This research is conducted by considering the Darcy–Forchheimer viscoelastic non-Newtonian fluids (NNF) generated by the movement of surface. Two types NNF namely Walter’s liquid B (WLB) and second grade (SG) fluids are chosen as the working fluids. Cattaneo–Christov energy diffusion model is carried out for the energy transmission analysis. Newtonian heating (NH) and Newtonian concentration (NC) conditions are imposed for the solutal and thermal analysis. The model is formulated by the application of boundary layer technique. These equations are converted into non dimensional model by the implication of similarity variables. The numeric solutions are executed by the utilization of Runge–Kutta–Fehlberg-45 order scheme. The results are presented by numeric benchmarks and graphical illustrations. A comparative discussion of WLB and SG fluids is reported. A comparative visualization shows that the higher velocity profile is achieved for SG fluid case while temperature and concentration profiles are larger in the case of SG fluid. The Brownian movement and thermophoretic constraints have similar influences on temperature. The Brownian movement constraint has reverse trends on concentration and temperature.
DarcyH. Les Fontaines Publiques De La Ville De Dijon. Paris: Victor Dalmont, 1856.
2.
ForchheimerP. Wasserbewegung durch boden. Zeitschrift Ver Deutsch Ing1901; 45: 1782–1788.
3.
MuskatM. The flow of homogeneous fluids through porous media. MI Edwards1946.
4.
GireeshaBJMahantheshBManjunathaPT, et al. Numerical solution for hydromagnetic boundary layer flow and heat transfer past a stretching surface embedded in nonDarcy porous medium with fluid-particle suspension. J Niger Math Soc2015; 34: 267–285.
5.
HayatTMuhammadTAl-MezalS, et al. Darcy–Forchheimer flow with variable thermal conductivity and Cattaneo–Christov heat flux. Int J Numer Methods Heat Fluid Flow2016; 26: 2355–2369.
6.
ShehzadSAAbbasiFMHayatT, et al. Cattaneo–Christov heat flux model for Darcy–Forchheimer flow of an Oldroyd-B fluid with variable conductivity and non-linear convection. J Mol Liq2016; 224: 274–278.
7.
AlzahraniAK. Importance of Darcy–Forchheimer porous medium in 3D convective flow of carbon nanotubes. Phys Lett A2018; 382: 2938–2943.
8.
KumarKGKhanMNOsmanM, et al. Slip flow over a non-Newtonian fluid through a Darcy–Forchheimer medium: numerical approach. Mod Phys Let B2019; 33(35): 1950448.
9.
RasoolGChamkhaAJMuhammadT, et al. Darcy–Forchheimer relation in Casson type MHD nanofluid flow over non-linear stretching surface. Propul Power Res2020; 9: 159–168.
10.
ReddyMGSudharaniMVVNLKumarKG, et al. Physical aspects of Darcy–Forchheimer flow and dissipative heat transfer of Reiner–Philippoff fluid. J Therm Anal Calorim2020; 141: 829–838.
11.
KumarKGReddyMGKhanMI, et al. Heat transfer and melting flow of a Reiner–Philippoff fluid over a surface with Darcy–Forchheimer medium. Case Stud Therm Eng2021; 28: 101649.
12.
ReddyMGPraveenaMMRudraswamyNG, et al. Impact of Cattaneo–Christov heat flux on hydromagnetic flow of non-Newtonian fluids filled with Darcy–Forchheimer porous medium. Wav Rand Comp Med2021.
13.
HussainMSheremetMA. Convective-radiative magnetized dissipative nanofluid (CNTswater) transport in porous media, using Darcy–Brinkman–Forchheimer model. Int Commun Heat Mass Transf2022; 139: 106–420.
14.
SharmaBKGandhiR. Combined effects of Joule heating and non-uniform heat source/sink on unsteady MHD mixed convective flow over a vertical stretching surface embedded in a Darcy–Forchheimer porous medium. Propul Power Res2022; 11: 276–292.
15.
JoshiNUpretiHPandeyAK. MHD Darcy–Forchheimer Cu-Ag/H2O-C2H6O2 hybrid nanofluid flow via a porous stretching sheet with suction/blowing and viscous dissipation. Int J Comput Methods Eng Sci Mech2022; 23: 527–535.
16.
UpretiHBartwalPPandeyAK, et al. Heat transfer assessment for Au-blood nanofluid flow in Darcy–Forchheimer porous medium using induced magnetic field and Cattaneo–Christov model. Numer Heat Transf Part B: Fund2023; 84: 415–431.
17.
UpretiHPandeyAKKumarM, et al. Darcy–Forchheimer flow of CNTs-H2O nanofluid over a porous stretchable surface with Xue model. Int J Mod Phys B2023; 37(2): 2350018.
18.
ChoiSUSEastmanJA. Enhancing thermal conductivity of fluids with nanoparticles. In: Conference: international mechanical engineering congress and exhibition, November 12–17, San Francisco, CA, 1995.
19.
BuongiornoJ. Convective transport in nanofluids. J Heat Transf2006; 128: 240–250.
20.
NayakMKMehmoodRMakindeOD, et al. Magnetohydrodynamic flow and heat transfer impact on ZnO-SAE50 nanolubricant flow over an inclined rotating disk. J Cent South Univ2019; 26: 1146–1160.
21.
KumarKGRahimi-GorjiMReddyMG, et al. Enhancement of heat transfer in a convergent/divergent channel by using carbon nanotubes in the presence of a Darcy–Forchheimer medium. Microsyst Technol2020; 26: 323–332.
22.
RanaSMehmoodRBhattiMM, et al. Swimming of motile gyrotactic microorganisms and suspension of nanoparticles in a rheological Jeffery fluid with Newtonian heating along elastic surface. J Cent South Univ2021; 28: 3279–3296.
23.
ReddyMGVijayakumariPKumarKG, et al. Zero-mass flux and Cattaneo–Christov heat flux through a Prandtl non-Newtonian nanofluid in Darcy–Forchheimer porous space. Heat Transf2021; 50: 220–233.
24.
PandeyAKUpretiHJoshiN, et al. Effect of natural convection on 3D MHD flow of MoS2-GO/H2O via porous surface due to multiple slip mechanisms. J Taibah Uni Sci2022; 16: 749–762.
25.
MahmudKRanaAAl-ZubaidiA, et al. Interaction of Lorentz force with cross swimming microbes in couple stress nano fluid past a porous Riga plate. Int Commun Heat Mass Transf2022; 138: 106347.
26.
MahmudKMehmoodRRanaS, et al. Flow of magnetic shear thinning nano fluid under zero mass flux and hall current. J Mol Liq2022; 352: 118732.
27.
PandeyAKUpretiHUddinZ. Magnetic SWCNT-Ag/H2O nanofluid flow over cone with volumetric heat generation. Int J Mod Phys B2023; 37(29): 2350253.
28.
MehmoodRAliIIjazS, et al. Radiative slip transport of magnetized gyrotactic micro-organisms submerged with nano fluid along a vertical stretching surface with suction/injection effects. Proc IMechE, Part N: J Nanomaterials, Nanoengineering and Nanosystems. Epub ahead of print 30May2023. DOI: 10.1177/239779142311768.
29.
UpretiHMishraSRPandeyAK, et al. Diversified role of fuzzified particle concentration on Casson gold-blood nanofluid flow through an elongating sheet for different shape nanoparticles. J Taibah Uni Sci2023; 17(1): 2254465.
30.
RanaSAlharbiKAMFatimaN, et al. Interaction of nanoparticles with micro organisms under Lorentz force in a polymer liquid with zero mass flux. J Taiwan Inst Chem Eng2023; 143: 104683.
31.
UpretiHPandeyAKJoshiN, et al. Thermodynamics and heat transfer analysis of magnetized Casson hybrid nanofluid flow via a Riga plate with thermal radiation. J Comput Biophys Chem2023; 22(3): 321–334.
32.
GuptaTPandeyAKKumarM. Effect of Thompson and Troian slip on CNT-Fe3O4/kerosene oil hybrid nanofluid flow over an exponential stretching sheet with Reynolds viscosity model. Mod Phys Lett B2024; 38(2): 2350209.
33.
BenharbitAMSiddiquiAM. Certain solutions of the equations of the planar motion of a second grade fluid for steady and unsteady cases. Acta Mech1992; 94: 85–96.
34.
ShenFTanWZhaoY, et al. The Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative model. Nonlinear Anal Real World Appl2006; 7: 1072–1080.
35.
FetecauCZafarAAVieruD, et al. Hydromagnetic flow over a moving plate of second grade fluids with time fractional derivatives having non-singular kernel. Chaos Solit Frac2020; 130: 109454.
36.
HaqSUShahSIAJanSA, et al. MHD flow of generalized second grade fluid with modified Darcy’s law and exponential heating using fractional Caputo–Fabrizio derivatives. Alex Eng J2021; 60: 3845–3854.
37.
JosephSP. Different families of new exact solutions for planar and nonplanar second grade fluid flows. Chin J Phys2022; 77: 1225–1235.
38.
KumarP. Stability of two superposed viscoelastic (Walters B’) fluid-particle mixtures in porous medium. Z Naturforsch1998; 54: 343–347.
39.
SharmaVRanaGC. Thermosolutal instability of Walters (Walters B’) visco-elastic rotating fluid permeated with suspended particles and variable gravity field in porous medium. Ind J Pure Appl Math2002; 6: 843–860.
40.
DharamendraAwasthiMK. Temporal instability of Walter’s B viscoelastic fluid film. J Phys Conf Ser2021; 1849: 012012.
41.
AwasthiMKDharamendraYadavD. Stability characteristics of Walter’s B viscoelastic fluid in a cylindrical configuration with heat transfer. Proc IMechE, Part C: J Mechanical Engineering Science2022; 236: 10370–10377.
42.
UllahIShafieSKhanI. Effects of slip condition and Newtonian heating on MHD flow of Casson fluid over a nonlinearly stretching sheet saturated in a porous medium. J King Saud Uni Sci2017; 29: 250–259.
43.
MuhammadKHayatTAlsaediA. Numerical study of Newtonian heating in flow of hybrid nanofluid (SWCNTs + CuO + Ethylene glycol) past a curved surface with viscous dissipation. J Therm Anal Calorim2021; 143: 1291–1302.
44.
KumarD. Radiation effect on magnetohydrodynamic flow with induced magnetic field and Newtonian heating/cooling: an analytic approach. Propul Power Res2021; 10: 303–313.
45.
AkinboBJOlajuwonBI. Impact of radiation and chemical reaction on stagnation-point flow of hydromagnetic Walters’ B fluid with Newtonian heating. Int Commun Heat Mass Transf2021; 121: 105–115.
46.
ZhangXShahRSaleemS, et al. Natural convection flow Maxwell fluids with generalized thermal transport and Newtonian heating. Case Stud Therm Eng2021; 27: 101–226.
47.
AbbasiFMHayatTShehzadSA, et al. Impact of Cattaneo–Christov heat flux on flow of two-types viscoelastic fluid in Darcy–Forchheimer porous medium. Int J Numer Methods Heat Fluid Flow2017; 27: 1955–1966.
48.
HayatTMuhammadTAlsaediA, et al. A comparative study for flow of viscoelastic fluids with Cattaneo–Christov heat flux. PLoS ONE2016; 11(5): 155185.
