Chemical and food processes rely on thermocapillary-induced convection in the presence of catalytic and cross diffusion (Soret/Dufour effect). This study's goal was to investigate the effects of thermocapillary-induced convection of chemically reacting hybridized nanofluids over a surface in a non-Darcy porous domain with viscous dissipation, activation energy, and cross diffusion. The mathematical model for the Marangoni fluid flow, heat, and mass transport was derived based on the Navier–Stokes equation. The governing mathematical model, derived through a set of partial differential equations, was changed into a set of ordinary differential equations using suitable transformations. The bvp4c function (MATLAB software) was used to find the model's solutions. Skin friction, amount of mass, and heat transport were calculated. Entropy generation was also examined. The results for different combinations of relevant parameters are shown in graphical form. It was found that the Marangoni number enhances thermal transport and suppresses solutal mixing. It was observed that the velocity and temperature increase with increased Marangoni ratio parameter (r); the opposite occurs with concentration. Thermal and solute boundary layer thicknesses increase with increased values of Darcy number. Concentration also increases with increased Fr, with no considerable change in temperature. The outcomes of the thermocapillary convection effect can be applied in crystal growth in microgravity, materials processing, and microfluidic thermal management.
Citation: Turki J. Alqurashi. Thermocapillary convection of chemically reacting hybrid nanofluid with catalytic, cross diffusion, and activation energy in a porous medium application to crystal growth[J]. AIMS Mathematics, 2026, 11(9): 31896-31918. doi: 10.3934/math.20261255
Chemical and food processes rely on thermocapillary-induced convection in the presence of catalytic and cross diffusion (Soret/Dufour effect). This study's goal was to investigate the effects of thermocapillary-induced convection of chemically reacting hybridized nanofluids over a surface in a non-Darcy porous domain with viscous dissipation, activation energy, and cross diffusion. The mathematical model for the Marangoni fluid flow, heat, and mass transport was derived based on the Navier–Stokes equation. The governing mathematical model, derived through a set of partial differential equations, was changed into a set of ordinary differential equations using suitable transformations. The bvp4c function (MATLAB software) was used to find the model's solutions. Skin friction, amount of mass, and heat transport were calculated. Entropy generation was also examined. The results for different combinations of relevant parameters are shown in graphical form. It was found that the Marangoni number enhances thermal transport and suppresses solutal mixing. It was observed that the velocity and temperature increase with increased Marangoni ratio parameter (r); the opposite occurs with concentration. Thermal and solute boundary layer thicknesses increase with increased values of Darcy number. Concentration also increases with increased Fr, with no considerable change in temperature. The outcomes of the thermocapillary convection effect can be applied in crystal growth in microgravity, materials processing, and microfluidic thermal management.
| [1] |
M. S. Faltas, E. A. Ashmawy, M. G. Nashwan, B. A. Ahmed, M. El-Sayed, Coupled thermophoretic and thermocapillary effects on the motion of a particle near an immiscible fluid interface, Case Stud. Thermal Eng. , 80 (2026), 107852. https://doi.org/10.1016/j.csite.2026.107852 doi: 10.1016/j.csite.2026.107852
|
| [2] |
R. A. Alsulami, K. Wasuwatthanakul, K. Premnath, M. Aljaghtham, S. Adam, Thermocapillary convection in superimposed fluids confined within superhydrophobic surfaces of a microchannel, Case Stud. Thermal Eng. , 66 (2025), 105704. https://doi.org/10.1016/j.csite.2024.105704 doi: 10.1016/j.csite.2024.105704
|
| [3] |
A. Ahmad, K. Ali, M. Ramzan, I. L. Popa, A. A. Almehizia, Numerical investigation of entropy generation in trihybrid nanofluid flow over an exponentially curved surface using the quasi-linearization technique, Case Stud. Thermal Eng. , 81 (2026), 107961. https://doi.org/10.1016/j.csite.2026.107961 doi: 10.1016/j.csite.2026.107961
|
| [4] |
S. Sivanandam, T. J. Alqurashi, H. M. Alshehri, Impact of activation energy and cross-diffusion effects on 3D convective rotating nanoliquid flow in a non-Darcy porous medium, Int. J. Numer. Methods Heat Fluid Flow, 34 (2024), 3281–3303. https://doi.org/10.1108/HFF-01-2024-0008 doi: 10.1108/HFF-01-2024-0008
|
| [5] |
S. Sivanandam, C. Thangaraj, M. Bhuvaneswari, MHD double diffusive convective squeezing ternary nanofluid flow between parallel plates with activation energy and viscous dissipation, Int. J. Numer. Methods Heat Fluid Flow, 34 (2024), 4409–4431. https://doi.org/10.1108/HFF-05-2024-0365 doi: 10.1108/HFF-05-2024-0365
|
| [6] |
M. I. Joyce, J. Kandasamy, S. Sivanandam, Effects of Stefan blowing and double stratification on convective hybrid nanoliquid flow with convective boundary and entropy generation, Multidiscip. Model. Mater. Struct. , 21 (2025), 747–763. https://doi.org/10.1108/MMMS-09-2024-0266 doi: 10.1108/MMMS-09-2024-0266
|
| [7] |
S. Sivasankaran, C. J. Ho, Buoyancy- and thermocapillary-induced convection of cold water in an open enclosure with variable fluid properties, Numer. Heat Transfer Part A Appl. , 58 (2010), 457–474. https://doi.org/10.1080/10407782.2010.508433 doi: 10.1080/10407782.2010.508433
|
| [8] |
S. Sivasankaran, M. Bhuvaneswari, Y. J. Kim, C. J. Ho, K. L. Pan, Numerical study on magneto-convection of cold water in an open cavity with variable fluid properties, Int. J. Heat Fluid Flow, 32 (2011), 932–942. https://doi.org/10.1016/j.ijheatfluidflow.2011.07.004 doi: 10.1016/j.ijheatfluidflow.2011.07.004
|
| [9] |
J. Park, J. Ryu, H. J. Sung, H. Kim, Control of solutal Marangoni-driven vortical flows and enhancement of mixing efficiency, J. Colloid Interface Sci. , 561 (2020), 408–415. https://doi.org/10.1016/j.jcis.2019.11.006 doi: 10.1016/j.jcis.2019.11.006
|
| [10] |
P. Agrawal, P. K. Dadheech, R. N. Jat, K. S. Nisar, M. Bohra, S. D. Purohit, Magneto Marangoni flow of γ-Al2O3 nanofluids with thermal radiation and heat source/sink effects over a stretching surface embedded in porous medium, Case Stud. Thermal Eng. , 23 (2021), 100802. https://doi.org/10.1016/j.csite.2020.100802 doi: 10.1016/j.csite.2020.100802
|
| [11] |
N. V. Ganesha, A. J. Chamkha, Q. M. Al-Mdallal, P. K. Kameswaran, Magneto-Marangoni nano-boundary layer flow of water and ethylene glycol based γ Al2O3 nanofluids with non-linear thermal radiation effects, Case Stud. Thermal Eng. , 12 (2018), 340–348. https://doi.org/10.1016/j.csite.2018.04.019 doi: 10.1016/j.csite.2018.04.019
|
| [12] |
B. Mahanthesh, B. J. Gireesha, N. S. Shashikumar, T. Hayat, A. Alsaedi, Marangoni convection in Casson liquid flow due to an infinite disk with exponential space dependent heat source and cross-diffusion effects, Results Phys. , 9 (2018), 78–85. https://doi.org/10.1016/j.rinp.2018.02.020 doi: 10.1016/j.rinp.2018.02.020
|
| [13] | M. I. Khan, S. Qayyum, F. Shah, R. N. Kumar, R. J. P. Gowda, B. C. Prasannakumara, et al., Marangoni convective flow of hybrid nanofluid (MnZnFe2O4-NiZnFe2O4-H2O) with Darcy Forchheimer medium, Ain Shams Eng. J. , 12 (2021), 3931–3938. |
| [14] |
Q. M. Al-Mdallal, N. Indumathi, B. Ganga, A. K. A. Hakeem, Marangoni radiative effects of hybrid-nanofluids flow past a permeable surface with inclined magnetic field, Case Stud. Thermal Eng. , 17 (2020), 100571. https://doi.org/10.1016/j.csite.2019.100571 doi: 10.1016/j.csite.2019.100571
|
| [15] |
L. Stricker, Numerical simulation of artificial microswimmers driven by Marangoni flow, J. Comput. Phys. , 347 (2017), 467–489. https://doi.org/10.1016/j.jcp.2017.07.007 doi: 10.1016/j.jcp.2017.07.007
|
| [16] |
N. V. Burmasheva, E. Y. Prosviryakov, On Marangoni shear convective flows of inhomogeneous viscous incompressible fluids in view of the Soret effect, J. King Saud Univ. Sci. , 32 (2020), 3364–3371. https://doi.org/10.1016/j.jksus.2020.09.023 doi: 10.1016/j.jksus.2020.09.023
|
| [17] |
Y. Alhendala, A. Turan, W. I. A. Aly, VOF simulation of Marangoni flow of gas bubbles in 2D-axisymmetric column, Procedia Comput. Sci. , 1 (2010), 673–680. https://doi.org/10.1016/j.procs.2010.04.072 doi: 10.1016/j.procs.2010.04.072
|
| [18] |
C. Thangaraj, S. Sivanandam, B. Marimuthu, Dufour and Soret effects on MHD squeezed nanoliquid flow between parallel plates by differential transform method, World J. Eng. , 22 (2025), 1127–1137. https://doi.org/10.1108/WJE-12-2023-0531 doi: 10.1108/WJE-12-2023-0531
|
| [19] |
V. S. Reddy, J. Kandasamy, S. Sivanandam, Joule heating, Dufour and Soret effects on MHD hybrid nanoliquid flow over a moving thin needle in a porous medium with thermal radiation, World J. Eng. , 22 (2025), 866–875. https://doi.org/10.1108/WJE-01-2024-0040 doi: 10.1108/WJE-01-2024-0040
|
| [20] |
J. Kandasamy, S. Sivanandam, Non-linear thermal radiation effect on double diffusive mixed convective stagnation point flow of tangent hyperbolic nanofluid with suction/injection, Aircr. Eng. Aerosp. Technol. , 97 (2025), 514–521. https://doi.org/10.1108/AEAT-05-2024-0131 doi: 10.1108/AEAT-05-2024-0131
|
| [21] |
V. S. Reddy, J. Kandasamy, S. Sivanandam, Impacts of Casson model on hybrid nanofluid flow over a moving thin needle with Dufour and Soret and thermal radiation effects, Math. Comput. Appl. , 28 (2023), 2. https://doi.org/10.3390/mca28010002 doi: 10.3390/mca28010002
|
| [22] |
M. K. Narayanaswamy, J. Kandasamy, S. Sivanandam, Impacts of Stefan blowing on hybrid nanofluid flow over a stretching cylinder with thermal radiation and Dufour and Soret effect, Math. Comput. Appl. , 27 (2022), 91. https://doi.org/10.3390/mca27060091 doi: 10.3390/mca27060091
|
| [23] |
K. Jagan, S. Sivasankaran, Soret & Dufour and triple stratification effect on MHD flow with velocity slip towards a stretching cylinder, Math. Comput. Appl. , 27 (2022), 25. https://doi.org/10.3390/mca27020025 doi: 10.3390/mca27020025
|
| [24] |
M. Jawad, A. Saeed, P. Kumam, Z. Shah, A. Khan, Analysis of boundary layer MHD Darcy-Forchheimer radiative nanofluid flow with Soret and Dufour effects by means of Marangoni convection, Case Stud. Thermal Eng. , 23 (2021), 100792. https://doi.org/10.1016/j.csite.2020.100792 doi: 10.1016/j.csite.2020.100792
|
| [25] |
T. Hayat, S. Asghar, A. Tanveer, A. Alsaedi, Chemical reaction in peristaltic motion of MHD couple stress fluid in a channel with Soret and Dufour effects, Results Phys. , 10 (2018), 69–80. https://doi.org/10.1016/j.rinp.2018.04.040 doi: 10.1016/j.rinp.2018.04.040
|
| [26] |
J. T. Hu, S. J. Mei, Combined thermal and moisture convection and entropy generation in an inclined rectangular enclosure partially saturated with porous wall: Nonlinear effects with Soret and Dufour numbers, Int. J. Mech. Sci. , 199 (2021), 106412. https://doi.org/10.1016/j.ijmecsci.2021.106412 doi: 10.1016/j.ijmecsci.2021.106412
|
| [27] |
S. A. Shehzad, Z. Abbas, A. Rauf, Z. Abdelmalek, Dynamics of fluid flow through Soret-Dufour impacts subject to upward and downward motion of rotating disk, Int. Commun. Heat Mass Transfer, 120 (2021), 105025. https://doi.org/10.1016/j.icheatmasstransfer.2020.105025 doi: 10.1016/j.icheatmasstransfer.2020.105025
|
| [28] |
U. S. Mahabaleshwara, K. R. Nagaraju, P. N. V. Kumar, M. N. Nadagouda, R. Bennacer, M. A. Sheremet, Effects of Dufour and Soret mechanisms on MHD mixed convective-radiative non-Newtonian liquid flow and heat transfer over a porous sheet, Thermal Sci. Eng. Prog. , 16 (2020), 100459. https://doi.org/10.1016/j.tsep.2019.100459 doi: 10.1016/j.tsep.2019.100459
|
| [29] |
M. A. Kumar, Y. D. Reddy, B. S. Goud, V. S. Rao, Effects of Soret, Dufour, Hall current and rotation on MHD natural convective heat and mass transfer past an accelerated vertical plate through a porous medium, Int. J. Thermofluids, 9 (2021), 100061. https://doi.org/10.1016/j.ijft.2020.100061 doi: 10.1016/j.ijft.2020.100061
|
| [30] |
A. A. Yinusa, M. G. Sobamowo, M. A. Usman, E. H. Abubakar, Exploration of three dimensional squeezed flow and heat transfer through a rotating channel with coupled Dufour and Soret influences, Thermal Sci. Eng. Prog. , 21 (2021), 100788. https://doi.org/10.1016/j.tsep.2020.100788 doi: 10.1016/j.tsep.2020.100788
|
| [31] |
B. Ali, S. Hussain, Y. F. Nie, A. K. Hussein, D. Habib, Finite element investigation of Dufour and Soret impacts on MHD rotating flow of Oldroyd-B nanofluid over a stretching sheet with double diffusion Cattaneo Christov heat flux model, Powder Technol. , 377 (2021), 439–452. https://doi.org/10.1016/j.powtec.2020.09.008 doi: 10.1016/j.powtec.2020.09.008
|
| [32] |
S. Maiti, S. Shaw, G. C. Shit, Fractional order model for thermochemical flow of blood with Dufour and Soret effects under magnetic and vibration environment, Colloids Surf. B Biointerfaces, 197 (2021), 111395. https://doi.org/10.1016/j.colsurfb.2020.111395 doi: 10.1016/j.colsurfb.2020.111395
|
| [33] |
A. Shojaei, A. J. Amiri, S. S. Ardahaie, K. Hosseinzadeh, D. D. Ganji, Hydrothermal analysis of non-Newtonian second grade fluid flow on radiative stretching cylinder with Soret and Dufour effects, Case Stud. Thermal Eng. , 13 (2019), 100384. https://doi.org/10.1016/j.csite.2018.100384 doi: 10.1016/j.csite.2018.100384
|
| [34] |
S. Hussain, M. Jamal, B. P. Geridonmez, Impact of power law fluid and magnetic field on double diffusive mixed convection in staggered porous cavity considering Dufour and Soret effects, Int. Commun. Heat Mass Transfer, 121 (2021), 105075. https://doi.org/10.1016/j.icheatmasstransfer.2020.105075 doi: 10.1016/j.icheatmasstransfer.2020.105075
|
| [35] |
S. N. A. Salleh, N. Bachok, N. M. Arifin, F. M. Ali, Influence of Soret and Dufour on forced convection flow towards a moving thin needle considering Buongiorno's nanofluid model, Alex. Eng. J. , 59 (2020), 3897–3906. https://doi.org/10.1016/j.aej.2020.06.045 doi: 10.1016/j.aej.2020.06.045
|
| [36] |
V. B. Bekezhanova, O. N. Goncharova, Influence of the Dufour and Soret effects on the characteristics of evaporating liquid flows, Int. J. Heat Mass Transfer, 154 (2020), 119696. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119696 doi: 10.1016/j.ijheatmasstransfer.2020.119696
|
| [37] |
H. Sardar, L. Ahmad, M. Khan, A. S. Alshomrani, Investigation of mixed convection flow of Carreau nanofluid over a wedge in the presence of Soret and Dufour effects, Int. J. Heat Mass Transfer, 137 (2019), 809–822. https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.132 doi: 10.1016/j.ijheatmasstransfer.2019.03.132
|
| [38] |
S. A. Khan, T. Hayat, A. Alsaedi, Irreversibility analysis in Darcy-Forchheimer flow of viscous fluid with Dufour and Soret effects via finite difference method, Case Stud. Thermal Eng. , 26 (2021), 101065. https://doi.org/10.1016/j.csite.2021.101065 doi: 10.1016/j.csite.2021.101065
|
| [39] |
A. M. Aly, ISPH method for MHD convective flow from grooves inside a nanofluid-filled cavity under the effects of Soret and Dufour numbers, Phys. A, 546 (2020), 124087. https://doi.org/10.1016/j.physa.2019.124087 doi: 10.1016/j.physa.2019.124087
|
Figures(22) / Tables(4)
Turki J. Alqurashi. Thermocapillary convection of chemically reacting hybrid nanofluid with catalytic, cross diffusion, and activation energy in a porous medium application to crystal growth[J]. AIMS Mathematics, 2026, 11(9): 31896-31918. doi: 10.3934/math.20261255
DownLoad: