Supervised by: Presented by: TITLE OF PROJECT LAYOUT OF PRESENSTATION Title Summary of Study Flow Assumptions Equations of Motion Results and Discussion.

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Presentation transcript:

Supervised by: Presented by:

TITLE OF PROJECT

LAYOUT OF PRESENSTATION Title Summary of Study Flow Assumptions Equations of Motion Results and Discussion Literature Review References

SUMMARY OF WORK We studied the bio-magnetic fluid flow in a parallel plate channel when both the plates are shrinking and the lower plate is porous. A magnetic field is applied perpendicular to the plane of the channel. The convective heat transfer with viscous dissipation is also analyzed. Numerical computations have been made for several values of the physical parameters namely magnetic parameter, suction parameter, Reynolds’ number R, Prandtl number Pr, Eckert number and local Eckert number. The effects of these parameters have been observed on fluid velocity and temperature distribution. The results are presented in graphical form.

FLOW ASSUMPTIONS

RESEARCH QUESTIONS

EQUATIONS OF MOTION

THE ORDINARY DIFFERENTIAL EQUATIONS

THE BOUNDARY CONDITIONS

RESULTS AND DISCUSSION The non linear ordinary differential equations (9) and (10) have been solved numerically with Mathematica software version 6. The effect of the parameters namely, R,, Pr, E C and E CX have been computed and presented in graphical form for velocity and temperature distribution.

Fig.5 shows that temperature increases with increasing values of suction parameter.

. Fig.6 shows that with the increasing values of R, temperature function initially decreases near the lower the plate and then increases onward in the channel.

Fig.7 shows that temperature increases with increasing values of Pr.

Fig.8 shows that temperature increases with increasing values of Ec.

Fig.5 shows that temperature increases with increasing values of E cx.

LITERATURE SURVEY Dynamics of biological fluids (like animal blood) in the presence of magnetic field is important because of its applications in bioengineering and medical science. Theoretical analysis and experimental observations of blood flow are very useful for the diagnosis of a number of cardiovascular diseases and development of pathological patterns in animal or human physiology. Blood is considered as an electrically conducting fluid as reported in [1, 2].

Tzirtzilakis and Tanoudis [7] studied the bio- magnetic fluid flow over a stretching sheet. Eldesoky [8] presented mathematical analysis of unsteady MHD blood flow through parallel plate channel with heat source. Tzirtzilakis [11] presented a mathematical model for blood flow in magnetic field. Misra and Sinha [12] presented a theoretical analysis for magnatohydrodynamic flow of blood in a capillary, with lumen being porous and wall permeable.

The analysis of blood flow through parallel plate channel can be employed in biomedical research to examine the effects of fluid shear stress on the structure and function of endothelial cells. The concept has been attributed to wide spread usage because of its simplicity and its various designs have been developed for different applications of biomedical research. Khalil et al. [14] and Krizanac-Bengez et al. [15] studied the effects of ischemia/reperfusion on inflammatory gene expression of endothelial cells. Li et al. [16] remarked that the blood shear stress causes cardiovascular diseases by regulating inflammatory reactions in the vascular endothelium.

A large quantity of heat is carried by the blood to different parts of the body, while it flows through the arterial tree. The Pennes [17] bioheat equation is the most common method that is available to describe blood perfusion in the tissue. Chen and Homes [18] presented a bioheat transfer model that accounts for the thermally significant blood vessels. Brink and Werner [19] presented a three-dimensional thermal and vascular model in which the convective heat exchange between the feeder vessels and tissue was computed by the values for the Nusselt number and the temperatures in and near individual vessels were predicted. Wang [20] investigated heat transfer to blood flow in a small tube. Tzirtzilakis and Tanoudis [21] obtained numerical solution of biomagnetic fluid flow over a stretching sheet with heat transfer.

LITERATURE REVIEW Pavlov (1974) studied the boundary layer flow of an electrically conducting fluid due to stretching of a plane elastic surface in the presence of a uniform transverse magnetic field. Kumaran et al. (2009) reported that magnetic field makes the streamlines steeper which results the boundary layer thinner. Sajjad and Kamal (2012) studied boundary layer flow for micro polar electrically conducting fluid on a rotating disk in the presence of magnetic field.

El-Hakiem et al. (1999) analyzed the effect of viscous and Joule heating on the flow of an electrically conducting and micro polar fluid past a plate whose temperature varies linearly with the distance from the leading edge in the presence of a uniform transverse magnetic field. Khidir (2013) investigated the effects of viscous dissipation and Ohmic heating on steady MHD convective flow due to a porous rotating disk taking into account the variable fluid properties in the presence of Hall current and thermal radiation.

Ibrahim et al. (2013) studied radiation and mass transfer effects on MHD free convection flow of a micro polar fluid past a stretching surface embedded in a non-Darcian porous medium with heat generation. The effect of thermal radiation and magnetic field on unsteady mixed convection flow and heat transfer over a porous stretching surface was discussed by Elbashbeshy et al.(2010).

Ashraf et al (2009) obtained numerical simulation for two dimensional flow of a micro polar fluid between an impermeable and a permeable disk. Hady (1996) studied the solution of a heat transfer to a micro polar fluid from a non isothermal stretching sheet with injection. Na and Pop (1997) investigated the boundary layer flow of micro polar fluid due to a stretching wall.

Hassanien et al. (1998) studied a numerical solution for heat transfer in a micro polar fluid over a stretching sheet. Chakrabarti and Gupta (1979) extended Pavlov's work to study the heat transfer when a uniform suction is applied at the stretching surface.

REFERENCES J. Singh and R. Rathee, Analytical Solution of Two- Dimensional Model of Blood Flow with Variable Viscosity through an Indented Artery Due to LDL Effect in the Presence of Magnetic Field, International Journal of Physical Sciences, 5 (12), 2010, N. Verma and R. S. Parihar, Effects of Magneto- Hydrodynamic and Hematocrit on Blood Flow in an Artery withMultiple Mild Stenosis, International Journal of AppliedMathematics and Computer Science, 1(1), 2009,

Tzirtzilakis E.E., Tanoudis GB, Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer. Int J Numer Methods Heat Fluid Flow, 13, 2003, 830–848. Islam M. Eldesoky, Mathematical Analysis of Unsteady MHD Blood Flow through Parallel Plate Channel with Heat Source, World Journal of Mechanics, 2, 2012, E. E. Tzirtzilakis, A mathematical model for blood flow in magnetic field, PHYSICS OF FLUIDS, 17, 2005,

J. C. Misra, A. Sinha, Effect of thermal radiation on MHD flow of blood and heat transfer in a permeable capillary in stretching motion, Heat Mass Transfer, 49, 2013, 617–628. Khalil, A. A., Aziz, F. A., Hall, J. C., Reperfusion injury. Plastic and Reconstructive Surgery 117, Krizanac-Bengez, L., Mayberg, M. R., Cunningham, E., Hossain, M., Ponnampalam, S., Parkinson, F. E., Janigro, D., Loss of shear stress induces leukocyte-mediated cytokine release and blood- brain barrier failure in dynamic in vitro blood-brain barrier model. Journal of Cellular Physiology 206, 2006, [16]Li, Y. J., Haga J. H., Chien, S., Molecular basis of the effects of shear stress on vascular endothelial cells. Journal of Biomechanics 38, 2005,

Elbashbeshy, E.M.A. and Aldawody, D.A., Effect of thermal radiation and magnetic field on unsteady mixed convection flow and heat transfer over a porous stretching surface.International Journal of Nonlinear Sciences. Vol. 9 (4), pp Ashraf, M., Kamal, M. A. and Syed, K.S., 2009.Numerical simulation of a micropolar fluid between a porous disk and a non- porous disk, Appl. Math. Modell, Vol.33, pp

[17] Pennes, H. H., 1948, Analysis of tissue and arterial blood temperatures in the resting human forearm, J. Appl. Physiol., 1 (2), Hassanien, I., Gorla,R. S. R. and A. A. Abdulah.,1998. Numerical solution for heat transfer in micropolar fluids over a stretching sheet, Applied Mechanics ForEngineers, vol. 3, pp Chakrabarti, A.andGupta,A. S., 1979.Hydromagnetic flow and heat transfer over a stretching sheet, Quarterly of Applied Mathematics, vol. 37(1), pp

[18]Chen, M. M. and Homles, K. R., Microvascular contributions in tissue heat transfer, Annals of the New York Academy of Sciences, 335, 1980, [19] Brinck, H. and Werner, J., Estimation of the thmermal effect of blood flow in a branching countercurrent network using a three-dimensional vascular model, Trans. ASME, J. biomech. Eng., 164, 1994, [20 ] C. Y. Wang, Heat Transfer to Blood Flow in a Small Tube," Journal of Biomechanical Engineering, 130 (2), 2008, doi: / [21] E. E. Tzirtzilakis and G. B. Tanoudis, Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer, International Journal of Numerical Methods for Heat & Fluid Flow, 13(7), 2003,