Casson Fluid Flow Past a Shrinking Surface with Heat and Mass Transfers
Abstract
In this study, we have numerically investigated the heat and mass transfers behaviour of Casson fluid flow past a porous shrinking sheet in existence of a magnetic field, thermal radiation, and suction or blowing at the surface. Applying suitable similarity transformations, the leading partial nonlinear differential equations of mass, flow, and heat transfer are converted into solvable ordinary differential equations, which can then be solved numerically with the help of the MATLAB bvp4c scheme. We have analyzed and shown graphically the implications of several non-dimensional controlling factors on the profiles of temperature, concentration, and velocity. Additionally, the Sherwood, Nusselt, and Skin friction for Casson fluids are examined and tabulated. The current study's findings for Casson fluid exhibit great consistency with previous research under specific circumstances.
Downloads
References
I.J. Grubka, and K.M. Bpbba, "Heat transfer characteristics of a continuous stretching surface with variable temperature," ASME J. Heat Transfer, 107, 248-250 (1985). https://doi.org/10.1115/1.3247387
W.H.H. Banks, "Similarity solutions of boundary layer equations for a stretching wall," J. Mech. Theor. Appl. 2, 375-392 (1983).
L.J. Crane, "Flow past a stretching plate," J. Appl. Math. Phys, (ZAMP), 21, 645-647 (1970). https://doi.org/10.1007/BF01587695
E. Magyari, and B. Keller, "Exact solution for self-similar boundary layer flows induced by permeable stretching walls," Eur. J. Mech. B/Fluids, 19, 109-122 (2000). https://doi.org/10.1016/S0997-7546(00)00104-7
S. Liao, and I. Pop, "On explicit analytic solutions of boundary layer equations about a flows in a porous medium or for a stretching wall," Int. J. Heat and Mass Transfer, 47, 75-85 (2004). https://doi.org/10.1016/S0017-9310(03)00405-8
C.Y. Wang, "Liquid film on an unsteady stretching sheet," Quart. Appl. Math. 48, 601-610 (1990). https://doi.org/10.1090/qam/1079908
M. Miklavcic, and C.Y. Wang, "Viscous flow due to a shrinking sheet," Quart. Appl. Math. 64, 283-290 (2006). https://doi.org/10.1090/S0033-569X-06-01002-5
T. Fang, and J. Zhang, "Closed-form exact solution of MHD viscous flow over a shrinking sheet," Commun. Nonlinear Sci. Num. Simulat. 14, 2853–2857 (2009). https://doi.org/10.1016/j.cnsns.2008.10.005
C.S.K. Raju, G. Neeraja, P.A. Dinesh, K. Vidya, and B.R. Kumar, "MHD Casson fluid in a suspension of convective conditions and cross diffusion across a surface of paraboloid of revolution," Alexandria Eng. J. 57(4), 3615-3622 (2018). https://doi.org/10.1016/j.aej.2017.11.022
M. Prameela, K. Gangadhar, and G.J. Reddy, "MHD free convective non-Newtonian Casson fluid flow over an oscillating vertical plate," Partial Differ. Equ. Appl. Math. 5, 100366 (2022). https://doi.org/10.1016/j.padiff.2022.100366
M.V. Krishna, "Chemical reaction, heat absorption and Newtonian heating on MHD free convective Casson hybrid nanofluids past an infinite oscillating vertical porous plate," Int. Commun. Heat Mass Transf. 138, 106327 (2022). https://doi.org/10.1016/j.icheatmasstransfer.2022.106327
M.S. Aghighi, A. Ammar, and H. Masoumi, "Double-diffusive natural convection of Casson fluids in an enclosure," Int. J. Mech. Sci. 236, 107754 (2022). https://doi.org/10.1016/j.ijmecsci.2022.107754
F. Hussain, M. Nazeer, M. Altanji, A. Saleem, and M.M. Ghafar, "Thermal analysis of Casson rheological fluid with gold nanoparticles under the impact of gravitational and magnetic forces," Case Stud. Therm. Eng. 28, 101433 (2021). https://doi.org/10.1016/j.csite.2021.101433
P.P. Humane, V.S. Patil, A.B. Patil, MD. Shamshuddin, and G.R. Rajput, "Dynamics of multiple slip boundaries effect on MHD Casson-Williamson double-diffusive nanofluid flow past an inclined magnetic stretching sheet," Proc. Inst. Mech. Eng. Part E: J. Process Mech. Eng. 236(5), (2022). https://doi.org/10.1177/09544089221078153
M. Awais, T. Salahuddin, and S. Muhammad, "Evaluating the thermo-physical characteristics of non-Newtonian Casson fluid with enthalpy change," Thermal Science and Engineering Progress, 42, 101948 (2023). https://doi.org/10.1016/j.tsep.2023.101948
E.N. Maraj, U. Faizan, and S. Shaiq, "Influence of joule heating and partial slip on casson nanofluid transport past a nonlinear stretching planar sheet," in: International Conference on Applied and Engineering Mathematics, ICAEM, (Taxila, Pakistan, 2019), pp.31 36. https://doi.org/10.1109/ICAEM.2019.8853731
K. Bhattacharyya, M.S. Uddin, and G.C. Layek, "Exact solution for thermal boundary layer in casson fluid flow over permeable shrinking sheet with variable wall temperature and thermal radiation," Alexandria Engineering Journal, 55, 1703-1712 (2016). https://doi.org/10.1016/j.aej.2016.03.010
D. Dey, and B. Chutia, "Dusty nanofluid flow with bioconvection past a vertical stretching surface," 34(6), 375-380 (2022). Journal of King Saud University- Engineering Sciences. https://doi.org/10.1016/j.jksues.2020.11.001
D. Dey, and R. Borah, "Stability analysis on dual solutions of second-grade fluid flow with heat and mass transfers over a stretching sheet," International Journal of Thermofluid Science and Technology, 8(2), 080203 (2021). https://doi.org/10.36963/IJTST.2021080203
D. Dey, and B. Chutia, "Modelling of multi-phase fluid flow with volume fraction past a permeable stretching vertical cylinder and its numerical study," Latin American Applied Research, 51(3), 165-171 (2021). https://doi.org/10.52292/j.laar.2021.604
Y. Khan, A. Hussain, and N. Faraz, "Unsteady linear viscoelastic fluid model over a stretching/shrinking sheet in the region of stagnation point flows," Sci. Iran. 19, 1541–1549 (2012). https://doi.org/10.1016/j.scient.2012.10.019
T. Hayat, T. Javed, and M. Sajid, "Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface," Phys. Lett. A, 372, 3264–3273 (2008). https://doi.org/10.1016/j.physleta.2008.01.069
T. Hayat, Z. Abbas, and N. Ali, "MHD flow and mass transfer of a upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species," Phys. Lett. A, 372, 4698–4704 (2008). https://doi.org/10.1016/j.physleta.2008.05.006
T. Hayat, S. Iram, T. Javed, and S. Asghar, "Shrinking flow of second grade fluid in a rotating frame: an analytic solution," Commun. Nonlinear Sci. Num. Simul. 15, 2932–2941 (2010). https://doi.org/10.1016/j.cnsns.2009.11.030
G.R. Rajput, M.D. Shamshuddin, Sulyman, and O. Salawu, "Thermosolutal convective non-Newtonian radiative Casson fluid transport over a vertical plate propagated by Arrhenius kinetics with heat source/sink," Heat Transfer, 50(3), 2829-2848 (2021). https://doi.org/10.1002/htj.22008
M.D. Shamshuddin, and W. Ibrahim, "Finite element numerical technique for magneto-micropolar nanofluid flow filled with chemically reactive Casson fluid between parallel plates subjected to rotatory system with electrical and Hall currents," Int. J. Model. Simul. 42(6), 985-1004 (2022). https://doi.org/10.1080/02286203.2021.2012634
W. Alghamdi, T. Gul, M. Nullah, A. Rehman, S. Nasir, A. Saeed, and E. Bonyah, "Boundary layer stagnation point flow of the casson hybrid nanofluid over an unsteady stretching surface," AIP Advances, 11, 015016 (2020). https://doi.org/10.1063/5.0036232
D. Dey, and R. Borah, "Dual solutions of boundary layer flow with heat and mass transfers over an exponentially shrinking cylinder: stability analysis," Latin American Applied Research, 50(4), 247–253 (2020). https://doi.org/10.52292/j.laar.2020.535
Z. Shah, P. Kumam, and W. Deebani, "Radiative MHD casson nanofluid flow with activation energy and chemical reaction over past nonlinearly stretching surface through entropy generation," Scientific Reports, 10(1), 4402 (2020). https://doi.org/10.1038/s41598-020-61125-9
S. Nadeem, R. Mehmood, and N.S. Akbar, "Nanoparticle analysis for non-orthogonal stagnation point flow of a third order fluid towards a stretching surface," J. Comput. Theor. Nanosci. 10, 2737–2747 (2013). https://doi.org/10.1166/jctn.2013.3274
S. Nadeem, R.U. Haq, Z.H. Khan, "Numerical study of MHD boundary layer flow of a Maxwell fluid past a stretching sheet in the presence of nanoparticles," J. Taiwan Inst. Chem. Eng. 45, 121–126 (2014). https://doi.org/10.1016/j.jtice.2013.04.006
H. Rosali, A. Ishak, and I. Pop, "Micropolar fluid flow towards a stretching/shrinking sheet in a porous medium with suction," Int. Commun. Heat Mass Transf. 39, 826–829 (2012). https://doi.org/10.1016/j.icheatmasstransfer.2012.04.008
N.A. Yacob, and A. Ishak, "Micropolar fluid flow over a shrinking sheet," Meccanica, 47, 293–299 (2012). https://doi.org/10.1007/s11012-011-9439-8
N.A. Yacob, A. Ishak, and I. Pop, "Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet in a micropolar fluid," Comput. Fluids, 47, 16–21 (2011). https://doi.org/10.1016/j.compfluid.2011.01.040
A. Ishak, Y.Y. Lok, and I. Pop, "Non-Newtonian power-law fluid flow past a shrinking sheet with suction," Chem. Eng. Commun. 199, 142–150 (2012). https://doi.org/10.1080/00986445.2011.578696
A. Ishak, Y.Y. Lok, and I. Pop, "Stagnation-point flow over a shrinking sheet in a micropolar fluid," Chem. Eng. Commun. 197, 1417–1427 (2010). https://doi.org/10.1080/00986441003626169
D. Dey, R. Borah, and A.S. Khound, "Stability analysis on dual solutions of MHD Casson fluid flow with thermal and chemical reaction over a permeable elongating sheet," Heat Transfer, 51(4), 3401-3417 (2022). https://doi.org/10.1002/htj.22456
T. Sarkar, S. Reza‐E‐Rabbi, S.M. Arifuzzaman, R. Ahmed, M.S. Khan, and S.F. Ahmmed, "MHD radiative flow of Casson and Williamson nanofluids over an inclined cylindrical surface with chemical reaction effects," Int. J. Heat Technol. 37, 1117‐1126 (2019). https://doi.org/10.18280/ijht.370421
K. Bhattacharyya, T. Hayat, and A. Ahmed, "Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer," Chin. Phys. B, 22(2), 024702 (2013). https://doi.org/10.1088/1674-1056/22/2/024702
D. Dey, R.K. Das, R. Borah, "A Simulation of Nanofluid Flow with Variable Viscosity and Thermal Conductivity Over a Vertical Stretching Surface," in: Emerging Technologies in Data Mining and Information Security. Lecture Notes in Networks and Systems, vol. 491, edited by P. Dutta, S. Chakrabarti, A. Bhattacharya, S. Dutta, V. Piuri, (Springer, Singapore, 2023). https://doi.org/10.1007/978-981-19-4193-1_18
S. Pramanik, "Casson Fluid Flow and Heat Transfer past an Exponentially Porous Stretching Sheet in Presence of Thermal Radiation," Ain Shams Engineering Journal, 5(1), 205-212 (2014). https://doi.org/10.1016/j.asej.2013.05.003
A.S. Oke, W.N. Mutuku, M. Kimathi, and I.L. Animasaun, "Insight into the dynamics of non-newtonian casson fluid over a rotating non-uniform surface subject to coriolis force," Nonlinear Engineering, 9(1), 398-411 (2020). https://doi.org/10.1515/nleng-2020-0025
D. Dey, and M. Hazarika, "Entropy generation of hydro-magnetic stagnation point flow of micropolar fluid with energy transfer under the effect of uniform suction / injection," Latin American Applied Research, 50(3), 209–214 (2020). https://doi.org/10.52292/j.laar.2020.206
Copyright (c) 2024 Rajesh Kumar Das, Debasish Dey
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
