Pulsatile Powell-Eyring Nanofluid Flow in a Channel with Inclined Magnetic Field and Chemical Reaction
Abstract
The current article addresses the impacts of the pulsatile flow of Powell-Eyring nanofluid
using Buongiorno’s model in a horizontal channel. It also describes the combined impacts of thermophoresis and Brownian motion. Blood is an example of a Powell-Eyring fluid. The Runge-Kutta (R-K) 4th-order method, along with the shooting technique, is used to determine solutions for velocity, temperature, and concentration. The impacts of different parameters, including an inclined magnetic field, chemical reaction, Lewis number, and heat source or sink parameter, are illustrated graphically. The mass flux distribution decreases due to an increase in the values of the Powell-Eyring fluid parameter.
Keywords:
Powell-Eyring nanofluid, inclined magnetic field, chemical reaction, pulsatile flow, mass fluxReferences
1. Choi S.U.S., Enhancing thermal conductivity of fluids with nanoparticles, [in:] Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA (ASME, FED 231/MD), 66: 99–105, 1995, https://cir.nii.ac.jp/crid/1571980074227838464
2. Kumar B., Srinivas S., Unsteady hydromagnetic flow of Eyring-Powell nanofluid over an inclined permeable stretching sheet with Joule heating and thermal radiation, Journal of Applied and Computational Mechanics, 6(2): 259–270, 2019, https://doi.org/10.22055/jacm.2019.29520.1608
3. Waqas H., Naeem H., Manzoor U., Sivasankaran S., Alharbi A.A., Alshomrani A.S., Muhammad T., Impact of electro-magneto-hydrodynamics in radiative flow of nanofluids between two rotating plates, Alexandria Engineering Journal, 61(12): 10307–10317, 2022, https://doi.org/10.1016/j.aej.2022.03.059
4. Alsaedi A., Hayat T., Qayyum S., Yaqoob R., Eyring-Powell nanofluid flow with nonlinear mixed convection: Entropy generation minimization, Computer Methods and Programs in Biomedicine, 186: 105183, 2020, https://doi.org/10.1016/j.cmpb.2019.105183
5. Buongiorno J., Convective transport in nanofluids, Journal of Heat Transfer, 128 (3): 240–250, 2006, https://doi.org/10.1115/1.2150834
6. Hayat T., Sajjad R., Muhammad T., Alsaedi A., Ellahi R., On MHD nonlinear stretching flow of Powell-Eyring nanomaterial, Results in Physics, 7: 535–543, 2017, https://doi.org/10.1016/j.rinp.2016.12.039
7. Kumar C.K., Srinivas S., Reddy A.S., MHD pulsating flow of Casson nanofluid in a vertical porous space with thermal radiation and Joule heating, Journal of Mechanics, 36(4): 535–549, 2020, doi: 10.1017 /jmech.2020.5.
8. Mallick B., Misra J.C., Peristaltic flow of Eyring-Powell nanofluid under the action of an electromag¬netic field, Engineering Science and Technology, an International Journal, 22(1): 266–281, 2019, https://doi.org/10.1016/j.jestch.2018.12.001
9. Sheikholeslami M., Chamkha A.J., Rana P., Moradi R., Combined thermophoresis and Brownian motion effects on nanofluid free convection heat transfer in an L-shaped enclosure, Chinese Journal of Physics, 55(6): 2356–2370, 2017, https://doi.org/10.1016/j.cjph.2017.09.011
10. Shehzad N., Zeeshan A., Ellahi R., Vafai K., Convective heat transfer of nanofluid in a wavy channel: Buongiorno’s mathematical model, Journal of Molecular Liquids, 222: 446–455, 2016, https://doi.org/10.1016/j.mo lliq.2016.07.052.
11. Hayat T., Shafiq A., Alsaedi A., Asghar S., Effect of inclined magnetic field in flow of third grade fluid with variable thermal conductivity, AIP Advances, 5: 087108, 2015, https://doi.org/10.1063/1.4928321
12. Kumar C.K., Srinivas S., Simultaneous effects of thermal radiation and chemical reaction on hydromagnetic pulsatile flow of a Casson fluid in a porous space, Engineering Transactions, 65(3): 461–481, 2017.
13. Acharya N., Maity S., Kundu P.K., Influence of inclined magnetic field on the flow of condensed nanomaterial over a slippery surface: the hybrid visualization, Applied Nanoscience, 10: 633–647, 2020. https://doi.org/10.1007/s13204-019-01123-0
14. Khan A.A., Naeem S., Ellahi R., Sait S.M., Vafai K., Dufour and Soret effects on Darcy-Forchheimer flow of second-grade fluid with the variable magnetic field and thermal conductivity, International Journal of Numerical Methods for Heat & Fluid Flow, 30(9): 4331–4347, 2020, https://doi.org/10.1108/HFF-11-2019-0837
15. Ahmed S.E., Elshehabey H.M., Oztop H.F., Natural convection of three-dimensional non-Newtonian nanofluids with Marangoni effects and inclined magnetic fields, International Communications in Heat and Mass Transfer, 137: 106288, 2022, https://doi.org/10.1016/j.icheatmasstransfer.2022.106288
16. Kaladhar K., Reddy K.M., Srinivasacharya D., Inclined magnetic field, thermal radiation, and Hall current effects on mixed convection flow between vertical parallel plates, Journal of Heat Transfer, 141(10): 102501, 2019, https://doi.org/10.1115/1.4044391
17. Nath R., Murugesan K., Impact of nanoparticle shape on thermo-solutal buoyancy induced lid-driven-¬cavity with inclined magnetic-field, Propulsion and Power Research, 11(1): 97–117, 2022, https://doi.org/10.1016/j jppr.2022.01.002.
18. Noreen S., Qasim M., Peristaltic flow with inclined magnetic field and convective boundary conditions, Applied Bionics and Biomechanics, 11 (1–2): 61–67, 2014, https://doi.org/10.1155/2014/426217
19. Bianco V., Trubatch A.D., Wei H., Yecko P., Quantifying volume loss of a magnetically localized ferrofluid bolus in pulsatile pipe flow, Journal of Magnetism and Magnetic Materials, 524: 167595, 2021, https://doi.org/10.1016/j.jmmm.2020.167595
20. Cheng Z., Jelly T.O., Illingworth S.J., Marusic I., Ooi A.S.H., Forcing frequency effects on turbulence dynamics in pulsatile pipe flow, International Journal of Heat and Fluid Flow, 82: 108538, 2020, https://doi.org/10.1016/j.ijheat%EF%AC%82uid%EF%AC%82ow.2020.108538
21. Govindarajulu K., Reddy A.S., Magnetohydrodynamic pulsatile flow of third grade hybrid nanofluid in a porous channel with Ohmic heating and thermal radiation effects, Physics of Fluids, 34: 013105, 2022, https://doi.org/10.1063/5.0074894
22. Radhakrishnamacharya G., Maiti M.K., Heat transfer to pulsatile flow in a porous channel, International Journal of Heat and Mass Transfer, 20(2): 171–173, 1977, https://doi.org/10.1016/0017-9310%2877%2990009-6
23. Srinivas S., Kumar C.K., Reddy A.S., Pulsating flow of Casson fluid in a porous channel with thermal radiation, chemical reaction and applied magnetic field, Nonlinear Analysis: Modelling and Control, 23(2): 213–233, 2018, https://doi.org/10.15388/NA.2018.2.5
24. Wang C.-Y., Pulsatile flow in a porous channel, Journal of Applied Mechanics, 38(2): 553–555, 1971, https://doi.org/10.1115/1.3408822
25. Datta N., Dalal D.C., Mishra S.K., Unsteady heat transfer to pulsatile flow of a dusty viscous incompressible fluid in a channel, International Journal of Heat and Mass Transfer, 36(7): 1783–1788, 1993, https://doi.org/10.1016/S0017-9310%2805%2980164-4
26. Horng T.-L., Lin W.-L., Liauh C.-T., Shih T.-C., Effects of pulsatile blood flow in large vessels on thermal dose distribution during thermal therapy , Medical Physics, 34(4): 1312–1320, 2007, https://doi.org/10.1118/1.2712415
27. Kumar C.K., Srinivas S., Pulsating hydromagnetic flow of Casson fluid in a vertical channel filled with non-Darcian porous medium, Heat Transfer, 50(6): 5225–5239, 2021, https://doi.org/10.1002/htj.22121
28. Sankar D.S., A two-fluid model for pulsatile flow in catheterized blood vessels, International Journal of Non-Linear Mechanics, 44(4): 337–351, 2009, https://doi.org/10.1016/j.ijnonlinmec.2008.12.008
29. Shawky H.M., Pulsatile flow with heat transfer of dusty magnetohydrodynamic Ree-Eyring fluid through a channel, Heat Mass Transfer, 45: 1261–1269, 2009, https://doi.org/10.1007/s00231-009-0502-0
30. Srinivas S., Kumar C.K., Reddy A.S., Dufour and Soret effects on pulsatile hydromagnetic flow of Casson fluid in a vertical non-Darcian porous space, Nonlinear Analysis: Modelling and Control, 27(4): 669–683, 2022, https://doi.org/10.15388/namc.2022.27.26678
31. Thamizharasan T., Reddy A.S., Pulsating hydromagnetic flow of Au-blood Jeffrey nanofluid in a chan¬nel with Joule heating and viscous dissipation, Nanoscience and Technology: An International Journal, 13(2): 1–13, 2022, https://doi.org/10.1615/NanoSciTechnolIntJ.2022039247
32. Wang X., Qiao Y., Qi H., Xu H., Numerical study of pulsatile non-Newtonian blood flow and heat transfer in small vessels under a magnetic field, International Communications in Heat and Mass Transfer, 133: 105930, 2022, https://doi.org/10.1016/j.icheatmasstransfer.2022.105930
2. Kumar B., Srinivas S., Unsteady hydromagnetic flow of Eyring-Powell nanofluid over an inclined permeable stretching sheet with Joule heating and thermal radiation, Journal of Applied and Computational Mechanics, 6(2): 259–270, 2019, https://doi.org/10.22055/jacm.2019.29520.1608
3. Waqas H., Naeem H., Manzoor U., Sivasankaran S., Alharbi A.A., Alshomrani A.S., Muhammad T., Impact of electro-magneto-hydrodynamics in radiative flow of nanofluids between two rotating plates, Alexandria Engineering Journal, 61(12): 10307–10317, 2022, https://doi.org/10.1016/j.aej.2022.03.059
4. Alsaedi A., Hayat T., Qayyum S., Yaqoob R., Eyring-Powell nanofluid flow with nonlinear mixed convection: Entropy generation minimization, Computer Methods and Programs in Biomedicine, 186: 105183, 2020, https://doi.org/10.1016/j.cmpb.2019.105183
5. Buongiorno J., Convective transport in nanofluids, Journal of Heat Transfer, 128 (3): 240–250, 2006, https://doi.org/10.1115/1.2150834
6. Hayat T., Sajjad R., Muhammad T., Alsaedi A., Ellahi R., On MHD nonlinear stretching flow of Powell-Eyring nanomaterial, Results in Physics, 7: 535–543, 2017, https://doi.org/10.1016/j.rinp.2016.12.039
7. Kumar C.K., Srinivas S., Reddy A.S., MHD pulsating flow of Casson nanofluid in a vertical porous space with thermal radiation and Joule heating, Journal of Mechanics, 36(4): 535–549, 2020, doi: 10.1017 /jmech.2020.5.
8. Mallick B., Misra J.C., Peristaltic flow of Eyring-Powell nanofluid under the action of an electromag¬netic field, Engineering Science and Technology, an International Journal, 22(1): 266–281, 2019, https://doi.org/10.1016/j.jestch.2018.12.001
9. Sheikholeslami M., Chamkha A.J., Rana P., Moradi R., Combined thermophoresis and Brownian motion effects on nanofluid free convection heat transfer in an L-shaped enclosure, Chinese Journal of Physics, 55(6): 2356–2370, 2017, https://doi.org/10.1016/j.cjph.2017.09.011
10. Shehzad N., Zeeshan A., Ellahi R., Vafai K., Convective heat transfer of nanofluid in a wavy channel: Buongiorno’s mathematical model, Journal of Molecular Liquids, 222: 446–455, 2016, https://doi.org/10.1016/j.mo lliq.2016.07.052.
11. Hayat T., Shafiq A., Alsaedi A., Asghar S., Effect of inclined magnetic field in flow of third grade fluid with variable thermal conductivity, AIP Advances, 5: 087108, 2015, https://doi.org/10.1063/1.4928321
12. Kumar C.K., Srinivas S., Simultaneous effects of thermal radiation and chemical reaction on hydromagnetic pulsatile flow of a Casson fluid in a porous space, Engineering Transactions, 65(3): 461–481, 2017.
13. Acharya N., Maity S., Kundu P.K., Influence of inclined magnetic field on the flow of condensed nanomaterial over a slippery surface: the hybrid visualization, Applied Nanoscience, 10: 633–647, 2020. https://doi.org/10.1007/s13204-019-01123-0
14. Khan A.A., Naeem S., Ellahi R., Sait S.M., Vafai K., Dufour and Soret effects on Darcy-Forchheimer flow of second-grade fluid with the variable magnetic field and thermal conductivity, International Journal of Numerical Methods for Heat & Fluid Flow, 30(9): 4331–4347, 2020, https://doi.org/10.1108/HFF-11-2019-0837
15. Ahmed S.E., Elshehabey H.M., Oztop H.F., Natural convection of three-dimensional non-Newtonian nanofluids with Marangoni effects and inclined magnetic fields, International Communications in Heat and Mass Transfer, 137: 106288, 2022, https://doi.org/10.1016/j.icheatmasstransfer.2022.106288
16. Kaladhar K., Reddy K.M., Srinivasacharya D., Inclined magnetic field, thermal radiation, and Hall current effects on mixed convection flow between vertical parallel plates, Journal of Heat Transfer, 141(10): 102501, 2019, https://doi.org/10.1115/1.4044391
17. Nath R., Murugesan K., Impact of nanoparticle shape on thermo-solutal buoyancy induced lid-driven-¬cavity with inclined magnetic-field, Propulsion and Power Research, 11(1): 97–117, 2022, https://doi.org/10.1016/j jppr.2022.01.002.
18. Noreen S., Qasim M., Peristaltic flow with inclined magnetic field and convective boundary conditions, Applied Bionics and Biomechanics, 11 (1–2): 61–67, 2014, https://doi.org/10.1155/2014/426217
19. Bianco V., Trubatch A.D., Wei H., Yecko P., Quantifying volume loss of a magnetically localized ferrofluid bolus in pulsatile pipe flow, Journal of Magnetism and Magnetic Materials, 524: 167595, 2021, https://doi.org/10.1016/j.jmmm.2020.167595
20. Cheng Z., Jelly T.O., Illingworth S.J., Marusic I., Ooi A.S.H., Forcing frequency effects on turbulence dynamics in pulsatile pipe flow, International Journal of Heat and Fluid Flow, 82: 108538, 2020, https://doi.org/10.1016/j.ijheat%EF%AC%82uid%EF%AC%82ow.2020.108538
21. Govindarajulu K., Reddy A.S., Magnetohydrodynamic pulsatile flow of third grade hybrid nanofluid in a porous channel with Ohmic heating and thermal radiation effects, Physics of Fluids, 34: 013105, 2022, https://doi.org/10.1063/5.0074894
22. Radhakrishnamacharya G., Maiti M.K., Heat transfer to pulsatile flow in a porous channel, International Journal of Heat and Mass Transfer, 20(2): 171–173, 1977, https://doi.org/10.1016/0017-9310%2877%2990009-6
23. Srinivas S., Kumar C.K., Reddy A.S., Pulsating flow of Casson fluid in a porous channel with thermal radiation, chemical reaction and applied magnetic field, Nonlinear Analysis: Modelling and Control, 23(2): 213–233, 2018, https://doi.org/10.15388/NA.2018.2.5
24. Wang C.-Y., Pulsatile flow in a porous channel, Journal of Applied Mechanics, 38(2): 553–555, 1971, https://doi.org/10.1115/1.3408822
25. Datta N., Dalal D.C., Mishra S.K., Unsteady heat transfer to pulsatile flow of a dusty viscous incompressible fluid in a channel, International Journal of Heat and Mass Transfer, 36(7): 1783–1788, 1993, https://doi.org/10.1016/S0017-9310%2805%2980164-4
26. Horng T.-L., Lin W.-L., Liauh C.-T., Shih T.-C., Effects of pulsatile blood flow in large vessels on thermal dose distribution during thermal therapy , Medical Physics, 34(4): 1312–1320, 2007, https://doi.org/10.1118/1.2712415
27. Kumar C.K., Srinivas S., Pulsating hydromagnetic flow of Casson fluid in a vertical channel filled with non-Darcian porous medium, Heat Transfer, 50(6): 5225–5239, 2021, https://doi.org/10.1002/htj.22121
28. Sankar D.S., A two-fluid model for pulsatile flow in catheterized blood vessels, International Journal of Non-Linear Mechanics, 44(4): 337–351, 2009, https://doi.org/10.1016/j.ijnonlinmec.2008.12.008
29. Shawky H.M., Pulsatile flow with heat transfer of dusty magnetohydrodynamic Ree-Eyring fluid through a channel, Heat Mass Transfer, 45: 1261–1269, 2009, https://doi.org/10.1007/s00231-009-0502-0
30. Srinivas S., Kumar C.K., Reddy A.S., Dufour and Soret effects on pulsatile hydromagnetic flow of Casson fluid in a vertical non-Darcian porous space, Nonlinear Analysis: Modelling and Control, 27(4): 669–683, 2022, https://doi.org/10.15388/namc.2022.27.26678
31. Thamizharasan T., Reddy A.S., Pulsating hydromagnetic flow of Au-blood Jeffrey nanofluid in a chan¬nel with Joule heating and viscous dissipation, Nanoscience and Technology: An International Journal, 13(2): 1–13, 2022, https://doi.org/10.1615/NanoSciTechnolIntJ.2022039247
32. Wang X., Qiao Y., Qi H., Xu H., Numerical study of pulsatile non-Newtonian blood flow and heat transfer in small vessels under a magnetic field, International Communications in Heat and Mass Transfer, 133: 105930, 2022, https://doi.org/10.1016/j.icheatmasstransfer.2022.105930
