## THERMAL SCIENCE

International Scientific Journal

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

**ABSTRACT**

The MHD flow of three immiscible fluids in a horizontal channel with isothermal walls in the presence of an applied electric and inclined magnetic field has been investigated in the paper. 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 ODE and closed-form solutions are obtained in three fluid regions of the channel. Separate solutions with appropriate boundary and interface conditions for each fluid have been determined. The analytical results for various values of the Hartmann number, magnetic field inclination angle, ratio of fluid viscosities, and electrical conductivities have been presented graphically to show their effect on the flow and heat transfer characteristics. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. TR 35016: Research of MHD flow in the channels, around the bodies and application in the development of the MHD pump]

**KEYWORDS**

PAPER SUBMITTED: 2018-05-21

PAPER REVISED: 2018-10-11

PAPER ACCEPTED: 2018-10-12

PUBLISHED ONLINE: 2019-01-19

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**Supplement 5**, PAGES [S1575 - S1589]

- Blum, E. Ya., Heat and Mass Transfer in MHD Flow Past Bodies, Magnetohydrodynamics, 6 (1970), 2, pp. 212-218
- Cramer, K. R., Pai, S. I., Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw-Hill, New York, USA, 1973
- El-Dabe, N., et al., Magnetohydrodynamic Non-Newtonian Nanofluid Flow over a Stretching Sheet through a Non-Darcy Porous Medium with Radiation and Chemical Reaction, Journal of Computational and Theoretical Nanoscience, 12 (2015), 12, pp. 5363-5371
- 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 Magnetohydrodynam-ic Pumps, Thermal Science, 18 (2014), Suppl. 2, pp. S551-S562
- Chandrasekhar, S., Sharma, V. M., Brownian Heat Transfer Enhancement in the Turbulent Regime, Fac-ta Universitatis Series: Mechanical Engineering, 14 (2016), 2, pp. 169-177
- Abou-Zeid, M., Homotopy Perturbation Method for MHD Non-Newtonian Nanofluid Flow through a Porous Medium in Eccentric Annuli with Peristalsis, Thermal Science, 21 (2017), 5, pp. 2069-2080
- Ghosh, S. K., Nandi, D. K., Magnetohydrodynamic Fully Developed Combined Convection Flow be-tween Vertical Plates Heated Asymmetrically, Journal of Technical Physics, 41 (2000), 2, pp. 173-185
- Bodosa, G., Borkakati, 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., et al., Hydromagnetic Free Convection Flow with Induced Magnetic Field Effects, Mec-canica, 45 (2010), 2, pp. 175-185
- 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), 1, 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, In-ternational Journal of Applied Mathematics and Computation, 1, (2009), 4, pp. 183-193
- Shail, R., On Laminar Two-Phase Flows in Magnetohydrodynamics, International Journal of Engineer-ing Science, 11 (1973), 10, pp. 1103-1108
- Lohrasbi, J., Sahai, V., Magnetohydrodynamic Heat Transfer in Two-Phase Flow between Parallel Plates, Applied Scientific Research, 45 (1988), 1, pp. 53-66
- 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
- Abou-Zeid, M., Magnetohydrodynamic Boundary Layer Heat Transfer to a Stretching Sheet Including Viscous Dissipation and Internal Heat Generation in a Porous Medium, Journal of Porous Media, 14 (2011), 11, pp. 1007-1018
- 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
- Nikodijević, D., et al., Flow and Heat Transfer of Two Immiscible Fluids in the Presence of Uniform In-clined Magnetic Field, Hindawi Publishing Corporation, Mahtematical Problems in Engineering, 2011 (2011), ID 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), 19-20, 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 Engi-neering, 133 (2011), 11, pp. 1-10
- 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 Magnetohydrodynamic-Based Micro-fluidic Devices, Journal of Fluids Engineering, 130 (2008), 9, ID 091204
- Yi, M., et al., A Magnetohydrodynamic Chaotic Stirrer, Journal of Fluid Mechanics, 468 (2002), Oct., pp. 153-177
- Weston, M. C., et al., Magnetic Fields for Fluid Motion, Analytical Chemistry, 82 (2010), 9, pp. 3411-3418
- Thorn, R., et al., Three-Phase Flow Measurement in the Petroleum Industry, Measurement Science and Technology, 24 (2013), 1, pp. 1-17
- Shaaban, A., Abou-Zeid, M., Effects of Heat and Mass Transfer on MHD Peristaltic Flow of a Non-Newtonian Fluid through a Porous Medium between Two Coaxial Cylinders, Mathematical Problems in Engineering, 2013 (2013), ID 819683