Main Article Content
The present study deals with two layered MHD immiscible fluid flow through porous medium in presence of heat transfer through parallel plate channel. The fluids are incompressible, and flow is fully developed. The fluids are of different viscosities and thermal conductivities so flowing without mixing each other. Two different phases are accounted for study and are electrically conducting. Temperature of the walls of parallel plate channel is constant. Rheological properties of the immiscible fluids are constant in nature. The flow is governed by coupled partial differential equations which are converted to ordinary differential equations and exact solutions are obtained. The velocity profile and temperature distribution are evaluated and solved numerically for different heights and viscosity ratios for the two immiscible fluids. The effect of magnetic field parameter M and porosity parameter K is discussed for velocity profile and temperature distribution. Combined effects of porous medium and magnetic fields are accelerating the flow which, can be helpful in draining oil from oil wells.
Rohsenow WM, Hartnett JP, Gneic EN. Handbook of heat transfer fundamentals. New York: Mac Graw – Hill; 1985.
Roming MF. The influence of electric and magnetic fields on heat transfer to electrically conducting fluids. Advances in Heat Transfer. 1: Academic Press New York; 1961.
Alpher RA. Heat transfer in magnetohydrodynamic flow between parallel plates. Int. J. Heat Mass Transfer. 1961;3:108-112.
Perlmutter M, Siegel R. Heat transfer to an electrically conducting fluid flowing in a channel with a transverse magnetic field. NASA, TN. 1961;865.
Siegel R. Effects of magnetic field on forced convection heat transfer in a parallel plate channel. J. Appl. Mech. 1958;25:415.
Alireza S, Sahai V. Heat transfer in developing magnetohydrodynamic Poiseuille flow and variable transport properties. I. J. Heat Mass Transfer. 1990;33(8):1711-1720.
Lohrasbi J, Sahai V. Magnetohydrodynamic heat transfer in two-phases flow between parallel plates. Appl. Sci. Res. 1989;45:53-66.
Malashetty MS, Leena V. Magnetohydrodynamic heat transfer in two-phase flow. Proc. ASME/ AICHE 27th National Heat Transfer Conference and Exposition. 1991;28-31.
Postlethwaite AW, Sluyter MM. MHD heat transfer problems and overview. Mechanical Engg. 1978;100:32-39.
Sinha KG, Deka PN. Two phase magnetohydrodynamic flow and heat transfer in a horizontal channel. Ganita. 2005;56(2):185-201.
Cruz DOA, Pinho FT. Analysis of isothermal flow of a Phan-Thien-Tanner fluid in a simplified model of a single- screw-extruder. J. Non-Newton. Fluid Mech. 2012;167–168,95–105.
Raju TL, Rao BN, Veeraiah P. MHD two-layered fluid slip-flow between parallel walls. International Journal of Emerging Trends in Engineering and Development. 2015;6.
Siddiqui AM, Zeb M, Haroon T, Azim Q. Exact solution for the heat transfer of two immiscible PTT fluids flowing in concentric layers through a pipe. Mathematics. 2019;7:81. DOI: 10.3390/math7010081
Siddiqui AM, Azim QA, Rana MA. On exact solutions of concentric n-layer flows of viscous fluids in a pipe. Nonlinear Science Letters A. 2010;1:93-102.
Eldesoky IM. Effect of relaxation time on MHD pulsatile flow of blood through porous medium in an artery under the effect of periodic body acceleration. Journal of Biological Systems. 2013;21(02):1350011. DOI: 10.1142/s0218339013500113
Eldesoky IM, Abumandour RM, Kamel MH, Abdelwahab ET. The combined influences of heat transfer, compliant wall properties and slip conditions on the peristaltic flow through tube. SN Applied Sciences. 2019;1(8). DOI: 10.1007/s42452-019-0915-4
Eldesoky IM, Abdelsalam SI, El-Askary WA, El-Refaey AM, Ahmed MM. Joint effect of magnetic field and heat transfer on particulate fluid suspension in a catheterized wavy tube. Bio Nano Science; 2019. DOI: 10.1007/s12668-019-00651-x
Eldesoky IM, Abdelsalam Sara I, El-Askary WA. The integrated thermal effect in conjunction with slip conditions on peristaltically induced particle-fluid transport in a catheterized pipe. Journal of Porous Media. 2020;23(7):695–713. DOI: 10.1615/JPorMedia.2020025581
Fakour M, Ganji DD, Abbasi M. Scrutiny of underdeveloped nanofluid MHD flow and heat conduction in a channel with porous walls. Case Studies in Thermal Engineering. 20147;4:202–214. DOI: 10.1016/j.csite.2014.10.003
Fakour M, Vahabzadeh A, Ganji DD, Hatami M. Analytical study of micropolar fluid flow and heat transfer in a channel with permeable walls. Journal of Molecular Liquids. 2015;204:198–204. DOI:10.1016/j.molliq.2015.01.040
Fakour M, Vahabzadeh A, Ganji DD. Study of heat transfer and flow of nanofluid in permeable channel in the presence of magnetic field. Propulsion and Power Research. 2015;4(1):50–62. DOI: 10.1016/j.jppr.2015.02.005
Fakour M, Ganji DD, Khalili A, Bakhshi A. Study of heat transfer in nanofluid Malashetty M.S., Umavathi J.C. and Prathap Kumar J (2001). Two-fluid magnetoconvection flow in an inclined channel. International Journal of Transport Phenomena. 2017;3:73-84.
Fakour M, Ganji DD, Khalili A, Bakhshi A. Study of heat transfer in nanofluid MHD flow in a channel with Permeable walls, begellhouse. Heat Transfer Research. 2017;48(3):221–238.
Fakour M, Rahbari A, Khodabandeh E, Ganji DD. Nanofluid thin film flow and heat transfer over an unsteady stretching elastic sheet by LSM. Journal of Mechanical Science and Technology. 2018;32(1):177–183. DOI: 10.1007/s12206-017-1219-5
Prakash O, Kumar D, Dwivedi YK. Free convection effects and radiative heat transfer in MHD stokes problem for the flow of dusty conducting fluid through porous medium. Pramana. 2012;78(3):429–438. DOI: 10.1007/s12043-011-0238-5
Rahbari A, Fakour M, Hamzehnezhad A, Vakilabadi MA, Ganji DD. Heat transfer and fluid flow of blood with nanoparticles through porous vessels in a magnetic field: A quasi-one dimensional analytical approach. Mathematical Biosciences. 2017;283:38–47. DOI: 10.1016/j.mbs.2016.11.009
Kumar R, Kumar D, Shrivastav RK. Thermal diffusion and mass transfer effects on MHD flow of a dusty gas through porous medium. ISRN Applied Mathematics. 2012;1–9. DOI: 10.5402/2012/568278
Surseh M, Sekar P. Mathematical analysis of unsteady MHD blood flow through parallel plate channel with heat source. International Journal of Engineering Technologies and Management Research. 2018;5(1):40-50. Available:https://doi.org/10.29121/ijetmr.v5.i1.2018.47