An investigation on the convective heat transportation features of a magnetised Williamson nanofluid over a radiative permeable sheet is presented in this article. The interaction of an irregular heat source/sink along with thermal radiation brings a novel approach to the flow phenomena. The nanofluid, comprising of two-phase model based upon the impact of Brownian and thermophoresis boosts up the thermal combined with solutal profile significantly under the influence of an applied magnetised field. The standard modelled partial differential equations are renovated into a couple of nonlinear ordinary differential equations by implementing suitable similarity transformations. Further, a numerical solution employing the Runge-Kutta fourth-order with an integrating shooting technique is adopted to resolve the resulting system of equations. The influence of pertinent parameters, including the magnetic field strength, thermal radiation parameter, and irregular heat source/sink parameters, is systematically analysed. The enhancement of heat transfer in nanofluid-based systems, influenced by magnetic fields and non-uniform heat sources or sinks, plays a critical role in various industrial and biological applications. This is particularly significant in designing and optimising of heat exchangers, electronic cooling systems, and energy-efficient processes, as well as in drug delivery systems. In an outstanding outcome it is revealed that, the dominance of elastic forces over the viscous forces for the increasing Williamson parameter significantly retards the velocity as well as temperature distribution.
SalahuddinTIqbalMABanoA, et al. Cattaneo-Christov heat and mass transmission of dissipated Williamson fluid with double stratification. Alex Eng J2023; 80: 553–558. https://doi.org/10.1016/j.aej.2023.09.012
2.
MaaitahHOlimatANQuranO, et al. Viscous dissipation analysis of Williamson fluid over a horizontal saturated porous plate at constant wall temperature. Int J Thermofluids2023; 19: 100361. https://doi.org/10.1016/j.ijft.2023.100361
3.
TajMSalahuddinT. A three-dimensional frictional flow study of Williamson fluid with chemical reaction. Mater Sci Eng B2023; 291: 116305. https://doi.org/10.1016/j.mseb.2023.116305
4.
MishraPKumarDReddyYD, et al. MHD Williamson micropolar fluid flow pasting a non-linearly stretching sheet under the presence of non-linear heat generation/ absorption. J Indian Chem Soc2023; 100: 100845. https://doi.org/10.1016/j.jics.2022.100845
5.
ShaheenSArainMBNisarKS, et al. A case study of heat transmission in a Williamson fluid flow through a ciliated porous channel: a semi-numerical approach. Case Stud Therm Eng2023; 41: 102523. https://doi.org/10.1016/j.csite.2022.102523
6.
AlmaneeaA. Numerical study on heat and mass transport enhancement in MHD Williamson fluid via hybrid nanoparticles. Alex Eng J2022; 61: 8343–8354. https://doi.org/10.1016/j.aej.2022.01.041
7.
ImranARajaMAZShoaibM, et al. Electro-osmotic transport of a Williamson fluid within a ciliated microchannel with heat transfer analysis. Case Stud Therm Eng2023; 45: 102904. https://doi.org/10.1016/j.csite.2023.102904
8.
MishraPKumarDKumarJ, et al. Analysis of MHD Williamson micropolar fluid flow in non-Darcian porous media with variable thermal conductivity. Case Stud Therm Eng2022; 36: 102195. https://doi.org/10.1016/j.csite.2022.102195
9.
KhanMIQayyumSHayatT, et al. Entropy optimization in flow of Williamson nanofluid in the presence of chemical reaction and Joule heating. Int J Heat Mass Transf2019; 133: 959–967. https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.168
10.
Prakash SharmaRMishraSRPattnaikPK, et al. Numerical study of slip flow of a micropolar fluid through a porous wedge surface with the impact of a chemical reaction and heat source/sink. Int J Mod Phys B 2024; 38(23): 2450314.
11.
NoranuarWNNMohamadAQShafieS, et al. Non-coaxial rotation flow of MHD Casson nanofluid carbon nanotubes past a moving disk with porosity effect. Ain Shams Eng J2021; 12: 4099–4110. https://doi.org/10.1016/j.asej.2021.03.011
12.
MaheshRMahabaleshwarUSKumarPNV, et al. Impact of radiation on the MHD couple stress hybrid nanofluid flow over a porous sheet with viscous dissipation. Results Eng2023; 17: 100905. https://doi.org/10.1016/j.rineng.2023.100905
13.
SadighiSAfsharHJabbariM, et al. Heat and mass transfer for MHD nanofluid flow on a porous stretching sheet with prescribed boundary conditions. Case Stud Therm Eng2023; 49: 103345. https://doi.org/10.1016/j.csite.2023.103345
14.
PadmaGNuslin BibiSKLalithaS. Hall effects on steady rotating MHD flow of heat generating fluid through porous medium with variable pressure gradient. Mater Today Proc2023; 92: 1508–1513. https://doi.org/10.1016/j.matpr.2023.06.006
15.
GoudBSSrilathaPMahendarD, et al. Thermal radiation effect on thermostatically stratified MHD fluid flow through an accelerated vertical porous plate with viscous dissipation impact. Partial Differ Equations Appl Math2023; 7: 100488. https://doi.org/10.1016/j.padiff.2023.100488
16.
SowmiyaCRushi KumarB. MHD Maxwell nanofluid flow over a stretching cylinder in porous media with microorganisms and activation energy. J Magn Magn Mater2023; 582: 171032. https://doi.org/10.1016/j.jmmm.2023.171032
17.
MattaSSiddulu MalgaBRameshwar GoudG, et al. Effects of viscous dissipation on MHD free convection flow past a semi-infinite moving vertical porous plate with heat sink and chemical reaction. Mater Today Proc2023; 92: 1629–1636. https://doi.org/10.1016/j.matpr.2023.06.108
18.
KodiRReddy VaddemaniRIjaz KhanM, et al. Unsteady magneto-hydro-dynamics flow of Jeffrey fluid through porous media with thermal radiation, Hall current and Soret effects. J Magn Magn Mater2023; 582: 171033. https://doi.org/10.1016/j.jmmm.2023.171033
19.
SwainKIbrahimSMDharmaiahG, et al. Numerical study of nanoparticles aggregation on radiative 3D flow of maxwell fluid over a permeable stretching surface with thermal radiation and heat source/sink. Results Eng2023; 19: 101208. https://doi.org/10.1016/j.rineng.2023.101208
20.
LoneSAAnwarSRaizahZ, et al. Analysis of the time-dependent magnetohydrodynamic Newtonian fluid flow over a rotating sphere with thermal radiation and chemical reaction. Heliyon2023; 9: e17751. https://doi.org/10.1016/j.heliyon.2023.e17751
21.
SharmaTSharmaPKumarN. Chemical reactive magnetized fluid flow through a vertical channel due to heat source and thermal radiation effects. Mater Today Proc2023; 78: 481–492. https://doi.org/10.1016/j.matpr.2022.10.298
22.
ThummaTPandaSMishraSR, et al. Mathematical modelling of heat and solutal rate with cross-diffusion effect on the flow of nanofluid past a curved surface under the impact of thermal radiation and heat source: sensitivity analysis. ZAMM - J Appl Math Mech / Zeitschrift Für Angew Math Und Mech2023; 103: e202300077. https://doi.org/10.1002/zamm.202300077
23.
PattnaikPKMishraSRPandaS, et al. Hybrid methodology for the computational behaviour of thermal radiation and chemical reaction on viscoelastic nanofluid flow. Math Probl Eng2022; 2022: 1–11. https://doi.org/10.1155/2022/2227811
24.
MishraSRPandaSVigneshS, et al. Radiative heat transfer on the peristaltic flow of an electrically conducting nanofluid through wavy walls of a tapered channel. Results Phys2023; 52: 106898. https://doi.org/10.1016/j.rinp.2023.106898
25.
Kumar RawatSYaseenMKhanU, et al. Insight into the significance of nanoparticle aggregation and non-uniform heat source/sink on titania–ethylene glycol nanofluid flow over a wedge. Arab J Chem2023; 16: 104809. https://doi.org/10.1016/j.arabjc.2023.104809
26.
ChuYMAbbasiAAl-KhaledK, et al. Mathematical modeling and computational outcomes for the thermal oblique stagnation point investigation for non-uniform heat source and nonlinear chemical reactive flow of Maxwell nanofluid. Case Stud Therm Eng2023; 41: 102626. https://doi.org/10.1016/j.csite.2022.102626
27.
HussainZAzeem KhanWMuhammadT, et al. Dynamics of gyrotactic microorganisms for chemically reactive magnetized 3D Sutterby nanofluid flow comprising non-uniform heat sink-source aspects. J Magn Magn Mater2023; 578: 170798. https://doi.org/10.1016/j.jmmm.2023.170798
28.
YasirMKhanMAlqahtaniAS, et al. Numerical study of axisymmetric hybrid nanofluid MgO-Ag/H2O flow with non-uniform heat source/sink. Alex Eng J2023; 75: 439–446. https://doi.org/10.1016/j.aej.2023.05.062
29.
KrishnaMVSwarnalathammaBVChamkhaAJ. Investigations of Soret, Joule and Hall effects on MHD rotating mixed convective flow past an infinite vertical porous plate. J Ocean Eng Sci2019; 4(3): 263–275.
30.
ChamkhaAJ. Non-Darcy fully developed mixed convection in a porous medium channel with heat generation/absorption and hydromagnetic effects. Numer Heat Transf A Appl1997; 32(6): 653–675.
31.
ChamkhaAJ. Hydromagnetic three-dimensional free convection on a vertical stretching surface with heat generation or absorption. Int J Heat Fluid Flow1999; 20(1): 84–92.
32.
KrishnaMVJyothiKChamkhaAJ. Heat and mass transfer on MHD flow of second-grade fluid through porous medium over a semi-infinite vertical stretching sheet. J Porous Media2020; 23(8): 751–765.
33.
ManjunathaSPuneethVGireeshaBJ, et al. Theoretical study of convective heat transfer in ternary nanofluid flowing past a stretching sheet. J Appl Comput Mech2022; 8(4): 1279–1286.
34.
ReddyMVMeenakumariRSucharithaG, et al. Heat and mass transfer analysis of conducting non-Newtonian nanofluid flows over an elongating sheet with a non-uniform heat source. Mod Phys Lett B2024; 38: 2450349.
35.
ReddyMVAjithkumarMLoneSA, et al. Magneto-Williamson nanofluid flow past a wedge with activation energy: Buongiorno model. Adv Mech Eng2024; 16(1): 16878132231223027.
36.
Vinodkumar ReddyMLakshminarayanaPVajraveluK, et al. Activation of energy in MHD Casson nanofluid flow through a porous medium in the presence of convective boundary conditions and suction/injection. Numer Heat Transf A Appl2025; 86: 1069–1085.
37.
Vinodkumar ReddyMLakshminarayanaP. Higher order chemical reaction and radiation effects on magnetohydrodynamic flow of a Maxwell nanofluid with Cattaneo–Christov heat flux model over a stretching sheet in a porous medium. J Fluid Eng2022; 144: 041204.
38.
ReddyMVLakshminarayanaP. Cross-diffusion and heat source effects on a three-dimensional MHD flow of Maxwell nanofluid over a stretching surface with chemical reaction. Eur Phys J Spec Top2021; 230: 1371–1379.
