The impact of exponentially varying viscosity on magnetized tangent hyperbolic nanofluid over a nonlinear stretching sheet with PHF and PMF conditions
DOI:
https://doi.org/10.24036/teknomekanik.v8i1.33772Keywords:
tangent hyperbolic nanofluid, variable heated viscosity, exponential stretching sheet, PHF and PMF, chebyshev spectral methodAbstract
This article aims to explore the characteristics of tangent hyperbolic nanofluid flow over a nonlinear exponentially stretching sheet with suction or injection embedded in a Darcy porous medium. We consider a non-Newtonian magnetohydrodynamic fluid with prescribed surface temperature and temperature-dependent viscosity, relevant to applications in aerospace, automotive and marine engineering, electronic cooling, solar-energy systems, and filtration. Given its fundamental importance, the study of prescribed exponential order heat flux (PHF) and prescribed mass flux (PMF) of hyperbolic tangent nanofluid became a key in research aimed at improving the efficiency and performance of these systems. The partial differential equations are converted into ODES by using transformation procedure. The system of transformed equations is numerically solved by Chebyshev spectral method. Graphical results illustrate the impact of key parameters on concentration, velocity, and temperature profiles, while tabulated data report the local Nusselt number, Sherwood number, and skin friction coefficient. Our results show that increasing both the power-law index and the variable-viscosity parameter reduces the fluid’s velocity while elevating its temperature and concentration. The comparative analysis confirms a high degree of agreement with previous studies. This research holds significant importance as it focuses on the extensive utilization of tangent hyperbolic nanofluids in cooling electronic components that produce substantial heat during their operation.
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W. Abbas, A. M. Megahed, M. H. Beniamean, and R. Awadalla, “Investigation of Slip Phenomenon of Tangent Hyperbolic Nanofluid Flow Due to a Vertical Sheet With Thermal Radiation,” Journal of Nonlinear Mathematical Physics, vol. 32, no. 1, p. 13, Mar. 2025, https://doi.org/10.1007/s44198-025-00266-9
I. Pop and D. B. Ingham, Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media. Elsevier, 2001. https://doi.org/10.1016/B978-0-08-043878-8.X5000-7
B. C. Sakiadis, “Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow,” AIChE Journal, vol. 7, no. 1, pp. 26–28, Mar. 1961, https://doi.org/10.1002/aic.690070108
L. J. Crane, “Flow past a stretching plate,” Zeitschrift für angewandte Mathematik und Physik ZAMP, vol. 21, no. 4, pp. 645–647, Jul. 1970, https://doi.org/10.1007/BF01587695
C. Y. Wang, “Liquid film on an unsteady stretching surface,” Q Appl Math, vol. 48, no. 4, pp. 601–610, Dec. 1990, https://doi.org/10.1090/qam/1079908
R. Cortell, “A note on magnetohydrodynamic flow of a power-law fluid over a stretching sheet,” Appl Math Comput, vol. 168, no. 1, pp. 557–566, Sep. 2005, https://doi.org/10.1016/j.amc.2004.09.046
M. Y. Malik, T. Salahuddin, A. Hussain, and S. Bilal, “MHD flow of tangent hyperbolic fluid over a stretching cylinder: Using Keller box method,” J Magn Magn Mater, vol. 395, pp. 271–276, Dec. 2015, https://doi.org/10.1016/j.jmmm.2015.07.097
M. Amjad, M. N. Khan, K. Ahmed, I. Ahmed, T. Akbar, and S. M. Eldin, “Magnetohydrodynamics tangent hyperbolic nanofluid flow over an exponentially stretching sheet: Numerical investigation,” Case Studies in Thermal Engineering, vol. 45, p. 102900, May 2023, https://doi.org/10.1016/j.csite.2023.102900
R. Ali, M. R. Khan, A. Abidi, S. Rasheed, and A. M. Galal, “Application of PEST and PEHF in magneto-Williamson nanofluid depending on the suction/injection,” Case Studies in Thermal Engineering, vol. 27, p. 101329, Oct. 2021, https://doi.org/10.1016/j.csite.2021.101329
M. Khan, A. Hussain, M. Y. Malik, T. Salahuddin, and F. Khan, “Boundary layer flow of MHD tangent hyperbolic nanofluid over a stretching sheet: A numerical investigation,” Results Phys, vol. 7, pp. 2837–2844, 2017, https://doi.org/10.1016/j.rinp.2017.07.061
K. S. Mekheimer, M. A. Seddeek, R. E. Abo-Elkhair, A. M. Salem, and A. A. Gadelhak, “The Thermal Flow of Maxwell Nanofluid Over a Stretching Sheet with Electro-Kinetic and Viscous Dissipation Effects: A Buongiorno’s Model,” 2025, pp. 221–252. https://doi.org/10.1007/978-981-96-1570-4_10
E. Alali and A. M. Megahed, “MHD dissipative Casson nanofluid liquid film flow due to an unsteady stretching sheet with radiation influence and slip velocity phenomenon,” Nanotechnol Rev, vol. 11, no. 1, pp. 463–472, Jan. 2022, https://doi.org/10.1515/ntrev-2022-0031
R. I. Yahaya, F. M. Ali, N. M. Arifin, N. S. Khashi’ie, and S. S. P. M. Isa, “MHD flow of hybrid nanofluid past a stretching sheet: double stratification and multiple slips effects,” Mathematical Modeling and Computing, vol. 9, no. 4, pp. 871–881, 2022, https://doi.org/10.23939/mmc2022.04.871
F. Shahzad et al., “Thermal analysis for Al2 O3–sodium alginate magnetized Jeffrey’s nanofluid flow past a stretching sheet embedded in a porous medium,” Sci Rep, vol. 12, no. 1, p. 3287, Feb. 2022, https://doi.org/10.1038/s41598-022-06983-1
W. Abbas, A. M. Megahed, M. A. Ibrahim, and A. A. M. Said, “Non-Newtonian Slippery Nanofluid Flow Due to a Stretching Sheet Through a Porous Medium with Heat Generation and Thermal Slip,” Journal of Nonlinear Mathematical Physics, vol. 30, no. 3, pp. 1221–1238, Jun. 2023, https://doi.org/10.1007/s44198-023-00125-5
C. Vittal, V. Tankasala, P. Ashok, S. Renuka, M. Chenna, and K. Reddy, “MHD Boundary Layer Flow and Heat Transfer to Sisko Nanofluid Over a Nonlinear Stretching Sheet,” International Journal of Engineering Research & Technology, vol. 12, no. 7, Aug. 2023, https://doi.org/10.17577/IJERTV12IS070138
N. S. Akbar, A. Al-Zubaidi, S. Saleem, and S. A. M. Alsallami, “Variable fluid properties analysis for thermally laminated 3-dimensional magnetohydrodynamic non-Newtonian nanofluid over a stretching sheet,” Sci Rep, vol. 13, no. 1, p. 3231, Feb. 2023, https://doi.org/10.1038/s41598-023-30233-7
H. A. Nabwey, A. M. Rashad, W. A. Khan, S. M. M. El-Kabeir, and S. AbdElnaem, “Heat transfer in MHD flow of Carreau ternary-hybrid nanofluid over a curved surface stretched exponentially,” Front Phys, vol. 11, Jun. 2023, https://doi.org/10.3389/fphy.2023.1212715
M. Naveed, M. Imran, and S. Gul, “Heat transfer analysis in hydromagnetic flow of couple stress fluid in presence of homogeneous and heterogeneous chemical reactions over a porous oscillatory stretchable sheet,” Advances in Mechanical Engineering, vol. 15, no. 2, Feb. 2023, https://doi.org/10.1177/16878132231155823
A. M. Amer, S. A. S. Al Rashdi, N. I. Ghoneim, and A. M. Megahed, “Tangent hyperbolic nanofluid flowing over a stretching sheet through a porous medium with the inclusion of magnetohydrodynamic and slip impact,” Results in Engineering, vol. 19, p. 101370, Sep. 2023, https://doi.org/10.1016/j.rineng.2023.101370
N. S. Yousef, A. M. Megahed, N. I. Ghoneim, M. Elsafi, and E. Fares, “Chemical reaction impact on MHD dissipative Casson-Williamson nanofluid flow over a slippery stretching sheet through porous medium,” Alexandria Engineering Journal, vol. 61, no. 12, pp. 10161–10170, Dec. 2022, https://doi.org/10.1016/j.aej.2022.03.032
Kh. S. Mekheimer, W. Abbas, M. M. Ghazy, A. M. A. Moawad, and R. E. Abo-Elkhair, “Unsteady squeezing Casson fluid through rotating discs under the variable magnetic field, cross diffusion and chemical reaction effects,” Int J Mod Phys B, vol. 38, no. 16, Jun. 2024, https://doi.org/10.1142/S0217979224502011
A. A. Gadelhak, Kh. S. Mekheimer, M. A. Seddeek, R. E. Abo-Elkhair, K. K. Ali, and A. M. Salem, “Energy Transport of Williamson Nano-fluid over a Curved Stretching Surface by Means of FDM,” Bionanoscience, vol. 13, no. 3, pp. 1116–1125, Sep. 2023, https://doi.org/10.1007/s12668-023-01120-2
S. U. S. Choi and J. A. Eastman, “Enhancing thermal conductivity of fluids with nanoparticles,” United States, 1995.
J. Buongiorno, L.-W. Hu, S. J. Kim, R. Hannink, B. Truong, and E. Forrest, “Nanofluids for Enhanced Economics and Safety of Nuclear Reactors: An Evaluation of the Potential Features, Issues, and Research Gaps,” Nucl Technol, vol. 162, no. 1, pp. 80–91, Apr. 2008, https://doi.org/10.13182/NT08-A3934
X.-Q. Wang and A. S. Mujumdar, “A review on nanofluids - part I: theoretical and numerical investigations,” Brazilian Journal of Chemical Engineering, vol. 25, no. 4, pp. 613–630, Dec. 2008, https://doi.org/10.1590/S0104-66322008000400001
W. A. Khan and I. Pop, “Boundary-layer flow of a nanofluid past a stretching sheet,” Int J Heat Mass Transf, vol. 53, no. 11–12, pp. 2477–2483, May 2010, https://doi.org/10.1016/j.ijheatmasstransfer.2010.01.032
T. Hayat, M. Waqas, M. I. Khan, and A. Alsaedi, “Analysis of thixotropic nanomaterial in a doubly stratified medium considering magnetic field effects,” Int J Heat Mass Transf, vol. 102, pp. 1123–1129, Nov. 2016, https://doi.org/10.1016/j.ijheatmasstransfer.2016.06.090
M. Ferdows, MD. Shamshuddin, S. O. Salawu, and K. Zaimi, “Numerical simulation for the steady nanofluid boundary layer flow over a moving plate with suction and heat generation,” SN Appl Sci, vol. 3, no. 2, p. 264, Feb. 2021, https://doi.org/10.1007/s42452-021-04224-0
P. S. Reddy and P. Sreedevi, “MHD boundary layer heat and mass transfer flow of nanofluid through porous media over inclined plate with chemical reaction,” Multidiscipline Modeling in Materials and Structures, vol. 17, no. 2, pp. 317–336, Jul. 2020, https://doi.org/10.1108/MMMS-03-2020-0044
V. B. Awati, A. Goravar, and A. Wakif, “Analysis of unsteady boundary layer flow of nanofluids with heat transfer over a permeable stretching/shrinking sheet via a shifted Chebyshev collocation method,” Waves in Random and Complex Media, pp. 1–27, Dec. 2022, https://doi.org/10.1080/17455030.2022.2157515
H. Maiti and S. Mukhopadhyay, “Existence of MHD boundary layer hybrid nanofluid flow through a divergent channel with mass suction and injection,” Chemical Engineering Journal Advances, vol. 14, p. 100475, May 2023, https://doi.org/10.1016/j.ceja.2023.100475
A. Shahid, M. M. Bhatti, R. Ellahi, and K. S. Mekheimer, “Numerical experiment to examine activation energy and bi-convection Carreau nanofluid flow on an upper paraboloid porous surface: Application in solar energy,” Sustainable Energy Technologies and Assessments, vol. 52, p. 102029, Aug. 2022, https://doi.org/10.1016/J.SETA.2022.102029
B. K. Sharma, U. Khanduri, N. K. Mishra, and Kh. S. Mekheimer, “Combined effect of thermophoresis and Brownian motion on MHD mixed convective flow over an inclined stretching surface with radiation and chemical reaction,” Int J Mod Phys B, vol. 37, no. 10, Apr. 2023, https://doi.org/10.1142/S0217979223500959
B. Jalili, M. Emad, P. Jalili, D. Domiri Ganji, S. Saleem, and E. M. Tag-eldin, “Thermal analysis of boundary layer nanofluid flow over the movable plate with internal heat generation, radiation, and viscous dissipation,” Case Studies in Thermal Engineering, vol. 49, p. 103203, Sep. 2023, https://doi.org/10.1016/J.CSITE.2023.103203
U. Hayat, R. Ali, S. Shaiq, and A. Shahzad, “A numerical study on thin film flow and heat transfer enhancement for copper nanoparticles dispersed in ethylene glycol,” REVIEWS ON ADVANCED MATERIALS SCIENCE, vol. 62, no. 1, Jun. 2023, https://doi.org/10.1515/rams-2022-0320
S. A. S. Al Rashdi, N. I. Ghoneim, A. M. Megahed, and A. M. Amer, “Enhancement of heat mass transmission characteristics through a non-Newtonian nanofluid model due to a convectively heated stretched sheet which exposed to a magnetic field,” Results in Engineering, vol. 18, p. 101180, Jun. 2023, https://doi.org/10.1016/J.RINENG.2023.101180
M. M. Magdy, W. Abbas, Kh. S. Mekheimer, and M. S. Emam, “Ferro-Fluid Flow and Heat Transfer over Unsteady Stretching Sheet in the Presence of a Nonuniform Magnetic Field,” Journal of Nonlinear Mathematical Physics, vol. 32, no. 1, p. 2, Jan. 2025, https://doi.org/10.1007/s44198-024-00250-9
B. Gebhart, “Effects of viscous dissipation in natural convection,” J Fluid Mech, vol. 14, no. 2, pp. 225–232, Oct. 1962, https://doi.org/10.1017/S0022112062001196
R. Cortell, “Viscous flow and heat transfer over a nonlinearly stretching sheet,” Appl Math Comput, vol. 184, no. 2, pp. 864–873, Jan. 2007, https://doi.org/10.1016/J.AMC.2006.06.077
M. Subhas Abel, E. Sanjayanand, and M. M. Nandeppanavar, “Viscoelastic MHD flow and heat transfer over a stretching sheet with viscous and ohmic dissipations,” Commun Nonlinear Sci Numer Simul, vol. 13, no. 9, pp. 1808–1821, Nov. 2008, https://doi.org/10.1016/J.CNSNS.2007.04.007
B. Ramandevi, J. V. R. Reddy, V. Sugunamma, and N. Sandeep, “Combined influence of viscous dissipation and non-uniform heat source/sink on MHD non-Newtonian fluid flow with Cattaneo-Christov heat flux,” Alexandria Engineering Journal, vol. 57, no. 2, pp. 1009–1018, Jun. 2018, https://doi.org/10.1016/j.aej.2017.01.026
L. Anitha, B. J. Gireesha, and M. L. Keerthi, “Irreversibility analysis of tangent hyperbolic fluid flow in a microchannel: a hybrid nanoparticles aspects,” Phys Scr, vol. 98, no. 3, p. 035220, Mar. 2023, https://doi.org/10.1088/1402-4896/acba53
G. Bayou, E. Haile, and G. Awgichew, “Heat and mass flux dynamics of tangent hyperbolic nanofluid flow with unsteady rotatory stretching disk over Darcy-Forchheimer porous medium,” Phys Scr, vol. 99, no. 12, p. 125206, Dec. 2024, https://doi.org/10.1088/1402-4896/ad8972
S. U. Khan, H. Waqas, S. A. Shehzad, and M. Imran, “Theoretical analysis of tangent hyperbolic nanoparticles with combined electrical MHD, activation energy and Wu’s slip features: a mathematical model,” Phys Scr, vol. 94, no. 12, p. 125211, Dec. 2019, https://doi.org/10.1088/1402-4896/ab399f
E. O. Fatunmbi, F. Mabood, H. Elmonser, and I. Tlili, “Magnetohydrodynamic nonlinear mixed convection flow of reactive tangent hyperbolic nano fluid passing a nonlinear stretchable surface,” Phys Scr, vol. 96, no. 1, p. 015204, Jan. 2021, https://doi.org/10.1088/1402-4896/abc3e9
L. Reid, “An Introduction to Biomedical Computational Fluid Dynamics,” 2021, pp. 205–222. https://doi.org/10.1007/978-3-030-76951-2_10
S. Sadighi, H. Afshar, M. Jabbari, and H. Ahmadi Danesh Ashtiani, “Heat and mass transfer for MHD nanofluid flow on a porous stretching sheet with prescribed boundary conditions,” Case Studies in Thermal Engineering, vol. 49, p. 103345, Sep. 2023, https://doi.org/10.1016/j.csite.2023.103345
M. I. Khan, S. Qayyum, T. Hayat, M. I. Khan, A. Alsaedi, and T. A. Khan, “Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection,” Phys Lett A, vol. 382, no. 31, pp. 2017–2026, Aug. 2018, https://doi.org/10.1016/j.physleta.2018.05.021
R. Ali, M. R. Khan, A. Abidi, S. Rasheed, and A. M. Galal, “Application of PEST and PEHF in magneto-Williamson nanofluid depending on the suction/injection,” Case Studies in Thermal Engineering, vol. 27, p. 101329, Oct. 2021, https://doi.org/10.1016/j.csite.2021.101329
N. Sher Akbar, A. Ebaid, and Z. H. Khan, “Numerical analysis of magnetic field effects on Eyring-Powell fluid flow towards a stretching sheet,” J Magn Magn Mater, vol. 382, pp. 355–358, May 2015, https://doi.org/10.1016/j.jmmm.2015.01.088
A. M. Megahed, M. G. Reddy, and W. Abbas, “Modeling of MHD fluid flow over an unsteady stretching sheet with thermal radiation, variable fluid properties and heat flux,” Math Comput Simul, vol. 185, pp. 583–593, Jul. 2021, https://doi.org/10.1016/j.matcom.2021.01.011
S. E. Waheed and A. M. Megahed, “Melting Heat Transfer Effects on Flow of a Micropolar Fluid with Heat Generation(Absorption) in Slip Flow Regime,” Applied Mathematics & Information Sciences, vol. 16, no. 1, pp. 35–44, Jan. 2022, https://doi.org/10.18576/amis/160104
J. Peddieson, Boundary Layer Theory for a Micropolar Fluid. Virginia Polytechnic Institute, 1968.
J. V. Tawade, C. N. Guled, S. Noeiaghdam, U. Fernandez-Gamiz, V. Govindan, and S. Balamuralitharan, “Effects of thermophoresis and Brownian motion for thermal and chemically reacting Casson nanofluid flow over a linearly stretching sheet,” Results in Engineering, vol. 15, p. 100448, Sep. 2022, https://doi.org/10.1016/j.rineng.2022.100448
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