Microrotating chemically reactive hybrid nanomaterial in a high porous medium influenced by Cattaneo-Christov double diffusion and non-linear slip

ABSTRACTA simultaneous heat and mass transfer due to microrotating Darcy-Forchheimer flow of hybrid nanofluid over a moving thin needle is investigated. Darcy-Forchheimer medium accommodating hybrid nanofluid flow yields greater heat transfer rate, thereby leading to greater mass transfer rate over thin needle in industrial applications such as blood flow problems, aerodynamics, transportation, coating of wires, lubrication, and geothermal power generation. The thermophoresis and Brownian motion phenomena are introduced to enrich thermal treatment. Heat and mass transfer are accompanied by Cattaneo-Christov heat and mass flux. The hybrid nanofluid is radiative and dissipative in nature. Arrhenius pre-exponential factor law is introduced. Entropy generation analysis is carried out. The 4th order Runge-Kutta method along with shooting technique is devised to get requisite numerical solution of the transformed non-dimensional system of equations. Darcy-Forchheimer effect to simultaneous heat and mass transfer of microrotating hybrid nanofluid flow over thin needle subject to non-linear slip is the novelty of present study which is beyond of previous investigations. Rise in Forchheimer number (strengthening Darcy Forchheimer medium) leads to surface viscous drag decreases by 11.11% for hybrid nanofluid and 10.78% for pure nanofluid indicating the control of momentum transfer, thereby regulating heat transfer rate effectively.KEYWORDS: Thin needleDarcy-Forchheimer effecthybrid nanofluidCattaneo-Christov heat mass fluxArrhenius pre-exponential factor law Nomenclature(u,v)=velocity components in the axial and radial directionsms−1ρCphnf=specific heat capacity of hybrid nanofluidJkg2m3K−1ρCpbf=specific heat capacity of base fluidJkg2m3K−1ρCpCu=specific heat capacity of CuJkg2m3K−1ρCpAl2O3=specific heat capacity of Al2O3Jkg2m3K−1ρhnf=effective density of hybrid nanofluidkgm−3ρCu=density of Cukgm−3ρAl2O3=density of Al2O3kgm−3ρbf=density of base fluidkgm−3μhnf=effective dynamic viscosity ofhybrid nanofluidkgm−1s−1μbf=effective dynamic viscosity of base fluidkgm−1s−1βhnf=thermal expansion coefficient of hybrid nanofluidK−1βbf=thermal expansion coefficient of base fluidK−1βCu=thermal expansion coefficient of CuK−1βAl2O3=thermal expansion coefficient of Al2O3K−1khnf=thermal conductivity of hybrid nanofluidWm−1K−1kbf=thermal conductivity of base fluid Wm−1K−1kCu=thermal conductivity of CuWm−1K−1kAl2O3=thermal conductivity of Al2O3Wm−1K−1σ∗=Stefan-Boltzmann constantWm−2K−4k∗=mean absorption coefficientK=porous medium permeabilityk=vortex viscosityϕCu=volume fraction of CuϕAl2O3=volume fraction of Al2O3ϕ=overall nanoparticle volume fractionT=fluid temperature in the boundary layerKTs=temperature on the surface of thin needleKT∞=ambient fluid temperatureKT0=reference temperatureKC=concentration in the boundary layerCs=concentration on the surface of thin needleC∞=ambient concentrationC0=reference concentrationαhnf=thermal diffusivity of hybrid nanofluid m2s−1F=cbK∗=inertia coefficient in the porous mediumcb=drag coefficientFr=xcbK∗=local inertia coefficientδE=relaxation time of heat flux sδC=relaxation time of mass flux sDB=Brownian diffusion coefficientDT=thermophoretic diffusion coefficientτ=heat capacity ratiokr2=chemical reaction rate constantEa=activation energy (J)kB=Boltzmann constant J/moleKm=a constanthT=heat transfer coefficienthC=mass transfer coefficientγ∗=Navier’s slip length (m)ξ∗=inverse of critical shear ratesΥ=spin gradient viscosityΓ=material parameterj=microrotation viscosityλ=mixed convection parameterSc=Schmidt numberFr=Forchheimer numberRe=Reynolds numberPr=Prandtl numberNr=radiation parameterB=micropolar parameterEc=Eckert numberΩ=porosity parameterNt=Thermophoresis parameterNb=Brownian motion parameterε=ratio parameterBr=Brinkman numberST=thermal stratified parameterSC=solutal stratified parameterβT=thermal Biot numberβC=solutal Biot numberδ=temperature difference parameterδ∗=concentration difference parameterωE=Deborah number for heat fluxωC=Deborah number for mass fluxΛ=chemical reaction rateE=activation energyΠ=velocity slip parameterξ=modified critical shear rateAcknowledgmentsThe authors extend their appreciation to the Department of Science and Technology (DST), Govt. of India for funding this work under grant number (MTR/2021/000631).Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationNotes on contributorsD. N. DashD.N. Dash is the research scholar in the department of Mechanical Engineering, ITER, Siksha ‘O’ Anusandhan (Deemed to be) University, Bhubaneswar-751030, Odisha, India.S. ShawDr. S.Shaw is currently working as Associate Professor, Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technlology, Palapye, Botswana.D. N. ThatoiProf. D.N. Thatoi received Bachelor degree in Mechanical Engineering from IGIT, Sarang, Odisha, India 1990. He received Master degree from BPUT,Rourkela in 2006 and Ph.D. degree from Siksha ‘O’ Anusandhan deemed to be university, INDIA in 2015. Currently he is working as professor in Mechanical Engineering, Faculty of Engineering, Siksha ‘O’ Anusandhan deemed to be university. He has authored and co-authored in 100 journals and international conferences.M. K. NayakDr. M.K. Nayak is currently working as Associate Professor in the Department of Mechanical Engineering, Siksha ‘O’ Anusandhan Deemed to be University, Odisha, India. His research area includes Fluid Dynamics, Heat Transfer, Energy and Environment. His name has been appeared in the list of World’s Top 2% of Scientists awarded by Stanford University, USA in the years 2020,2021,2022 and 2023. He has published 150 research articles to his credit. He has guided 5 Ph.D students and 10 M.Sc students in the areas of Fluid Dynamics, Heat Transfer and Energy.