Entropy optimization in CNTs based nanomaterial flow induced by rotating disks: A study on the accuracy of statistical declaration and probable error

BACKGROUND CNTs (Carbon nanotubes) being allotropes of carbon, made of graphene and diameters of single and multi-walls carbon nanotubes are typically 0.8 to 2 nm and 5 to 20 mn, although diameter of MWCNTs can exceed 100 nm. Carbon nanotubes lengths range from less than 100 nm to 0.5 m. Their impressive structural, electronic and mechanical attributes subject to their small size and mass, their high electrical and thermal conductivities, and their strong mechanical potency. CNTs based materials are successfully applied in medicine and pharmacy subject to their huge surface area that is proficient of conjugating or adsorbing with a wide variety of genes, drugs, antibodies, vaccines and biosensors etc. Therefore, we have presented a theoretical study about mathematical modeling of CNTs based viscous material flow between two rotating disks. Both types of nanotubes i.e., SWCNTs and MWCNTs are considered. Xue model is used for the mathematical modeling. Fluid flow is due to rotating disks. Main focus here is given to probable error and statistical declaration. Entropy is calculated for both single and multi-walls nanotubes. METHOD Nonlinear PDEs are first converted into ODEs and then computed for homotopy convergent solutions. RESULTS AND CONCLUSION Statistical declaration and probable error for skin friction and Nusselt number are numerically computed and discussed through Tables. From obtained outcomes it is concluded that magnitude of skin friction increases at both disks surface for higher values of Reynolds number, lower stretching parameter and porosity parameter while it decays for both of disks versus larger rotation parameter. Nusselt number or heat transfer rate also enhances at both disks in the presence of radiation and Reynolds number while it decays against Eckert number.

[1]  Ahmed Alsaedi,et al.  Modern developments about statistical declaration and probable error for skin friction and Nusselt number with copper and silver nanoparticles , 2017 .

[2]  S Nadeem,et al.  Analytical study of third grade fluid over a rotating vertical cone in the presence of nanoparticles , 2015 .

[3]  L. Bian,et al.  Thermal environment and strain energy related micro-model for properties of carbon nanotubes , 2019, Materials Science and Engineering: B.

[4]  T Hayat,et al.  Nanomaterial based flow of Prandtl-Eyring (non-Newtonian) fluid using Brownian and thermophoretic diffusion with entropy generation , 2019, Comput. Methods Programs Biomed..

[5]  Lioua Kolsi,et al.  Experimental and numerical study on heat transfer performance of three-dimensional natural convection in an enclosure filled with DWCNTs-water nanofluid , 2017 .

[6]  Ahmed Alsaedi,et al.  A comparative study of Casson fluid with homogeneous-heterogeneous reactions. , 2017, Journal of colloid and interface science.

[7]  Mustafa Turkyilmazoglu,et al.  Three dimensional MHD stagnation flow due to a stretchable rotating disk , 2012 .

[8]  Lioua Kolsi,et al.  Free convection heat transfer and entropy generation analysis of MWCNT-MgO (15% − 85%)/Water nanofluid using Lattice Boltzmann method in cavity with refrigerant solid body-Experimental thermo-physical properties , 2017 .

[9]  Ahmed Alsaedi,et al.  Joule heating and viscous dissipation in flow of nanomaterial by a rotating disk , 2017 .

[10]  B. J. Gireesha,et al.  Marangoni convective MHD flow of SWCNT and MWCNT nanoliquids due to a disk with solar radiation and irregular heat source , 2017 .

[11]  Ahmed Alsaedi,et al.  Current progresses about probable error and statistical declaration for radiative two phase flow using Ag H 2 O and Cu H 2 O nanomaterials , 2017 .

[12]  Ahmed Alsaedi,et al.  Modeling and analyzing flow of third grade nanofluid due to rotating stretchable disk with chemical reaction and heat source , 2018 .

[13]  Tufail A. Khan,et al.  Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection , 2018, Physics Letters A.

[14]  Tasawar Hayat,et al.  Entropy generation minimization (EGM) in nonlinear mixed convective flow of nanomaterial with Joule heating and slip condition , 2018 .

[15]  Shijun Liao,et al.  Homotopy Analysis Method in Nonlinear Differential Equations , 2012 .

[16]  G. C. Shit,et al.  Entropy generation on MHD flow and convective heat transfer in a porous medium of exponentially stretching surface saturated by nanofluids , 2017 .

[17]  Tasawar Hayat,et al.  MHD peristaltic motion of Johnson-Segalman fluid in an inclined channel subject to radiative flux and convective boundary conditions , 2019, Comput. Methods Programs Biomed..

[18]  A. Bejan,et al.  Entropy Generation Through Heat and Fluid Flow , 1983 .

[19]  Tasawar Hayat,et al.  Optimization of entropy generation and dissipative nonlinear radiative Von Karman's swirling flow with Soret and Dufour effects , 2018 .

[20]  A. Rashad,et al.  Transpiration and Thermophoresis Effects on Non-Darcy Convective Flow Past a Rotating Cone with Thermal Radiation , 2016 .

[21]  A. Alsaedi,et al.  Entropy generation in dissipative flow of Williamson fluid between two rotating disks , 2018, International Journal of Heat and Mass Transfer.

[22]  Tasawar Hayat,et al.  Entropy generation in Darcy-Forchheimer bidirectional flow of water-based carbon nanotubes with convective boundary conditions , 2018, Journal of Molecular Liquids.

[23]  A. Bejan.  Second law analysis in heat transfer , 1980 .

[24]  Tasawar Hayat,et al.  Impact of Cattaneo–Christov heat flux model in flow of variable thermal conductivity fluid over a variable thicked surface , 2016 .

[25]  Precious Sibanda,et al.  Entropy generation in a second grade magnetohydrodynamic nanofluid flow over a convectively heated stretching sheet with nonlinear thermal radiation and viscous dissipation , 2018, Results in Physics.

[26]  Ahmed Alsaedi,et al.  Non-Darcy flow of water-based single (SWCNTs) and multiple (MWCNTs) walls carbon nanotubes with multiple slip conditions due to rotating disk , 2018, Results in Physics.

[27]  M Ijaz Khan,et al.  Theoretical and mathematical analysis of entropy generation in fluid flow subject to aluminum and ethylene glycol nanoparticles , 2019, Comput. Methods Programs Biomed..

[28]  M Ijaz Khan,et al.  Investigation of physical aspects of cubic autocatalytic chemically reactive flow of second grade nanomaterial with entropy optimization , 2020, Comput. Methods Programs Biomed..

[29]  Ahmed Alsaedi,et al.  Entropy generation minimization (EGM) for convection nanomaterial flow with nonlinear radiative heat flux , 2018, Journal of Molecular Liquids.

[30]  R. Meland,et al.  Flow of a power-law fluid over a rotating disk revisited , 2001 .

[31]  T. Hayat,et al.  Melting Heat in Radiative Flow of Carbon Nanotubes with Homogeneous-Heterogeneous Reactions , 2018 .

[32]  M. Waqas,et al.  Simulation of revised nanofluid model in the stagnation region of cross fluid by expanding-contracting cylinder , 2019, International Journal of Numerical Methods for Heat & Fluid Flow.

[33]  M. Saidi,et al.  Heat transfer and pressure drop characteristics of nanofluid in unsteady squeezing flow between rotating porous disks considering the effects of thermophoresis and Brownian motion , 2016 .

[34]  B. J. Gireesha,et al.  Brinkman-Forchheimer slip flow subject to exponential space and thermal-dependent heat source in a microchannel utilizing SWCNT and MWCNT nanoliquids , 2019, Heat Transfer-Asian Research.

[35]  Taseer Muhammad,et al.  MHD flow of SWCNT and MWCNT nanoliquids past a rotating stretchable disk with thermal and exponential space dependent heat source , 2019, Physica Scripta.

[36]  Ahmed Alsaedi,et al.  Flow between two stretchable rotating disks with Cattaneo-Christov heat flux model , 2017 .

[37]  Ahmed Alsaedi,et al.  Nanofluid flow due to rotating disk with variable thickness and homogeneous-heterogeneous reactions , 2017 .

[38]  Mustafa Turkyilmazoglu,et al.  Flow and heat simultaneously induced by two stretchable rotating disks , 2016 .

[39]  Tasawar Hayat,et al.  Entropy generation for flow of Sisko fluid due to rotating disk , 2018, Journal of Molecular Liquids.

[40]  Ahmed Alsaedi,et al.  Entropy generation in radiative flow of Ree-Eyring fluid due to due rotating disks , 2019, International Journal of Numerical Methods for Heat & Fluid Flow.

[41]  M Ijaz Khan,et al.  Heat transport and entropy optimization in flow of magneto-Williamson nanomaterial with Arrhenius activation energy , 2020, Comput. Methods Programs Biomed..

[42]  M. Waqas,et al.  A mathematical and computational framework for heat transfer analysis of ferromagnetic non-Newtonian liquid subjected to heterogeneous and homogeneous reactions , 2020 .

[43]  A. Bejan.  Entropy Generation Minimization , 2016 .

[44]  Liancun Zheng,et al.  Flow and heat transfer of nanofluids over a rotating disk with uniform stretching rate in the radial direction , 2017 .

[45]  Mohammad Mehdi Rashidi,et al.  Entropy generation as a practical tool of optimisation for non-Newtonian nanofluid flow through a permeable stretching surface using SLM , 2017, J. Comput. Des. Eng..

[46]  M. Turkyilmazoglu.  Exact solutions for the incompressible viscous fluid of a porous rotating disk flow , 2009 .

[47]  T. Hayat,et al.  Non-Darcy flow of water-based carbon nanotubes with nonlinear radiation and heat generation/absorption , 2018 .

[48]  SamehE. Ahmed,et al.  Entropy generation due to double diffusive convective flow of Casson fluids over nonlinearity stretching sheets with slip conditions , 2017 .