Stability Analysis and RSM Approach on MHD Radiative Hybrid Nanofluid Flow between Squeezing Circular Porous Disks

Abstract:

This study investigates the combined stability and sensitivity study of MHD radiative squeezed hybrid nanofluid flow between two parallel circular porous disks. Although numerous studies have examined magnetohydrodynamic (MHD) flows, thermal radiation effects, squeezed-flow configurations, and nanofluids in porous media, existing literature typically addresses these effects in isolation or in simplified combinations. Most prior works have focused on single-nanoparticle nanofluids, neglecting the enhanced thermo-physical behavior of hybrid nanofluids containing two different nanoparticles. The hybrid nanofluid comprises a base fluid embedded with two distinct nanoparticles, enhancing its thermal and flow properties. Several complex interactions including magnetic fields, thermal radiation, resistance in porous media, and squeezing effects influence the flow and thermal characteristics. A system of nonlinear partial differential equations is constructed and then converted into a dimensionless form through the application of similarity transformations. Subsequently, the dimensionless equations are solved using a power series method, and the resulting solutions are analyzed through the Hermite–Padé approximation scheme. A comparison between the current data and a published result has been made with a good agreement. The effect of flow parameters such as porosity parameter, squeeze number, Prandtl number, Eckert number, and radiation parameter on velocity and temperature fields is illustrated graphically. The skin friction coefficient and local heat transfer rate are also evaluated for the relevant physical parameters. The stability of the local heat transfer rate is examined through a bifurcation curve, which indicates that the lower branch represents a stable and physically realizable solution, while the upper branch corresponds to an unstable state. Sensitivity analysis is performed to measure the influence of key dimensionless parameters such as the squeeze number, porosity parameter, and radiation parameter on the local Nusselt number and the result of our model is significant. This work has potential applications in thermal management systems, energy devices, and advanced cooling technologies.

• Periodical: Nano Hybrids and Composites (Volume 51)
• Pages: 75-95
• DOI: https://doi.org/10.4028/p-sN82UO
• Online since: May 2026
• Authors: Sumaiya Akter, Md. Sarwar Alam*, Abdul Awal
• Keywords: Hermite-Padé Approximation Method, Hybrid Nanofluid, Porous Circular Disk, Sensitivity Analysis, Squeezed Flow, Stability Study

References

[1] S. Ishizawa, The Unsteady Laminar Flow between Two Parallel Discs with Arbitrarily Varying Gap Width, JSME International Journal Series B-fluids and Thermal Engineering 9 (1966) 533- 550.

DOI: 10.1299/jsme1958.9.533

[2] D. Srinivasacharya, N. Srinivasacharyulu, O. Odelu, Flow and heat transfer of couple stress fluid in a porous channel with expanding and contracting walls, Int. Com. in Heat and Mass Transfer 36 (2) (2009) 180-185.

DOI: 10.1016/j.icheatmasstransfer.2008.10.005

[3] M.M. Rashidi, T. Hayat, E. Erfani, S.A.M. Pour, A. A. Hendi, Simultaneous effects of partial slip and thermal-diffusion and diffusion-thermo on steady MHD convective flow due to a rotating disk, Communications in Nonlinear Science and Numerical Simulation 16 (11) (2011) 4303-4317.

DOI: 10.1016/j.cnsns.2011.03.015

[4] M.M. Rashidi, S.A. M. Pour, T. Hayat, S. Obaidat, Analytic approximate solutions for steady flow over a rotating disk in porous medium with heat transfer by Homotopy analysis method, Computers & Fluids 54 (30) (2012) 1-9.

DOI: 10.1016/j.compfluid.2011.08.001

[5] U. Khan, N. Ahmed, S.I. Khan, Z.A. Zaidi, Y.X. Jun, S.T. Mohyud-Din, On unsteady two dimensional and axisymmetric squeezing flow between parallel plates, Alexandria Engineering Journal 53 (2) (2014) 463-468.

DOI: 10.1016/j.aej.2014.02.002

[6] U. Khan, N. Ahmed, Z.A. Zaidi, M. Asadullah, S.T. Mohyud-Din, MHD squeezing flow between two infinite plates, Ain Shams Engineering Journal 5 (1) (2014) 187-192.

DOI: 10.1016/j.asej.2013.09.007

[7] S. Choi, J.A. Estamn, Enhancing thermal conductivity of fluids with nanoparticles, in: Int. Engineering Congress and Exhibition, San Francisco, CA, 1995.

[8] V. K. Tiwari, A. K. Prasad, V. Singh, K. K. Jana, M. Misra, C. D. Prasad, Nanoparticle and Process Induced Super-Toughened Piezoelectric Hybrid Materials, Journal of Macromolecule 46 (2013) 5595–5603.

DOI: 10.1021/ma400603h

[9] G. Domairry, M. Hatami, Squeezing Cu-water nanofluid flow analysis between parallel plates by DTM-Pade method, J. Mol. Liq. 193 (2014) 37-44.

DOI: 10.1016/j.molliq.2013.12.034

[10] R.U. Haq, N.F.M. Noor, Z.H. Khan, Numerical simulation of water-based magnetite nanoparticles between two parallel disks, Adv. Powder Technol. 27 (2016) 1568–1575.

DOI: 10.1016/j.apt.2016.05.020

[11] N. Ahmed, A. U. Khan, S.T. Mohyud-Din, Influence of shape factor on flow of magneto-nanofluid squeezed between parallel disks, Alexandria Engineering Journal 57 (2018) 1893-1903.

DOI: 10.1016/j.aej.2017.03.031

[12] J. C. Umavathi, S. L. Patil, B. Mahanthesh, O. A. Bég, Unsteady squeezing flow of a magnetized nano-lubricant between parallel disks with Robin boundary conditions, J. of Nanomaterials Nanoengineering and Nanosystems 235 (3-4) (2021) 1-15.

DOI: 10.1177/23977914211036562

[13] T. Hussain, H. Xu, Time-dependent squeezing bio-thermal MHD convection flow of a micropolar nanofluid between two parallel disks with multiple slip effects, Case Studies in Thermal Engineering 31 (2022) 101850.

DOI: 10.1016/j.csite.2022.101850

[14] O.A. Famakinwa, O.K. Koriko, K.S. Adegbie, Effects of viscous dissipation and thermal radiation on time dependent incompressible squeezing flow of CuO-Al2O3∕water hybrid nanofluid between two parallel plates with variable viscosity, J. of Comp. Math. And Data Sci. 5 (2022) 100062.

DOI: 10.1016/j.jcmds.2022.100062

[15] A. Shaheen, M. Imran, H. Waqas, M. Raza, S. Rashid, Thermal transport analysis of squeezing hybrid nanofluid flow between two parallel plates, Ad. in Mech. Eng. 15(1) (2023) 1-15.

DOI: 10.1177/16878132221147453

[16] S. H. H. Karouei, M. B. Shani, M. Sekaloo, S. H. H. Eimeni, P. Pasha, D. D. Ganji, Computational modeling of magnetized hybrid nanofluid flow and heat transfer between parallel surfaces with suction/injection, Int. J. of Thermofluids 22 (2024) 100613.

DOI: 10.1016/j.ijft.2024.100613

[17] G. B. Zegeye, E. Haile, G. Awgichew, Viscous dissipation and Joule heating effects of Carreau nanofluid axisymmetric flow past unsteady radially stretching porous disk, Int. J. of Thermofluids 22 (2024) 100655.

DOI: 10.1016/j.ijft.2024.100655

[18] H. Alahmadi, R. Nawaz, A numerical study on nanoparticles shape effects in modulating heat transfer in silver-water nanofluid over a polished rotating disk, Int. J. of Thermofluids 22 (2024) 100666.

DOI: 10.1016/j.ijft.2024.100666

[19] M. Usman, A. Nazir, Z. Naheed, S.T. Mohy-ud-Din, Adomian's decomposition method to squeezing flow and heat transfer between two parallel disks with velocity slip and temperature jump, Adv. Diabetes Metabol. 1 (2) (2013) 37-44.

DOI: 10.13189/adm.2013.010201

[20] G. Domairry, A. Aziz, Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by homotopy perturbation method, Math. Probl. Eng. (2009) 603916.

DOI: 10.1155/2009/603916

[21] M. Sheikholeslami, M. Azimi, D.D. Ganji, Application of differential transformation method for nanofluid flow in a semipermeable channel considering magnetic field effect, Int. J. Comput. Eng. Sci. Mech. 3 (2015) 1-10.

[22] M. S. Alam, M. A. H. Khan, M. A. Alim, Irreversibility analysis of variable thermal conductivity MHD radiative flow in porous channel with different nanoparticles, Journal of Porous Media 19(5) (2016) 423-439.

DOI: 10.1615/jpormedia.v19.i5.40

[23] M. S. Alam, M. A. Alim, and M. A. H. Khan, Entropy Generation Analysis for Variable Thermal Conductivity MHD Radiative Nanofluid Flow through Channel. Journal of Applied Fluid Mechanics 9(3) (2016) 1123-1134.

DOI: 10.18869/acadpub.jafm.68.228.24475

[24] D. C. Paul, M. A. Hye, M. M. Islam, M. Z. Hosen, M. S. Alam, Study on Shape Effect of MHD Radiative Ag-water and CuO-water Nanofluid Flow in a Semi Porous Channel, Defect and Diffusion Forum 430 (2024) 93-106.

DOI: 10.4028/p-1sbxuh

[25] A. Awal, M. S. Alam, R. A. Rouf, M. A. Hye, Stabilty study of MHD squeezed nanofluid flow through parallel porous disks with shape factor effect, International Journal of Thermofluids 23 (2024) 100787.

DOI: 10.1016/j.ijft.2024.100787

[26] A. Awal, M. S. Alam, Irreversibility and Sensitivity analysis of MHD squeezing various shaped nanofluid flow between parallel permeable disks, International Journal of Thermofluids 26 (2025) 101109.

DOI: 10.1016/j.ijft.2025.101109

[27] M. Borzuei, Z. Baniamerian, Role of nanoparticles on critical heat flux in convective boiling of nanofluids: Nanoparticle sedimentation and Brownian motion, Int. Journal of Heat and Mass Transfer 150 (2020) 119299.

DOI: 10.1016/j.ijheatmasstransfer.2019.119299

[28] K.A. Kalbani, S. Alam, M. Rahman, Finite Element Analysis of Unsteady Natural Convective Heat Transfer and Fluid Flow of Nanofluids inside a Tilted Square Enclosure in the Presence of Oriented Magnetic Field, American Journal of Heat and Mass Transfer 3 (2016) 186-224.

DOI: 10.7726/ajhmt.2016.1012

[29] N.S. Khashi'ie, N.M. Arifin, I. Pop, N.S. Wahid, Flow and heat transfer of hybrid nanofluid over a permeable shrinking cylinder with Joule heating: A comparative analysis, Alexandria Engineering Journal 59(3) (2020) 17871798.

DOI: 10.1016/j.aej.2020.04.048

[30] MAPPLE 6.0, Maplesoft, GLOBEtrotter Software Inc.

[31] H. Padé, Sur Ia représentation approachée d`une function pourdes fractions rationnelles, Annales Scientifiques de l'École Normalle Supérieure 9 (1892) 1-93.

DOI: 10.24033/asens.378

[32] C. Hermite, Sur Ia générealization des fractions continues algébriques, Annali di Mathematica Pura e Applicata 21 (1893) 289-308.

DOI: 10.1007/bf02420446

[33] P.G. Drazin, Y. Tourigny, Numerical study of bifurcation by analytic continuation of a function defined by a power series, SIAM Journal of Applied Mathematics 56 (1996) 1-18.

DOI: 10.1137/s0036139994272436

[34] M.A.H. Khan, High-Order Differential Approximants. Journal of Computational and Applied Mathematics 149 (2002) 457-468.

DOI: 10.1016/s0377-0427(02)00561-7

[35] G.E.P. Box, K.B. Wilson, On the Experimental Attainment of Optimum Conditions, Journal of the Royal Statistical Society: Series B (Methodological) 13(1) (1951) 1-38.