Heat transfer optimization of MHD unsteady separated stagnation-point flow of a hybrid ferrofluid with heat generation
DOI:
https://doi.org/10.24425/ather.2025.154909Abstract
The heat transfer optimization for magnetohydrodynamic unsteady stagnation-point flows and the thermal progress with the effect of heat generation is performed using the response surface methodology. The first step in this study involves reducing the mathematical model of partial differential equations and boundary conditions into non-linear ordinary differential equations via similarity transformations. Numerical solutions of the emerged system are obtained using the bvp4c solver. As observed from this study, the magnitude of the skin friction coefficient and heat transfer rate rises with the suction parameter. The statistical analysis and optimization done using the response surface methodology revealed that the suction parameter highly impacts the local Nusselt number. The maximum sensitivity of the heat transfer rate is towards the magnetic and suction parameters.References
[1] Khan, M., Sarfraz, M., & Zehra, R. (2022). Energy transport near Homann stagnation point flow over a spiraling disk with Cattaneo–Christov theory. International Journal of Modern Physics B, 36(25), 2250171. https://doi.org/10.1142/S0217979222501715
[2] Choi, S.U.S., & Eastman, J.A. (1995). Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress & Exposition, Nov. 12–17, San Francisco, USA.
[3] Eastman, J.A., Choi, S.U.S., Li, S., Yu, W., & Thompson, L.J. (2001). Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Applied Physics Letters, 78(6), 718–720. https://doi.org/10.1063/1.1341218
[4] Sarfraz, M., Muhammad, K., Alrihieli, H.F., & Abdelmohimen, M.A.H. (2025). Heat and mass transfer analysis in Walter's B nanofluid flow. ZAMM, 105(1), e202300951. https://doi.org/10.1002/zamm.202300951
[5] Anuar, N.S., Bachok, N., & Pop, I. (2021). Influence of MHD hybrid ferrofluid flow on stretching/shrinking surface. Mathematics, 9(22), 2932. https://doi.org/10.3390/math9222932
[6] Saranya, S., Al-Mdallal, Q.M., & Javed, S. (2021). Shifted Legendre method for viscous-ohmic hybrid ferrofluid flow. Nanomaterials, 11(6), 1512. https://doi.org/10.3390/nano11061512
[7] Waini, I., Khashi’ie, N.S., Kasim, A.R.M., Zainal, N.A., Hamzah, K.B., Arifin, N.M., & Pop, I. (2022). Unsteady MHD flow of hybrid ferrofluid due to rotating disk. Mathematics, 10(10), 1658. https://doi.org/10.3390/math10101658
[8] Khashi’ie, N.S., Waini, I., Zainal, N.A., Hamzah, K.B., Kasim, A.R.M., Arifin, N.M., & Pop, I. (2022). Thermal progress of unsteady stagnation flow in hybrid ferrofluid. Nanomaterials, 12(18), 3205. https://doi.org/10.3390/nano12183205
[9] Rosli, W.M.H.W., Mohamed, M.K.A., Sarif, N.M., & Ong, H.R. (2023). Convective boundary layer flow of Williamson hybrid ferrofluid. Journal of Advanced Research in Fluid Mechanics, 112(1), 176–188. https://doi.org/10.37934/arfmts.112.1.176188
[10] Idris, S., Jamaludin, A., Nazar, R., & Pop, I. (2023). Heat transfer of magnetized hybrid ferrofluid flow. Heliyon, 9(5), e15907. https://doi.org/10.1016/j.heliyon.2023.e15907
[11] Zainodin, S., Jamaludin, A., Nazar, R., & Pop, I. (2023). Chemical reaction and slip effects on hybrid ferrofluid flow. Alexandria Engineering Journal, 68, 111–126. https://doi.org/10.1016/j.aej.2023.01.011
[12] Zainal, N.A., Nazar, R., Naganthran, K., & Pop, I. (2022). Unsteady separated stagnation-point flow of hybrid nanofluid. Mathematics, 10(11), 1933. https://doi.org/10.3390/math10111933
[13] Khan, A., Jamshed, W., Eid, M.R., Pasha, A.A., Tag El Din, E.S.M., Khalifa, H.A.E.-W., & Alharbi, S.K. (2022). Unsteady electro-hydrodynamic stagnation flow of hybrid nanofluid. Symmetry, 14(10), 2136. https://doi.org/10.3390/sym14102136
[14] Mahmood, Z., & Khan, U. (2023). Unsteady 3D stagnation flow of ternary hybrid nanofluid. Science Progress, 106(1), 00368504231152741. https://doi.org/10.1177/00368504231152741
[15] Khashi’ie, N.S., Arifin, N.M., & Pop, I. (2022). Axisymmetric radiative hybrid nanofluid flow over stretching surface. Chinese Journal of Physics, 78, 169–179. https://doi.org/10.1016/j.cjph.2022.06.003
[16] Sarfraz, M., Khan, M., Al Zubaidi, A., & Saleem, S. (2023). Thermodynamic efficiency of Homann-Agrawal hybrid nanofluid flow. Alexandria Engineering Journal, 82, 178–185. https://doi.org/10.1016/j.aej.2023.09.074
[17] Khan, M., Sarfraz, M., Mehmood, S., & Ullah, M.Z. (2022). Irreversibility analysis of hybrid nanofluid over rotating cylinder. Journal of Applied Biomaterials & Functional Materials, 20. https://doi.org/10.1177/22808000221120329
[18] Sarfraz, M., & Khan, M. (2024). Energy optimization of hybrid nanomaterials. Scientia Iranica, 31(1), 71–82. https://doi.org/10.24200/sci.2023.60254.6689
[19] Sarfraz, M., Yasir, M., & Khan, M. (2023). Thermal conductivity comparison in hybrid nanofluids. Nanoscale Advances, 50(23), 6695–6704. https://doi.org/10.1039/D3NA00503H
[20] Wahid, N.S., Arifin, N.M., Khashi’ie, N.S., & Pop, I. (2020). Hybrid nanofluid slip flow over stretching sheet. Mathematics, 9(1), 30. https://doi.org/10.3390/math9010030
[21] Eid, M.R., & Nafe, M.A. (2022). Thermal conductivity variation in hybrid nanofluid flow. Waves in Random and Complex Media, 32(3), 1103–1127. https://doi.org/10.1080/17455030.2020.1810365
[22] Bakar, S.A., Wahid, N.S., Arifin, N.M., & Khashi’ie, N.S. (2022). Hybrid nanofluid flow in Darcy–Forchheimer medium. Waves in Random and Complex Media. https://doi.org/10.1080/17455030.2021.2020375
[23] Yasir, M., & Khan, M. (2024). Thermal efficiencies of hybrid ferrofluid. Alexandria Engineering Journal, 90, 120–128. https://doi.org/10.1016/j.aej.2024.01.055
[24] Zainal, N.A., Nazar, R., Naganthran, K., & Pop, I. (2020). 3D MHD Homann stagnation flow of hybrid nanofluid. Mathematics, 8(5), 784. https://doi.org/10.3390/math8050784
[25] Pop, I., Rostami, M.N., & Dinarvand, S. (2021). Dual similarity solutions in hybrid nanofluid flow. International Journal of Numerical Methods for Heat & Fluid Flow, 31(11), 3319–3342. https://doi.org/10.1108/HFF-09-2019-0714
[26] Khashi’ie, N.S., Wahid, N.S., Arifin, N.M., & Pop, I. (2022). MHD unsteady stagnation-point flow of hybrid nanofluid. ZAMM, 102(6), e202100410. https://doi.org/10.1002/zamm.202100410
[27] Zainodin, S., Jamaludin, A., Nazar, R., & Pop, I. (2023). MHD mixed convection hybrid ferrofluid flow. Symmetry, 15(4), 878. https://doi.org/10.3390/sym15040878
[28] Algehyne, E.A., Ahammad, N.A., Elnair, M.E., Zidan, M., Alhusayni, Y.Y., El-Bashir, B., & Alzahrani, F. (2023). Entropy optimization of blood hybrid nanofluid flow. Scientific Reports, 13(1), 9856. https://doi.org/10.1038/s41598-023-36931-6
[29] Mishra, S., Panda, S., & Baithalu, R. (2024). Heat transfer in hybrid nanofluid flow over cone. Partial Differential Equations in Applied Mathematics, 11, 100825. https://doi.org/10.1016/j.padiff.2024.100825
[30] Yahaya, R.I., Arifin, N.M., Mustafa, M.S., Pop, I., Ali, F.M., & Isa, S.S.P.M. (2025). Mixed convection hybrid nanofluid flow over cone/wedge. Case Studies in Thermal Engineering, 66, 105768. https://doi.org/10.1016/j.csite.2025.105768
[31] Dholwy, S. (2016). MHD unsteady stagnation-point flow over moving plate. ZAMM, 96, 707–720. https://doi.org/10.1002/zamm.2014
