Magnetohydrodynamic flow of Casson fluid through an oscillatory stretching sheet an unsteady and incompressible condition
Hamdullah Khan
Department of Mathematics and Statistics, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan
Search for more papers by this authorCorresponding Author
Waris Khan
Department of Mathematics and Statistics, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan
Correspondence
Waris Khan, Department of Mathematics and Statistics, Hazara University, Mansehra, Khyber Pakhtunkhwa, 21120, Pakistan.
Email: [email protected]
Maria Altaib Badawi, Department of Computer Science and Information College of Science at Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
Email: [email protected]
Search for more papers by this authorYasser Elmasry
Department of Mathematics - College of Science, King Khalid University, Abha, Saudi Arabia
Search for more papers by this authorCorresponding Author
Maria Altaib Badawi
Department of Computer Science and Information College of Science Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
Correspondence
Waris Khan, Department of Mathematics and Statistics, Hazara University, Mansehra, Khyber Pakhtunkhwa, 21120, Pakistan.
Email: [email protected]
Maria Altaib Badawi, Department of Computer Science and Information College of Science at Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
Email: [email protected]
Search for more papers by this authorAdel Thaljaoui
Department of Computer Science and Information College of Science Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
Search for more papers by this authorHamdullah Khan
Department of Mathematics and Statistics, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan
Search for more papers by this authorCorresponding Author
Waris Khan
Department of Mathematics and Statistics, Hazara University, Mansehra, Khyber Pakhtunkhwa, Pakistan
Correspondence
Waris Khan, Department of Mathematics and Statistics, Hazara University, Mansehra, Khyber Pakhtunkhwa, 21120, Pakistan.
Email: [email protected]
Maria Altaib Badawi, Department of Computer Science and Information College of Science at Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
Email: [email protected]
Search for more papers by this authorYasser Elmasry
Department of Mathematics - College of Science, King Khalid University, Abha, Saudi Arabia
Search for more papers by this authorCorresponding Author
Maria Altaib Badawi
Department of Computer Science and Information College of Science Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
Correspondence
Waris Khan, Department of Mathematics and Statistics, Hazara University, Mansehra, Khyber Pakhtunkhwa, 21120, Pakistan.
Email: [email protected]
Maria Altaib Badawi, Department of Computer Science and Information College of Science at Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
Email: [email protected]
Search for more papers by this authorAdel Thaljaoui
Department of Computer Science and Information College of Science Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
Search for more papers by this authorAbstract
The effectiveness of an unstable, incompressible, electrically conducting Casson fluid that spontaneously passes over a starched sheet of variable heat, mass movement, with a steady magnetic field, and chemical reaction field is examined in this paper. Using the appropriate similarity transformation to solve the governing equations of the flow model non-dimensional mathematically. As the magnetic parameter increased, it was observed that the velocity profile decreased while the thermal profile compacted. With an increasing electric field parameter and a decreasing unstable field parameter, the velocity profile has dropped. The magnetic field, Schmidt number, and electric field parameter increase the Skin friction coefficient while the Casson parameter decreases. Because of the rising Schmidt number, Brownian motion and thermophoretic characteristics, the local Nusselt number has decreased. Moreover, heat profile has decreased while the velocity profile has dropped in response to an augmenting magnetic parameter. While as higher Schmidt number reduces the thermal profile; however, it causes the thermophoresis, thermal radiation and Brownian motion characteristics to increase.
CONFLICT OF INTEREST STATEMENT
The authors declare no conflicts of interest.
Open Research
DATA AVAILABILITY STATEMENT
On reasonable request, the corresponding author will provide the data that support the study's conclusions.
REFRENCES
- 1Crane, L.J.: Flow past a stretching plate. ZAMP 21(4), 645–647 (1970).
- 2Khan, W., Pop, I.: Boundary-layer flow of a nanofluid past a stretching sheet. Int. J. Heat Mass Transfer 53(11–12), 2477–2483 (2010).
- 3Goud, B.S., Kumar, P.P., Malga, B.S.: Effect of heat source on an unsteady MHD free convection flow of Casson fluid past a vertical oscillating plate in porous medium using finite element analysis. Partial Differ. Equ. Appl. Math. 2, 100015 (2020).
10.1016/j.padiff.2020.100015 Google Scholar
- 4Ijaz Khan, M., Alzahrani, F.: Activation energy and binary chemical reaction effect in nonlinear thermal radiative stagnation point flow of Walter-B nanofluid: Numerical computations. Int. J. Mod. Phys. B 34(13), 2050132 (2020).
- 5Butt, A., Tufail, M., Ali, A.: Three-dimensional flow of a magnetohydrodynamic Casson fluid over an unsteady stretching sheet embedded into a porous medium. J. Appl. Mech. Tech. Phys. 57(2), 283–292 (2016).
- 6Das, B., Batra, R.: Secondary flow of a Casson fluid in a slightly curved tube. Int. J. Non-Linear Mech. 28(5), 567–577 (1993).
- 7Hayat, T., Shehzad, S., Alsaedi, A., Alhothuali, M.: Mixed convection stagnation point flow of Casson fluid with convective boundary conditions. Chin. Phys. Lett. 29(11), 114704 (2012).
- 8Raju, C., Sandeep, N., Sugunamma, V., Babu, M.J., Reddy, J.R.: Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface. Eng. Sci. Technol. Int. J. 19(1), 45–52 (2016).
- 9Ezaier, Y., Hader, A., Latif, A.: Significance of deposition and diffusion retention on the performance of the composite membrane. Waves Random Complex Media 10, 2079758–2079778 (2022).
- 10Sandeep, N., Koriko, O.K., Animasaun, I.L.: Modified kinematic viscosity model for 3D-Casson fluid flow within boundary layer formed on a surface at absolute zero. J. Mol. Liq. 221, 1197–1206 (2016).
- 11Kumar, G., Rizvi, S.: Casson Fluid Flow Past on Vertical Cylinder in the Presence of Chemical Reaction and Magnetic Field. Appl. Appl. Math. 16(1), 28 (2021).
- 12Rajput, U., Kumar, S.: Rotation and radiation effects on MHD flow past an impulsively started vertical plate with variable temperature. Int. J. Math. Anal. 5(24), 1155–1163 (2011).
- 13Rajput, U., Kumar, G.: Unsteady MHD flow past an impulsively started inclined plate with variable temperature and mass diffusion in the presence of Hall current. Appl. Appl. Math. 11(2), 13 (2016).
- 14Skelland, A.H.P.: Non-Newtonian Flow and Heat Transter, John Wiley and Sons Inc. (1967).
- 15Kataria, H., Patel, H.: Heat and mass transfer in magnetohydrodynamic (MHD) Casson fluid flow past over an oscillating vertical plate embedded in porous medium with ramped wall temperature. Propuls. Power Res. 7(3), 257–267 (2018).
- 16Reddy, M.G.: Thermal radiation and chemical reaction effects on MHD mixed convective boundary layer slip flow in a porous medium with heat source and Ohmic heating. Eur. Phys. J. Plus. 129(3), 1–17 (2014).
- 17Jonnadula, M., Polarapu, P., Reddy, G.: Influence of thermal radiation and chemical reaction on MHD flow, heat and mass transfer over a stretching surface. Proc. Eng. 127, 1315–1322 (2015).
- 18Nadeem, S., Faraz, N.: Thin film flow of a second grade fluid over a stretching/shrinking sheet with variable temperature-dependent viscosity. Chin. Phys. Lett. 27(3), 034704 (2010).
- 19Nadeem, S., Zaheer, S., Fang, T.: Effects of thermal radiation on the boundary layer flow of a Jeffrey fluid over an exponentially stretching surface. Numer. Algorithms 57(2), 187–205 (2011).
- 20Hayat, T., Qasim, M.: Radiation and magnetic field effects on the unsteady mixed convection flow of a second grade fluid over a vertical stretching sheet. Int. J. Numer. Methods Fluids 66(7), 820–832 (2011).
- 21Nadeema, S., Hayat, T., Malika, M.Y., Rajputa, S.A.: Thermal radiation effects on the flow by an exponentially stretching surface: A series solution. Z. Naturforsch. 65(6–7), 495–503 (2010).
10.1515/zna-2010-6-703 Google Scholar
- 22Nadeem, S., Hussain, A., Khan, M.: HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet. Commun. Nonlinear Sci. Numer. Simul. 15(3), 475–481 (2010).
- 23Hari Krishna, Y., Reddy, G.V.R., Makinde, O.D.: Chemical reaction effect on MHD flow of Casson fluid with porous stretching sheet. In: Defect and Diffusion Forum, vol. 389, pp. 100–109. Trans Tech Publications, Switzerland (2018).
- 24Kasaeian, A., et al.: Nanofluid flow and heat transfer in porous media: A review of the latest developments. Int. J. Heat Mass Transfer 107, 778–791 (2017).
- 25Tamoor, M., Waqas, M., Khan, M.I., Alsaedi, A., Hayat, T.: Magnetohydrodynamic flow of Casson fluid over a stretching cylinder. Results Phys. 7, 498–502 (2017).
- 26Hayat, T., Waqas, M., Khan, M.I., Alsaedi, A.: Analysis of thixotropic nanomaterial in a doubly stratified medium considering magnetic field effects. Int. J. Heat Mass Transfer 102, 1123–1129 (2016).
- 27Hayat, T., Waqas, M., Khan, M.I., Alsaedi, A.: Impacts of constructive and destructive chemical reactions in magnetohydrodynamic (MHD) flow of Jeffrey liquid due to nonlinear radially stretched surface. J. Mol. Liq. 225, 302–310 (2017).
- 28Venkata Ramudu, A.C., Anantha Kumar, K., Sugunamma, V., Sandeep, N.: Heat and mass transfer in MHD Casson nanofluid flow past a stretching sheet with thermophoresis and Brownian motion. Heat Transfer 49(8), 5020–5037 (2020).
- 29Khanafer, K., Vafai, K., Lightstone, M.: Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int. J. Heat Mass Transfer 46(19), 3639–3653 (2003).
- 30Kakaç, S., Pramuanjaroenkij, A.: Review of convective heat transfer enhancement with nanofluids. Int. J. Heat Mass Transfer 52(13–14), 3187–3196 (2009).
- 31Nield, D., Kuznetsov, A.: The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int. J. Heat Mass Transfer 52(25–26), 5792–5795 (2009).
- 32Yirga, Y., Tesfay, D.: Heat and mass transfer in MHD flow of nanofluids through a porous media due to a permeable stretching sheet with viscous dissipation and chemical reaction effects. Int. J. Mech. Aero. Indust. Mechatron Engin. 9(5), 1–8 (2015).
- 33Hayat, T., Nawaz, M., Obaidat, S.: Axisymmetric magnetohydrodynamic flow of micropolar fluid between unsteady stretching surfaces. Appl. Math. Mech. 32(3), 361–374 (2011).
10.1007/s10483-011-1421-8 Google Scholar
- 34Barik, R.N., Dash, G.C.: Thermal radiation effect on an unsteady magnetohydrodynamic flow past inclined porous heated plate in the presence of chemical reaction and viscous dissipation. Appl. Math. Comput. 226, 423–434 (2014).
- 35Bhattacharyya, K.: MHD stagnation-point flow of Casson fluid and heat transfer over a stretching sheet with thermal radiation. J. Thermodyn., 1–9 (2013), https://doi.org/10.1155/2013/169674.
10.1155/2013/169674 Google Scholar
- 36Piazza, R., Parola, A.: Thermophoresis in colloidal suspensions. J. Phys.: Condens. Matter. 20(15), 153102 (2008).