Effect of Arrhenius Activation Energy in MHD Micropolar Nanofluid Flow Along a Porous Stretching Sheet with Viscous Dissipation and Heat Source
Abstract
A numerical study of the heat and mass transfer of a micropolar nanofluid flow over a stretching sheet embedded in a porous medium is carried out in this investigation. The main objective of this work is to investigate the influence of Arrhenius activation energy, heat source and viscous dissipation on the fluid velocity, microrotation, temperature, and concentration distribution. The equations governing the flow are transformed into ordinary differential equations using appropriate similarity transformations and solved numerically using bvp4c solver in MATLAB. Graphs are plotted to study the influences of important parameters such as magnetic parameter, porosity parameter, thermophoresis parameter, Brownian motion parameter, activation energy parameter and Lewis number on velocity, microrotation, temperature and concentration distribution. The graphical representation explores that the velocity of the liquid diminishes for increasing values of magnetic parameter, whereas the angular velocity increases with it. This study also reports that an enhancement of temperature and concentration distribution is observed for the higher values of activation energy parameter, whereas the Lewis number shows the opposite behavior. The effects of various pertinent parameters are exposed realistically on skin friction coefficient, Nusselt and Sherwood numbers via tables. A comparison with previous work is conducted, and the results show good agreement.
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References
A.C. Eringen, “Simple Microfluids,” International Journal of Engineering Science, 2(2), 205-217 (1964). https://doi.org/10.1016/0020-7225(64)90005-9
A.C. Eringem, “Theory of Micropolar Fluids,” Journal of Mathematics and Mechanics, 16(1), 1–18 (1966). http://dx.doi.org/10.1512/iumj.1967.16.16001
N.T. Eldabe, E.F. Elshehawey, M.E. Elbarbary, and N.S. Elgazery, “Chebyshev Finite Difference Method for MHD Flow of a Micropolar Fluid past a Stretching Sheet with Heat Transfer,” Journal of Applied Mathematics and Computation, 160, 437-450 (2005). https://doi.org/10.1016/j.amc.2003.11.013
N.T. Eldabe, and E.M.O. Mahmoud, “Chebyshev Finite Difference Method for Heat and Mass Transfer in a Hydromagnetic Flow of a Micropolar Fluid Past a Stretching Surface with Ohmic Heating and Viscous Dissipation,” Applied Mathematics and Computation, 177, 561-571 (2006). https://doi.org/10.1016/j.amc.2005.07.071
S. Nadeem, and A. Hussain, “MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method,” Appl. Math. Mech.-Engl. 30, 1569–1578 (2009). https://doi.org/10.1007/s10483-009-1208-6
K. Bhattacharyya, “Steady boundary layer flow and reactive mass transfer past an exponentially stretching surface in an exponentially moving free stream,” Journal of the Egyptian Mathematical Society, 20(3), 223-228 (2012). https://doi.org/10.1016/j.joems.2012.08.018.
R. Muhaimin, Kandasamy, and A.B. Khamis, “Effects of heat and mass transfer on nonlinear MHD boundary layer flow over a shrinking sheet in the presence of suction,” Applied Mathematics and Mechanics, 29, 1309–1317 (2008). https://doi.org/10.1007/s10483-008-1006-z
I.C. Mandal, and S. Mukhopadhyay, “Heat transfer analysis for fluid flow over an exponentially stretching porous sheet with surface heat flux in porous medium,” Ain Shams Engineering Journal, 4(1), 103-110 (2013). https://doi.org/10.1016/j.asej.2012.06.004.
E.M. Elbashbeshy, “Heat and mass transfer along a vertical plate with variable surface tension and concentration in the presence of the magnetic field,” International Journal of Engineering Science, 35, 515-522 (1997). https://doi.org/10.1016/S0020-7225(96)00089-4
I.A. Hassanien, and R.S.R. Gorla, “Heat transfer to a micropolar fluid from a non-isothermal stretching sheet with suction and blowing,” Acta Mechanica, 84, 191–199 (1990). https://doi.org/10.1007/BF01176097
D. Pal, and S. Chatterjee, “MHD mixed convection stagnation-point flow of a micropolar fluid in a porous medium towards a heated stretching sheet with thermal radiation,” Mathematical Modelling and Analysis, 17(4), 498-518 (2012). https://doi.org/10.3846/13926292.2012.706653
M.A. El-Aziz, “Viscous dissipation effect on mixed convection flow of a micropolar fluid over an exponentially stretching sheet,” Canadian Journal of Physics, 87(4), 359-368 (2009). https://doi.org/10.1139/P09-047
M. Hussain, M. Ashraf, S. Nadeem, and M. Khan, “Radiation effects on the thermal boundary layer flow of a micropolar fluid towards a permeable stretching sheet,” Journal of the Franklin Institute, 350(1), 194-210 (2013). https://doi.org/10.1016/j.jfranklin.2012.07.005
D. Pal, and G. Mandal, “Thermal radiation and MHD effects on boundary layer flow of micropolar nanofluid past a stretching sheet with non-uniform heat source/sink,” International Journal of Mechanical Sciences, 126, 308-318 (2017). https://doi.org/10.1016/j.ijmecsci.2016.12.023
L. Kumar, “Finite Element Analysis of Combined Heat and Mass Transfer in Hydromagnetic Micropolar Flow along a Stretching Sheet,” Computational Materials Science, 46, 841-848 (2009). http://dx.doi.org/10.1016/j.commatsci.2009.04.021
B.S. Goud, and M.M. Nandeppanavar, “Ohmic heating and chemical reaction effect on MHD flow of micropolar fluid past a stretching surface,” Partial Differential Equations in Applied Mathematics, 4, 100104 (2021). https://doi.org/10.1016/j.padiff.2021.100104
S.M. Atif, S. Hussain, and M. Sagheer, “Magnetohydrodynamic stratified bioconvective flow of micropolar nanofluid due to gyrotactic microorganisms,” AIP Advances, 9(2), 025208 (2019). https://doi.org/10.1063/1.5085742
C. Zemedu, and W. Ibrahim, “Nonlinear Convection Flow of Micropolar Nanofluid due to a Rotating Disk with Multiple Slip Flow,” Mathematical Problems in Engineering, 2020, 4735650 (2020). https://doi.org/10.1155/2020/4735650
I. Waini, A. Ishak, and I. Pop, “Radiative and magnetohydrodynamic micropolar hybrid nanofluid flow over a shrinking sheet with Joule heating and viscous dissipation effects,” Neural Comput & Applic, 34, 3783–3794 (2022). https://doi.org/10.1007/s00521-021-06640-0
B.K. Sharma, U. Khanduri, N.K. Mishra, and K.S. Mekheimer, “Combined effect of thermophoresis and Brownian motion on MHD mixed convective flow over an inclined stretching surface with radiation and chemical reaction,” International Journal of Modern Physics B, 37, 2350095 (2022). http://dx.doi.org/10.1142/S0217979223500959
M.M. Bhatti, M.H. Doranehgard, and R. Ellahi, “Electro‐magneto‐hydrodynamic Eyring‐Powell fluid flow through micro‐parallel plates with heat transfer and non‐Darcian effects,” Mathematical Methods in the Applied Sciences, 46(1), 11642-11656 (2022). http://dx.doi.org/10.1002/mma.8429
S.A. Khan, B. Ali, C. Eze, K.T. Lau, L. Ali, J. Chen, and J. Zhao, “Magnetic dipole and thermal radiation impacts on stagnation point flow of micropolar based nanofluids over a vertically stretching sheet: finite element approach,” Processes, 9(7), 1089 (2021). https://doi.org/10.3390/pr9071089
U. Khan, A. Zaib, I. Pop, S.A. Bakar, and A. Ishak, “Unsteady micropolar hybrid nanofluid flow past a permeable stretching/shrinking vertical plate,” Alexandria Engineering Journal, 61(12), 11337-11349 (2022). https://doi.org/10.1016/j.aej.2022.05.011
M.S. Kausar, A. Hussanan, M. Waqas, and M. Mamat, “Boundary layer flow of micropolar nanofluid towards a permeable stretching sheet in the presence of porous medium with thermal radiation and viscous dissipation,” Chinese Journal of Physics, 78(6), 435–452 (2022). http://dx.doi.org/10.1016/j.cjph.2022.06.027
S. Akbar, and M. Sohail, “Three Dimensional MHD Viscous Flow under the Influence of Thermal Radiation and Viscous Dissipation,” International Journal of Emerging Multidisciplinaries: Mathematics, 1(3), 106–117 (2022). https://doi.org/10.54938/ijemdm.2022.01.3.122
G.L. Devi, H. Niranjan, and S. Sivasankaran, “Effects of chemical reactions, radiation, and activation energy on MHD buoyancy induced nanofluid flow past a vertical surface,” Scientia Iranica, 29(1), 90-100 (2022). https://doi.org/10.24200/sci.2021.56835.4934
S. Li, K. Raghunath, A. Alfaleh, F. Ali, A. Zaib, M.I. Khan, S. M. ElDin, and V. Puneeth, “Effects of activation energy and chemical reaction on unsteady MHD dissipative Darcy–Forchheimer squeezed flow of Casson fluid over horizontal channel,” Scientific Reports, 13, 2666, (2023). https://doi.org/10.1038/s41598-023-29702-w
H. Dessie, “Effects of Chemical Reaction, Activation Energy and Thermal Energy on Magnetohydrodynamics Maxwell Fluid Flow in Rotating Frame,” Journal of Nanofluids, 10(1), 67–74 (2021). https://doi.org/10.1166/jon.2021.1767
A. Anjum, S. Masood, M. Farooq, N. Rafiq, and M.Y. Malik, “Investigation of binary chemical reaction in magnetohydrodynamic nanofluid flow with double stratification,” Adv. Mech. Eng. 13(5), (2021). https://doi.org/10.1177/16878140211016264
A.K. Gautam, A.K. Verma, K. Bhattacharyya, S. Mukhopadhyay, and A.J. Chamkha, “Impacts of activation energy and binary chemical reaction on MHD flow of Williamson nanofluid in Darcy–Forchheimer porous medium: a case of expanding sheet of variable thickness,” Waves in Random and Complex Media, (2021). https://doi.org/10.1080/17455030.2021.1979274
B. Saidulu, and K.S. Reddy, “Evaluation of Combined Heat and Mass Transfer in Hydromagnetic Micropolar Flow along a Stretching Sheet when Viscous Dissipation and Chemical Reaction Is Present,” Partial Differential Equations in Applied Mathematics, 7, 100467 (2023). https://doi.org/10.1016/j.padiff.2022.100467
S.U. Rehman, A. Mariam, A. Ullah, M.I. Asjad, M.Y. Bajuri, B.A. Pansera, and A. Ahmadian, “Numerical Computation of Buoyancy and Radiation Effects on MHD Micropolar Nanofluid Flow over a Stretching/Shrinking Sheet with Heat Source,” Case Studies in Thermal Engineering, 25, 100867 (2021). https://doi.org/10.1016/j.csite.2021.100867
D. Rees, and I. Pop, “Free convection boundary-layer flow of a micropolar fluid from a vertical flat plate,” IMA Journal of Applied Mathematics, 61(2), 179-197 (1998). https://doi.org/10.1093/imamat/61.2.179
L.J. Grubka, and K.M. Bobba, “Heat Transfer Characteristics of a Continuous, Stretching Surface with Variable Temperature”. ASME J. Heat Transfer, 107, 248-250 (1985). http://dx.doi.org/10.1115/1.3247387
M.A. Seddeek, and A.M. Salem, “Laminar mixed convection adjacent to vertical continuously stretching sheets with variable viscosity and variable thermal diffusivity,” Heat Mass Transf. 41, 1048–1055 (2005). http://dx.doi.org/10.1007/s00231-005-0629-6
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