, 2003.

[6] J. C. Misra, G. C. Shit, “Biomagnetic viscoelastic fluid flow over a stretching sheet,” Applied Mathematics and Computation, vol. 210(2), pp. 350–361. 2009.

[7] E. E. Tzirtzilakis and N. G. Kafoussias, “Three dimensional magnetic fluid boundary layer flow over a linearly stretching sheet,” J. of Heat transfer, vol. 132, pp. 011702-1-8, 2010.

[8] E. E. Tzirtzilakis, and N. G. Kafoussias, “Biomagnetic fluid flow over a stretching sheet with nonlinear temperature dependent magnetization,” Z. Angew. Math. Phys (ZAMP), vol. 8, pp. 54-65, 2003.

[9] J. C. Misra, G. C. Shit, H. J. Rath, “Flow and heat transfer of a MHD viscoelastic fluid in a channel with stretching walls: Some applications to haemodynamics,” Computers & Fluids, vol. 37, pp. 1–11, 2008.

[10] N. G. Kafoussias, E. E. Tzirtzilakis, and A. Raptis, “Free forced convective boundary layer flow of a biomagnetic fluid under the action of localized magnetic field,” Canadian J. of physics, vol. 86, pp. 447-457, 2008.

[11] M. G. Murtaza, E. E. Tzirtzilakis, and M. Ferdows, “Effect of electrical conductivity and magnetization on the biomagnetic fluid flow over a stretching sheet,” Z. angew. Math. Phys (ZAMP), vol. 68, pp. 93, 2017.

[12] H. I. Anderson, “Slip flow past a stretching surface,” Acta Mech., vol. 158, pp. 121-125, 2002.

[13] K. Bhattacharyya, G. C. Layek, R. S. Gorla, “Boundary Layer Slip Flow and Heat Transfer Past a stretching Sheet with Temperature Dependent Viscosity,” Thermal Energy and Power Engineering, vol. 2(1), pp. 38-43, 2013.

[14] T. Akyildiz, D. A. Siginer, K. Vajravelu, J. R. Cannon, R. A.Van Gorder, “Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet,” Mathematical Methods in the Applied Sciences doi:10.1002/mma.1181.

[15] A. Robert. Van Gorder and Kuppalapalle Vajravelu, “A note on flow geometries and the similarity solutions of the boundary layer equations for a nonlinearly stretching sheet,” Arch Appl Mech, vol. 80, pp. 1329–1332, 2010.

[16] N. G. Kafoussias and E. W. Williams, “An improved approximation technique to obtain numerical solution of a class of two-point boundary value similarity problems in fluid mechanics,” Int. J. numer methods fluid, vol. 17, pp. 145-162, 1993.

[17] R. Cortell “Viscous flow and heat transfer over a nonlinearly stretching sheet,” Appl Math Comput, vol. 84, pp. 864–873, 2007.