Scientia Iranica

Scientia Iranica

Effects of heat transfer on magnetohydrodynamics suction-injection model of viscous fluid flow through differential transformation and Hermite wavelet techniques

Document Type : Research Article

Authors
1 Department of Mathematics, Davangere University, Davangere, India.
2 Department of Mathematics, Bangalore University, Bangalore, India.
Abstract
This study investigates the magnetohydrodynamic flow and heat transfer between two parallel disks, considering suction and injection effects at the disks. The governing equations describing the flow and thermal transport are derived based on the principles of mass, momentum, and energy conservation for an electrically conducting fluid. As the governing Partial Differential Equations (PDEs) are highly nonlinear, similarity transformations are applied to transform them into coupled Ordinary Differential Equations (ODEs). Numerical techniques, namely the Hermite Wavelet Method (HWM) and Differential Transformation Technique (DTT), are then employed to solve the transformed equations. Parametric effects of several influential parameters such as the Prandtl number (Pr), Squeeze number (S), Hartmann number (M), and Thermophoresis parameter (Nt) on the velocity and temperature profiles are systematically analyzed. Comparisons are made with previous findings in the literature. The results indicate significant dependence of flow behavior and heat transfer on the governing parameters. Velocity and temperature distributions in the boundary layer are presented and discussed in detail. The proposed mathematical model and numerical approach provide useful insights into heat transfer characteristics for parallel disk systems and similar engineering applications involving magnetohydrodynamic flows with suction or injection effects.
Keywords
Subjects

References
1.Schulz, M. Control Theory in Physics and Other Fields of Science: Concepts, Tools, and Applications, Springer Science & Business Media (2006).
2.Ivancevic, V.G. and Ivancevic, T.T. Applied Differential Geometry: A Modern Introduction, World Scientific (2007).
3.Sun, H., Zhang, Y., Baleanu, D., et al.  “A new collection of real-world applications of fractional calculus in science and engineering”, Communications in Nonlinear Science and Numerical Simulation, 64, pp. 213-231 (2018). https://doi.org/10.1016/j.cnsns.2018.04.019
4.Raghunatha, K.R. and Vinod, Y. “Viscous flow by expanding or shrinking the gap with permeable walls through Hermite wavelet method”, International Journal of Applied and Computational Mathematics, 9(3), 22 (2023).     https://doi.org/10.1007/s40819-023-01502-w
5.Raghunatha, K.R. and Siddanagowdru, S.O. “Investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by DTM”, Heat Transfer, 51(4), pp. 3562-3572 (2022). https://doi.org/10.1002/htj.22463
6.Sarp, Ü., Evirgen, F., İkikardeş, S. “Applications of differential transformation method to solve systems of ordinary and partial differential equations”, Institute of Science and Technology, Balıkesir Üniversitesi, 20(2), pp. 135-156 (2018). https://doi.org/10.25092/baunfbed.423145
7.Sheikholeslami, M., Azimi, M., & Ganji, D.D.  “Application of differential transformation method for nanofluid flow in a semi-permeable channel considering magnetic field effect”, International Journal for Computational Methods in Engineering Science and Mechanics, 16(4), pp. 246-255 (2015). https://doi.org/10.1080/15502287.2015.1048384
8.Shiralashetti, S.C. and Kumbinarasaiah, S. “Laguerre wavelets collocation method for the numerical solution of the Benjamina-Bona-Mohany equations”, Journal of Taibah University for Science, 13(1), pp. 9-15 (2019). https://doi.org/10.1080/16583655.2018.1515324
9.Shiralashetti, S.C. and Hanaji, S.I. “Taylor wavelet collocation method for Benjamin-Bona-Mahony partial differential equations”, Results in Applied Mathematics, 9, 100139 (2021).  https://doi.org/10.1016/j.rinam.2020.100139
10.Shiralashetti, S.C., Kumbinarasaiah, S. “Cardinal B-spline wavelet based numerical method for the solution of generalized Burgers-Huxley equation”, Int. J. Appl. Comput., 4, 73 (2018).  https://doi.org/10.1007/s40819-018-0505-y
11.Raghunatha, K.R., Vinod, Y., Nagappanavar, S.N., et al. “Unsteady Casson fluid flow on MHD with an internal heat source”, Journal of Taibah University for Science, 17(1), 2271691 (2023).  https://doi.org/10.1080/16583655.2023.2271691
12.Shiralashetti, S.C. and Kumbinarasaiah, S. “Hermite wavelets operational matrix of integration for the numerical solution of nonlinear singular initial value problems”, Alexandria Engineering Journal, 57(4), pp. 2591-2600 (2018). https://doi.org/10.1016/j.aej.2017.07.014
13.Shiralashetti, S.C. and Kumbinarasaiah, S. “New generalized operational matrix of integration to solve nonlinear singular boundary value problems using Hermite wavelets”, Arab Journal of Basic and Applied Sciences, 26(1), pp. 385-396 (2019). https://doi.org/10.1080/25765299.2019.1646090
14.Kumbinarasaiah, S. and Raghunatha, K.R., “The applications of Hermite wavelet method to nonlinear differential equations arising in heat transfer”, International Journal of Thermofluids, 9, 100066 (2021). https://doi.org/10.1016/j.ijft.2021.100066
15.Srinivasa, K., Baskonus, H.M., and Guerrero Sánchez, Y. “Numerical solutions of the mathematical models on the digestive system and covid-19 pandemic by Hermite wavelet technique”, Symmetry, 13(12), 2428 (2021).  https://doi.org/10.3390/sym13122428
16.Kumbinarasaiah, S., Raghunatha, K.R., Rezazadeh, M. et al. “A solution of coupled nonlinear differential equations arising in a rotating micropolar nanofluid flow system by Hermite wavelet technique”, Engineering with Computers, 38, pp. 3351-3372 (2022). https://doi.org/10.1007/s00366-021-01462-z
17.Kumbinarasaiah, S. and Raghunatha, K.R. “Numerical solution of the Jeffery-Hamel flow through the wavelet technique”, Heat Transfer, 51, pp. 1568-1584 (2022). https://doi.org/10.1002/htj.22364
18.Raghunatha, K.R. and Kumbinarasaiah, S. “Application of Hermite wavelet method and differential transformation method for nonlinear temperature distribution in a rectangular moving porous fin”, International Journal of Applied and Computational Mathematics, 8, pp. 1-20 (2022). https://doi.org/10.1007/s40819-021-01226-9
19.Faheem, M., Khan, A. and Raza, A, et al. “A high-resolution Hermite wavelet technique for solving space-time-fractional partial differential equations”, Mathematics and Computers in Simulation, 194, pp. 588-609 (2022). https://doi.org/10.1016/j.matcom.2021.12.012
20.Vinod, Y. and Raghunatha, K.R. “Application of Hermite wavelet method for heat transfer in a porous media”, Heat Transferer, 52(1), pp. 983-999 (2023). https://doi.org/10.1002/htj.22726
21.Kumar, S., Kumar, R., Momani, S., et al. “A study on fractional COVID‐19 disease model by using Hermite wavelets”, Mathematical Methods in the Applied Sciences, 46(7), pp. 7671-7687 (2023).  https://doi.org/10.1002/mma.7065
22.Leal, L.G. “Particle motions in a viscous fluid”, Annual Review of Fluid Mechanics, 12(1), pp. 435-476 (1980). https://doi.org/10.1146/annurev.fl.12.010180.002251
23.MacCormack, R.W. “A numerical method for solving the equations of compressible viscous flow”, AIAA Journal, 20(9) (1982). https://doi.org/10.2514/3.51188
24.Jalili, B., Roshani, H., Jalili, P., et al. “The magnetohydrodynamic flow of viscous fluid and heat transfer examination between permeable disks by AGM and FEM”, Case Studies in Thermal Engineering, 45, 102961 (2023). https://doi.org/10.1016/j.csite.2023.102961
25.Zhang, L., Tariq, N.,  Bhatti, M.M. “Study of nonlinear quadratic convection on magnetized viscous fluid flow over a non-Darcian circular elastic surface via spectral approach”, Journal of Taibah University for Science, 17(1), 2183702 (2023). https://doi.org/10.1080/16583655.2023.2183702
26.Zaturska, M.B., Drazin P.G., and Banks, W.H.H “On the flow of a viscous fluid driven along a channel by suction at porous walls”, Fluid Dynamics Research, 4(3), 151 (1988).  https://doi.org/10.1016/0169-5983(88)90021-4
27.Attia, H.A. “The effect of suction and injection on the unsteady flow between two parallel plates with variable properties”, Journal of Applied Science and Engineering, 8(1) (2005). https://doi.org/10.6180/jase.2005.8.1.03
28.Mahmood, M., Hossain, M.A., Asghar, S., et al. “Application of homotopy perturbation method to deformable channel with wall suction and injection in a porous medium”, International Journal of Nonlinear Sciences and Numerical Simulation, 9(2), pp. 195-206 (2008). https://doi.org/10.1515/IJNSNS.2008.9.2.195
29.Yuan, S.W. and Finkelstein, A.B. “Laminar pipe flow with injection and suction through a porous wall”, Transactions of the American Society of Mechanical Engineers, 78(4), pp.  719-724 (1956). https://doi.org/10.1115/1.4013794
30.Abdollahi, S.A., Alizadeh, A., Chiniforooshan Esfahani, I.  “Investigating heat transfer and fluid flow betwixt parallel surfaces under the influence of hybrid nanofluid suction and injection with numerical analytical technique”, Alexandria Engineering Journal, 70, pp. 423-439 (2023). https://doi.org/10.1016/j.aej.2023.02.040
31.Fardi, M. and Khan, Y. “Numerical simulation of squeezing Cu-Water nanofluid flow by a kernel-based method”, International Journal of Modeling, Simulation, and Scientific Computing, 13(01), 2250005 (2022). https://doi.org/10.1142/S1793962322500052
32.Fardi, M. and Machado, J.T. “Reproducing Kernel method to detect the temperature distribution for annular fins with temperature-dependent thermal conductivity” Journal of Applied Nonlinear Dynamics, 11(2), pp. 283-295 (2022). https://doi.org/10.5890/JAND.2022.06.002
33.Ahmad, S., Ullah, H., Hayat, T., et al. “Computational analysis of time-dependent viscous fluid flow and heat transfer”, International Journal of Modern Physics B, 34(13), 20501416 (2020). https://doi.org/10.1142/S0217979220501416
34.Žukauskas, A. “Enhancement of forced convection heat transfer in viscous fluid flows”, International Journal of Heat and Mass Transfer, 37(1), pp. 207-212 (1994).  https://doi.org/10.1016/0017-9310(94)90022-1
35.Ismail, M.,  Fartaj, A.,  Karimi, M.  “Numerical investigation on heat transfer and fluid flow behaviors of viscous fluids in a minichannel heat exchanger”, Numerical Heat Transfer Part A Applications, 64(1), pp. 1-29 (2013). https://doi.org/10.1080/10407782.2013.773803
36.Rosenberg, D.E. and Hellums, J.D. “Flow development and heat transfer in variable-viscosity fluids”, Industrial & Engineering Chemistry Fundamentals, 4(4), pp. 417-422 (1965). https://doi.org/10.1021/i160016a010
37.Bathe, K.J. and Dong, J. “Solution of incompressible viscous fluid flow with heat transfer using ADINA-F”, Computers & Structures, 26(1-2), pp. 17-31 (1987).  https://doi.org/10.1016/0045-7949(87)90233-1
38.Anwar, T., Kumam P., Asifa, et al. “Generalized unsteady MHD natural convective flow of Jeffery model with ramped wall velocity and Newtonian heating; A Caputo-Fabrizio approach”, Chinese Journal of Physics, 68, pp. 849-865 (2020). https://doi.org/10.1016/j.cjph.2020.10.018
39.Anwar, T., Khan, I., Kumam, P., et al. “Impacts of thermal radiation and heat consumption/generation on unsteady MHD convection flow of an Oldroyd-B fluid with ramped velocity and temperature in a generalized Darcy medium”, Mathematics, 8(1), 130 (2020).  https://doi.org/10.3390/math8010130
40.Anwar, T., Kumam, P., Asifa, et al. “An exact analysis of radiative heat transfer and unsteady MHD convective flow of a second-grade fluid with ramped wall motion and temperature”, Heat Transfer, 50(1), pp. 196-219 (2021).  https://doi.org/10.1002/htj.21871
41.Asifa,  Kumam, P.,  Tassaddiq, A., et al. “Modeling and simulation-based investigation of unsteady MHD radiative flow of rate type fluid; a comparative fractional analysis”, Mathematics and Computers in Simulation, 201, pp.  486-507 (2022).  https://doi.org/10.1016/j.matcom.2021.02.005
42.Anwar, T., Kumam, P. and Watthayu, W. “Unsteady MHD natural convection flow of Casson fluid incorporating thermal radiative flux and heat injection/suction mechanism under variable wall conditions”, Scientific Reports, 11(1), 4275 (2021).  https://doi.org/10.1038/s41598-021-83691-2
43.Sa'adAldin, A. and Qatanani, N. “On unsteady MHD flow through the porous medium between two parallel flat plates”, An-Najah University Journal for Research-A (Natural Sciences), 30(1), pp. 173-186 (2015).  https://doi.org/ 10.35552/anujr.a.30.1.1184 
44.Nesliturk, A.I. and Tezer-Sezgin M. “The finite element method for MHD flow at high Hartmann numbers”, Computer Methods in Applied Mechanics and Engineering, 194(9-11), pp. 1201-1224 (2005). 
https://doi.org/10.1016/j.cma.2004.06.035
45.Guled, C.N., Tawade, J.V., Kumam, P., et al. “The heat transfer effects of MHD slip flow with suction and injection and radiation over a shrinking sheet by optimal homotopy analysis method”, Results in Engineering, 18, 101173 (2023).  https://doi.org/10.1016/j.rineng.2023.101173
46.Akbar, N.S., Akhtar, S., Maraj, E.N, et al. “Heat transfer analysis of MHD viscous fluid in a ciliated tube with entropy generation”, Mathematical Methods in the Applied Sciences, 46(10), pp. 11495-11508 (2023).  https://doi.org/10.1002/mma.7906
47.Shah, N.A., Ebaid, A., Oreyeni T., et al. “MHD and porous effects on free convection flow of viscous fluid between vertical parallel plates: Advance thermal analysis”, Waves in Random and Complex Media, 36(3), pp. 4233-4245 (2023).  https://doi.org/10.1080/17455030.2023.2186717
48.Bhargavi, N., Poornima, T., and Souayeh, B.  “Magnetohydrodynamic conjugate heat transfer analysis on a viscous fluid past a vertical permeable plate”, International Journal of Modern Physics B, 38(16), 2450211 (2023). https://doi.org/10.1142/S0217979224502114
49.Raghunatha, K.R. and Vinod, Y. “Effects of heat transfer on MHD suction-injection model of viscous fluid flow through differential transformation and Bernoulli wavelet techniques”, Heat Transfer, 52(7), pp. 4914-4945 (2023). https://doi.org/10.1002/htj.22911
50.Fardi, M., Pishkar, I., Alidousti, J., et al. “Numerical investigation of the MHD suction-injection model of viscous fluid using a Kernal-based method”, Archive of Applied Mechanics, 91, pp. 4205-4221 (2021).  https://doi.org/10.1007/s00419-021-02003-2
51.Zhou, J.K., Differential Transformation and its Applications for Electrical Circuits, Scientific Research, Huazhong University Press, Wuhan China (1986).
52.Vinod, Y., Raghunatha, K.R., and Kiran Kumar, D.L.  “Application of differential transformation and Hermite wavelet methods for micropolar flow through a permeable channel”, Heat Transfer, 52(4), pp. 3094‐3118 (2023).  https://doi.org/10.1002/htj.22818
53.Joneidi, A.A., Ganji, D.D., and Babaelahi, M.  “Differential transformation method to determine fin efficiency of convective straight fins with temperature-dependent thermal conductivity”, International Communications in Heat and Mass Transfer, 36(7), pp. 757-762 (2009).https://doi.org/10.1016/j.icheatmasstransfer.2009.03.020
Volume 32, Issue 20
Transactions on Mechanical Engineering
November and December 2025 Article ID:7510

  • Receive Date 07 February 2023
  • Revise Date 07 January 2024
  • Accept Date 17 April 2024