Restricted accessResearch articleFirst published online 2025
Comprehensive study of Maxwell-Buongiorno models with suction-injection and cubic stratification: Unlocking complex heat and mass transfer mechanisms in nonlinear convection
Heat and mass transmissions are improved by cubic stratification in nonlinear mixed convection, which has important applications in the energy, electronics, and medical technology sectors. The advancement of cooling systems and environmental management depends on nanofluids, which are valued for their exceptional thermal qualities. Nanofluids are essential in modern thermal and engineering applications because of their exceptional heat transmission characteristics. To examine heat and mass transfer in a non-Newtonian Maxwell nanofluid across a vertically extended surface, this study uses the Buongiorno model, which incorporates Brownian diffusion and thermophoresis effects. Such configurations are major in polymer processing, thermal coating, and biomedical applications. Convective boundary conditions, cubic stratification, and the effects of suction and injection velocity are all considered in this inquiry. Through parametric analysis, the effects of heat source or sink are explored, offering insights to optimize thermal management systems in applications involving nanofluid-based porous media. The NDSolve (Built-in) numerical approach is utilized to resolve the nonlinear regulating formulas. A visual representation is provided of the influences of different factors on concentration, temperature outline, and fluid flow. The skin friction, local Nusselt, and Sherwood numbers have been computed and examined numerically. The important findings show that temperature profile and concentration profile are both noticeably lessened by raising the thermal and solutal stratification value. In contrast, increasing the mixed convection parameter raises the temperature and velocity profiles. Additionally, the transport dynamics of nanoparticles are influenced by the substantial temperature boost caused by thermophoresis and Brownian motion effects. The findings exhibit strong agreement with earlier studies when compared to those published in the recent literature.
HayatTAliNAsgharS.Hall effects on peristaltic flow of a Maxwell fluid in a porous medium. Phys Lett A2007; 363(5–6): 397–403.
2.
KhanNMChuYIjaz KhanM, et al. Modeling and dual solutions for magnetized mixed convective stagnation point flow of upper convected Maxwell fluid model with second-order velocity slip. Math Methods Appl Sci2020.
3.
KhanMNNadeemSAhmadS, et al. Mathematical analysis of heat and mass transfer in a Maxwell fluid. Proc IMechE, Part C: J Mechanical Engineering Science2021; 235(20): 4967–4976.
4.
MuhammadTAlsaediAShehzadSA, et al. A revised model for Darcy-Forchheimer flow of Maxwell nanofluid subject to convective boundary condition. Chin J Phys2017; 55(3): 963–976.
5.
KhanMMalikMYSalahuddinT, et al. Change in viscosity of Maxwell fluid flow due to thermal and solutal stratifications. J Mol Liq2019; 288: 110970.
6.
AhmadSKhanMNNadeemS.Mathematical analysis of heat and mass transfer in a Maxwell fluid with double stratification. Phys Scr2020; 96(2): 025202.
7.
DingXZhangFZhangG, et al. Modeling of hydraulic fracturing in viscoelastic formations with the fractional Maxwell model. Comput Geotech2020; 126: 103723.
8.
SubbaraoKElangovanKGangadharK.Entropy analysis in a second-grade nanoliquid influenced by an exponential space-dependent heat source and Arrhenius activation energy. Heat Transf2022; 51(6): 5679–5699.
9.
Hari BabuBSwarnalathammaBVVeera KrishnaM. Diffusion-thermo and thermo-diffusion impacts on MHD natural convection flow of Maxwell nanofluids over a stretching sheet. Case Stud Therm Eng2024; 61: 105016.
10.
GangadharKKumariMAWajdiK, et al. Heat transport magnetization for burgers fluid in a porous medium with convective heating and heterogeneous-homogeneous response. Case Stud Therm Eng2023; 48: 103087.
11.
SekineMTsukamotoNMasuharaY, et al. Experimental study on thermal stratification in water pool with vertical heat source. Ann Nucl Energy2024; 207: 110681.
12.
MuzammalMFarooqMAlotaibiH.Transportation of melting heat in stratified Jeffrey fluid flow with heat generation and magnetic field. Case Stud Therm Eng2024; 58: 104465.
13.
AhmadSHafeezMFarooqM.Investigation of variable thermal relaxation time in non-Fourier heat transfer flow with nonlinear thermal stratification. Proc IMechE, Part E: J Process Mechanical Engineering2024; 238(2): 810–818.
14.
ShiQ-HKhanMNAbbasN, et al. Heat and mass transfer analysis in the MHD flow of radiative Maxwell nanofluid with non-uniform heat source/sink. Waves Random Complex Media2024; 34(4): 3450–3473.
15.
JabeenIFarooqMRizwanM, et al. Analysis of nonlinear stratified convective flow of Powell-Eyring fluid: Application of modern diffusion. Adv Mech Eng2020; 12(10): 1687814020959568.
16.
MalikHTFarooqMAhmadS.Significance of nonlinear stratification in convective Falkner-Skan flow of Jeffrey fluid near the stagnation point. Int Commun Heat Mass Transf2021; 120: 105032.
17.
KhanQFarooqMAhmadS.Convective features of squeezing flow in nonlinear stratified fluid with inclined rheology. Int Commun Heat Mass Transf2021; 120: 104958.
18.
ShafiqAÇolakABSindhuTN, et al. Optimization of Darcy-Forchheimer squeezing flow in nonlinear stratified fluid under convective conditions with artificial neural network. Heat Transf Res2022; 53: 67–89.
19.
KhanMImranM.Ann-driven insights into heat and mass transfer dynamics in chemical reactive fluids across variable-thickness surfaces. Heat Transf2024; 53(8): 4551–4571.
20.
RehmanKUShatanawiW.Thermal analysis on mutual interaction of temperature stratification and solutal stratification in the presence of non-linear thermal radiations. Case Stud Therm Eng2022; 35: 102080.
21.
SreedeviPReddyPS.Unsteady boundary layer heat and mass transfer flow of nanofluid over porous stretching sheet with non-uniform heat generation/absorption and double stratification. J Nanofluids2023; 12(8): 2067–2077.
22.
SanthiMRaoKVSReddyPS, et al. Heat and mass transfer analysis of steady and unsteady nanofluid flow over a stretching sheet with double stratification. Adv Nanosci Technol Int J2019; 10: 247–277.
23.
UddinIUllahIAliR, et al. Numerical analysis of nonlinear mixed convective MHD chemically reacting flow of Prandtl–Eyring nanofluids in the presence of activation energy and Joule heating. J Therm Anal Calorim2021; 145: 495–505.
24.
BalamuruganRVanav KumarA.Mixed convection of transient MHD stagnation point flow over a stretching sheet with quadratic convection and thermal radiation. Heat Transf2024; 53(2): 584–609.
25.
KhanMZhangZLuD.Numerical simulations and modeling of MHD boundary layer flow and heat transfer dynamics in Darcy-Forchheimer media with distributed fractional-order derivatives. Case Stud Therm Eng2023; 49: 103234.
26.
KhanMRasheedAAnwarMS, et al. Application of fractional derivatives in a Darcy medium natural convection flow of MHD nanofluid. Ain Shams Eng J2023; 14(9): 102093.
27.
KhanMLoneSARasheedA, et al. Computational simulation of Scott-Blair model to fractional hybrid nanofluid with Darcy medium. Int Commun Heat Mass Transf2022; 130: 105784.
28.
PatilPMShankarHFSheremetMA.Quadratic mixed convective nanofluid flow past a moving yawed cylinder in the presence of thermal radiation and diffusive liquids. Heat Transf2022; 51(5): 4306–4330.
29.
PatilPMGoudarB.Quadratic combined convective flow about yawed cylinder in presence of time variations and magnetic effects: entropy analysis. Int J Ambient Energy2023; 44(1): 1047–1057.
30.
PatilPMGoudarB.Entropy generation analysis from the time-dependent quadratic combined convective flow with multiple diffusions and nonlinear thermal radiation. Chin J Chem Eng2023; 53: 46–55.
31.
SalahuddinTKhanMMahmoodZ, et al. Effect of varying the temperature dependent viscosity of Maxwell nanofluid flow near a sensor surface with activation enthalpy. Chaos Solitons Fractals2025; 194: 116247.
32.
JeelaniMBAbbasA.Thermal transport in MHD Maxwell hybrid nanofluid flow over inclined stretching porous sheet with effects of chemical reaction, solar radiation and porous medium. Case Stud Therm Eng2025; 68: 105915.
33.
KhanKAVivas-CortezMIshfaqK, et al. Exploring the numerical simulation of Maxwell nanofluid flow over a stretching sheet with the influence of chemical reactions and thermal radiation. Results Phys2024; 60: 107635.
34.
IslamSAliMYReza-E-RabbiS.Comparative simulation of nonlinear radiative nano Casson and maxwell fluids with periodic magnetic force and sensitivity analysis. Heliyon2024; 10(7): e29306.
35.
RamarAArulmozhiABalamuralitharanS, et al. Melting heat effect in MHD flow of maxwell fluid with zero mass flux. Case Stud Therm Eng2024; 53: 103910.
36.
JamshedWShahzadFSafdarR, et al. Implementing renewable solar energy in presence of Maxwell nanofluid in parabolic trough solar collector: a computational study. Waves Random Complex Media2024; 34(5): 4320–4351.
37.
JawadMAlamMHameedMK, et al. Numerical simulation of Buongiorno’s model on Maxwell nanofluid with heat and mass transfer using Arrhenius energy: a thermal engineering implementation. J Therm Anal Calorim2024; 149(11): 5809–5822.
38.
SreedeviPReddyPS.Thermally radiative nanofluid heat transfer analysis inside a closed chamber with gyrotactic microorganisms. Int J Numer Methods Heat Fluid Flow2024; 34(12): 4206–4232.
39.
BhartyMSrivastavaAKMahatoH, et al. Maxwell–Cattaneo double-diffusive convection of Kuvshiniski viscoelastic nanofluid in a Brinkman–Darcy porous medium. Z. Für Naturforschung A2024; 79: 1093–1116.
40.
KhanMZhangZLuD, et al. Efficient numerical scheme for studying dual-phase chemical reactions in unsteady Sisko fluid flow with relaxation times. Ain Shams Eng J2024; 15(4): 102588.
41.
KhanMLuDRasoolG, et al. Fractional numerical analysis of γ-Al2O3 nanofluid flows with effective Prandtl number for enhanced heat transfer. J Comput Des Eng2024; 11(4): 319–331.
42.
BasitMAImranMTahirM, et al. Numerical analysis of mathematical model for heat and mass transfer through bioconvective Maxwell nanofluid flow subject to Darcy-Forcheimer and Lorentz forces. Int J Heat Fluid Flow2024; 106: 109322.
43.
NaziaSSeshaiahBSudarsana ReddyP, et al. Silver–ethylene glycol and copper–ethylene glycol based thermally radiative nanofluid characteristics between two rotating stretchable disks with modified Fourier heat flux. Heat Transf2023; 52(1): 289–316.
44.
SreedeviPSudarsana ReddyP.Comparative study of convective Oldroyd-B nanofluid and hybrid nanofluid flow, heat and mass transfer analysis over stretching sheet with Cattaneo-Christov heat flux model. J Nanofluids2024; 13(3): 839–850.
45.
KhanMImranMKhanW.A neural network approach to modeling magnetohydrodynamic stagnation point Ree-Eyring flow over a convectively heated stretched surface. Int J Model Simul2024; 1–14.
46.
AlgehyneEAAlamraniFMHaqI, et al. A numerical analysis of three-dimensional MHD convective flow of Maxwell nanofluids over an extending surface with Cattaneo–Christov heat and mass flux. Multiscale Multidiscip. Model. Exp. Des2025; 8(3): 193.
47.
SyamMMMorsiFEidaAA, et al. Investigating convective Darcy–Forchheimer flow in Maxwell nanofluids through a computational study. Partial Differ Equ Appl Math2024; 11: 100863.
48.
SangeethaEDePDasR.Hall and ion effects on bioconvective Maxwell nanofluid in non-darcy porous medium. Spec Top Rev Porous Media Int J2023; 14: 1–30.
49.
MalikMFShahSAABilalM, et al. New insights into the dynamics of heat and mass transfer in a hybrid (Ag-TiO2) nanofluid using modified Buongiorno model: A case of a rotating disk. Results Phys2023; 53: 106906.
50.
KanwalSShahSAABariqA, et al. Insight into the dynamics of heat and mass transfer in nanofluid flow with linear/nonlinear mixed convection, thermal radiation, and activation energy effects over the rotating disk. Sci Rep2023; 13(1): 23031.
51.
ZureigatHTashtoushMAJassarAFA, et al. A solution of the complex fuzzy heat equation in terms of complex Dirichlet conditions using a modified Crank–Nicolson method. Adv Math Phys2023; 2023(1): 1–8.
52.
HaiderJAAhmadSGhazwaniHA, et al. Results validation by using finite volume method for the blood flow with magnetohydrodynamics and hybrid nanofluids. Mod Phys Lett B2024; 38(24): 2450208.
53.
Ali KhanSYasminSWaqasH, et al. Entropy optimized Ferro-copper/blood based nanofluid flow between double stretchable disks: application to brain dynamic. Alex Eng J2023; 79: 296–307.
