Numerical analysis of particulate Reiner–Rivlin flow in an asymmetric convergent channel with a heat source and magnetic field

Abstract

ABSTRACTThe goal of the current investigation is to examine the impact of magnetic field and heat source effects on a Reiner–Rivlin particulate flow through an asymmetric channel (convergent channel). The transformed governing equations are solved by employing the shooting technique with the RK4 method. To check the convergence of the computational results, a grid independence test has been performed. The impact of influential parameters on fluid as well as particle phases of velocity and temperature fields have been analyzed graphically. The present results exactly match previously published results in some limited cases. As the Reynolds number and magnetic parameter increase, the fluid phase velocity increases on the left side and decreases on the right part of the channel. Different fields, including metal steam resistors, paper production, and fibre suspension, are significantly impacted by the magnetic field’s effect on Reiner–Rivlin fluid through asymmetric channels.KEYWORDS: Reiner–Rivlin fluidtwo-phase flowparticle suspensionnumerical solutionconvergent channel Nomenclature U0=Radial velocity along center line m/sV0=Suction/Injection velocity m/su=Fluid phase velocity m/sup=Particle phase velocity m/sf=Dimensionless fluid phase velocityg=Dimensionless particle phase velocityT=Fluid phase temperature KTp=Particle phase temperature Kh=Dimensionless fluid phase temperatureH=Dimensionless particle phase temperatureS=Drag coefficient of the interaction for the force exerted by one face on the otherH0=Magnetic field intensity A/mCP=Specific heat of the fluid J/kg−1K−1Cm=Specific heat of the particles J/kg−1K−1K=Thermal conductivity of the fluid W/mKRe=Reynolds number U0r0υR=Cross flow Reynolds number V0r0υL=Ratio of the densities of the particle and fluid phase ρpρM2=Magnetic parameter σH02μe2r2ρυPr=Prandtl number μcpkN=Inelastic number υ1r2Greek symbols=r,θ=Polar coordinatesυ=Kinematic viscosityμ=Coefficient of viscosityα=Angle of the channelρ=Density of the fluidρp=Density of the particleμB=Plastic dynamic viscosityμe=Magnetic permeability of the fluidβ=Fluid particle interaction parameter for velocityβt=Fluid particle interaction parameter for temperatureAcknowledgmentsThe authors are thankful to the Department of Science and Technology, Government of India, for financing, as part of the DST-FIST venture for HEIs (Grant No. SR/FST/MS-I/2018/23(C)).Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationNotes on contributorsS. H. C. V. Subba BhattaDr. S. H. C. V. Subba Bhatta has completed his P.hD from S K University, Anantapur. He is working as a Professor in Department of Mathematics, M S Ramaiah Institute of Technology, Bengaluru. His interested areas are as follows, Two-phase flows, flow through non uniform channels, heat transfer etc.S. Ram PrasadDr S. Ram Prasad has completed his P.hD from VTU, Beagavi. He is working as an Assistant Professor in Department of Mathematics, M S Ramaiah Institute of Technology, Bengaluru. His interested areas are as follows, Two-phase and multi-phase flows, Nano fluids, Newtonian and non-Newtonian flow through non uniform channels etc.B.J. GireeshaDr. B. J. Gireesha has completed his P.hD from Kuvempu University, Shimoga. He is working as a Professor in Department of Mathemaics, Kuvempu University, Shankaraghtta. His interested areas are as fallows Fluid Mechanics, Heat Transfer Analysis, Nanofluids, Dusty Fluids, Heat Transfer Through FINS, Micro Fluidics.