## THERMAL SCIENCE

International Scientific Journal

### FLOW AND HEAT TRANSFER OF THREE IMMISCIBLE FLUIDS IN THE PRESENCE OF UNIFORM MAGNETIC FIELD

**ABSTRACT**

The magnetohydrodynamic flow of three immiscible fluids in a horizontal channel with isothermal walls in the presence of an applied magnetic field has been investigated. All three fluids are electrically conducting, while the channel plates are electrically insulated. The general equations that describe the discussed problem under the adopted assumptions are reduced to ordinary differential equations and closed-form solutions are obtained in three fluid regions of the channel. Separate solutions with appropriate boundary conditions for each fluid have been obtained and these solutions have been matched at the interface using suitable boundary conditions. The analytical results for various values of the Hartmann number, the ratio of fluid heights and thermal conductivities have been presented graphically to show their effect on the flow and heat transfer characteristics. [Projekat Ministarstva nauke Republike Srbije, br. TR 35016]

**KEYWORDS**

PAPER SUBMITTED: 2014-02-03

PAPER REVISED: 2014-06-02

PAPER ACCEPTED: 2014-06-04

PUBLISHED ONLINE: 2014-09-06

**THERMAL SCIENCE** YEAR

**2014**, VOLUME

**18**, ISSUE

**3**, PAGES [1019 - 1028]

- Blum, E. L., et al., Heat Exchange and Mass Exchange in Magnetic Field, Zinatne, 223, 1967
- Cramer, K. R., Pai, S. I., Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw-Hill, New York, N. Y., USA, 1973
- Soundalgekar, V. M., Uplekar, A. G., Hall Effects in MHDCouette Flow with Heat Transfer, IEEE Transactions on Plasma Science, PS-14, (1986) 4, pp. 579-583
- Attia, H. A., Hall Current Effects on the Velocity and Temperature Fields of an Unsteady Hartmann Flow, Canadian Journal of Physics, 76 (1998), 9, pp. 739-746
- Kiyasatfar, M., et al., Investigation of Thermal Behavior and Fluid Motion in DC Magnetohydrodynamic Pumps, Thermal Science, 18 (2014), Suppl. 2, pp. S551-S562
- Vyas, P., Srivastava, N., Radiative MHD Compressible Couette Flow in a Parallel Channel with a Naturally Permeable Wall, Thermal Science, 18 (2014), Suppl. 2, pp. S573-S585
- Yang, H. K., Yu, C. P., Combined Forced and Free Convection MHD Channel Flow in Entrance Region, International Journal of Heat and Mass Transfer, 17 (1974), 6, pp. 681-691
- Bodosa, G., Borkakati, A. K., MHD Couette Flow with heat Transfer between Two Horizontal Plates in the Presence of a Uniform Transverse Magnetic Field, Journal of Theoretical and Applied Mechanics, 30 (2003) 1, pp. 1-9
- Ghosh, S. K., A Note on Steady and Unsteady Hydromagnetic Flow in a Rotating Channel in the Presence of Inclined Magnetic Field, International Journal of Engineering Science, 29 (1991) 8, pp. 1013-1016
- Borkakati, A. K., Chakrabarty, S., Unsteady Free Convection MHD Flow between Two Heated Vertical Parallel Plates in Induced Magnetic Field, Indian Journal of Theoretical Physics, 47 (1999), pp. 143-160
- Aydin, O., Avci, M., Laminar Forced Convection with Viscous Dissipation in a Couette-Poiseuille Flow between Parallel Plates, Applied Energy, 83 (2006), 8, pp. 856-867
- Singha, K. G., Analytical Solution to the Problem of MHD Free Convective Flow of an Electrically Conducting Fluid between Two Heated Parallel Plates in the Presence of an induced Magnetic Field,, International Journal of Applied Mathematics and Computation, 1 (2009), 4, pp. 183-193
- Shail, R., On Laminar Two-Phase Flows in Magnetohydrodynamics", International Journal of Engineering Science, 11 (1973), 10, pp. 1103-1108
- Lohrasbi, J., Sahai, V., Magnetohy-Drodynamic Heat Transfer in Two-Phase Flow between Parallel Plates, Applied Scientific Research, 45 (1988), 1, pp. 53-66
- Malashetty, M. S., et al., Convective Magnetohydrodynamic Two Fluid Flow and Heat Transfer in an Inclined channel, Heat and Mass Transfer, 37 (2001), 2-3, pp. 259-264
- Malashetty,M. S., et al., Two Fluid Flow and Heat Transfer in an Inclined Channel Containing Porous and Fluid Layer, Heat and Mass Transfer, 40 (2004), 11, pp. 871-876
- Umavathi, J. C., et al., Oscillatory Hartmann Two-Fluid Flow and Heat Transfer in a Horizontal Channel, International Journal of Applied Mechanics and Engineering, 11 (2006), 1, pp. 155-178
- Umavathi, J. C., et al., Unsteady Two-Fluid Flow and Heat Transfer in a Horizontal Channel, Heat and Mass Transfer, 42 (2005), 2, pp. 81-90
- Nikodijevi}, D., et al., Flow and Heat Transfer of Two Immiscible Fluids in the Presence of Uniform Inclined Magnetic Field, Mathematical Problem in Engineering, Vol. 2011, doi: 10.1155/2011/132302
- Haiwang, L., et al., Analytical Model of Mixed Electroosmotic/Pressure Driven Three Immiscible Fluids in a Rectangular Microchannel, International Journal of Heat and Mass Transfer, 52 (2009), pp. 4459-4469
- Hormozia, S., et al., Multi-Layer Channel Flows with Yield Stress Fluids, Journal of Non-Newtonian Fluid Mechanics, 166 (2011), 5-6, pp. 262-278
- Li, J., et al., Analysis of Multi-Layer Immiscible Fluid Flow in a Microchannel, Journal of Fluids Engineering, DOI: 10.1115/1.4005134
- Haim, H. B., et al., A Magneto-Hydrodynamically Controlled Fluidic Network, Sensors and Actuators B, 88 (2003), 2, pp. 205-216
- Hussameddine, S. K., et al., Analytical Prediction of Flow Field in Magneto-Hydrodynamic-Based Microfluidic Devices, Journal of Fluids Engineering, DOI: 10.1115/1.2953302
- Yi, M., et al., A Magnetohy-Drodynamic Chaotic Stirrer, Journal of Fluid Mechanics, 468 (2002), pp. 153-177
- Weston, M. C., et al., Magnetic Fields for Fluid Motion, Analytical Chemistry, 82 (2010), 9, pp. 3411-3418