Heat Generation Effect on 3D MHD Flow of Casson Fluid Via Porous Stretching/Shrinking Surface with Velocity Slip Condition
Abstract
There are extensive range of applications related to nuclear industry, industrial manufacturing, science and engineering processing, in which the boundary layer hydromagnetic motion of Casson liquids perform vital role. Casson liquid is a useful liquid in the nuclear industry for optimizing the design and operation of nuclear reactors. Researchers have investigated transfer of heat in liquid motions with linear stratification, which is a phenomenon where the temperature varies linearly with height, affecting various fields such as medical equipment, glass fiber production, electronic devices, polymer sheets, paper production, filaments, and medicine. However, the most discussion of heat transfer problems is to get numerical solutions of a comprehensive Casson liquid model with heat generation described by the BVP4 via shooting method. In this study, a new velocity slip boundary condition is applied at the stretching or shrinking surface. These conditions are grounded in the previously established Buongiorno model, providing a more practical and realistic approach compared to previous study. The time independent Gov. Eqs. changed into a set of couple non-linear ODEs with help of suitable similarity conversions. The equations are evaluating via R-K-F by help of MATLAB software programming.
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References
N. Casson, in: Rheology of disperse systems in Flow Equation for Pigment Oil Suspensions of the Printing Ink Type. Rheology of Disperse Systems, edited by C.C. Mill, (Pergamon Press, London, UK, 1959). pp. 84-102.
P. Barnoon, and D. Toghraie, “Numerical investigation of laminar flow and heat transfer of non-Newtonian nanofluid within a porous medium,” Powder Technology, 325, 78-91 (2018). https://doi.org/10.1016/j.powtec.2017.10.040
P.K. Kameswaran, S. Shaw, and P. Sibanda, “Dual solutions of Casson fluid flow over a stretching or shrinking sheet,” Sadhana, 39, 1573-1583 (2014). https://doi.org/10.1007/s12046-014-0289-7
U.S. Mahabaleshwar, G.P. Vanitha, and B.A. Souayeh, “Study of Casson Viscous Gas Flows and Heat Transfer Across a Linear Stretching/Shrinking Sheet by Considering Induced Slip, Mass Transpiration, Inclined Magnetic Force, and Radiation Effect,” BioNanoSci. 13, 1052–1063 (2023). https://doi.org/10.1007/s12668-023-01128-8
K.A. Duguma, O.D. Makinde, and L.G. Enyadene, “Stability Analysis of Dual Solutions of Convective Flow of Casson Nanofluid past a Shrinking/Stretching Slippery Sheet with Thermophoresis and Brownian Motion in Porous Media,” Journal of Mathematics, 2023, 1-25 (2023). https://doi.org/10.1155/2023/5954860
H. Himanshu, S.R. Mishra, A.K. Pandey, and Priya Bartwal, “Shape factor analysis in stagnation point flow of Casson nanofluid over a stretching/shrinking sheet using Cattaneo-Christov model,” Numerical Heat Transfer, Part B: Fundamentals, 1–17 (2023). https://doi.org/10.1080/10407790.2023.2265555
N. Vishnu Ganesh, Q.M. Al-Mdallal, R. Kalaivanan, and K. Reena, “Arrhenius kinetics driven nonlinear mixed convection flow of Casson liquid over a stretching surface in a Darcian porous medium,” Heliyon, 9(6), E16135 (2023). https://doi.org/10.1016/j.heliyon.2023.e16135
B.S. Goud, Y.D. Reddy, and Adnan, “Numerical Investigation of the Dynamics of Magnetized Casson Fluid Flow over a Permeable Wedge Subject to Dissipation and Thermal Radiations,” Surface Review and Latter, 31, 2450054 (2024). https://doi.org/10.1142/S0218625X24500549
K.U. Rehman, A.A. Khan, M.Y. Malik, and O.D. Makinde, “Thermophysical aspects of stagnation point magnetonanofluid flow yields by an inclined stretching cylindrical surface: a non-Newtonian fluid model,” J Braz. Soc. Mech. Sci. Eng. 39, 3669-3682 (2017). https://doi.org/10.1007/s40430-017-0860-3
S.A. Gaffar, V. Ramachandra Prasad, and B. Vijaya, Computational study of non‑Newtonian Eyring–Powell fluid from a vertical porous plate with biot number effects, J Braz. Soc. Mech. Sci. Eng. (2017) 1-35. https://doi.org/10.1007/s40430-017-0761-5
M. Imtiaz, T. Hayat, and A. Alsaedi, “Mixed convection flow of Casson nanofluid over a stretching cylinder with convective boundary conditions,” Advanced Powder Tech. 27, 2245-2256 (2016). https://doi.org/10.1016/j.apt.2016.08.011
M. Ramzan, M. Bilal, and J.D. Chung, “Influence of homogeneous-heterogeneous reactions on MHD 3D Maxwell fluid flow with Cattaneo-Christov heat flux and convective boundary condition,” J. Mole. Liq. 230, 415-422 (2017). https://doi.org/10.1016/j.molliq.2017.01.061
M.M. Bhatti, and M.M. Rashidi, “Effects of thermo-diffusion and thermal radiation on Williamson nanofluid over a porous shrinking/stretching sheet,” J. Mole. Liq. 221, 567-573 (2016). https://doi.org/10.1016/j.molliq.2016.05.049
G.M. Moatimid, and M.A. Hassan, “Convection instability of non-Newtonian Walter’s nanofluid along a vertical layer,” J. Egyptian Math. Soc. 25, 220-229 (2017). https://doi.org/10.1016/j.joems.2016.09.001
A. Rauf, M.K. Siddiq, F.M. Abbasi, M.A. Meraj, M. Ashraf, and S.A. Shehzad, “Influence of convective conditions on three dimensional mixed convective hydromagnetic boundary layer flow of Casson nanofluid,” J. Magn. Magnet. Mater. 416, 200-207 (2016). https://doi.org/10.1016/j.jmmm.2016.04.092
M. Adel, M.M. Khader, and Hijaz Ahmad, “MHD nanofluid flow and heat transfer caused by a stretching sheet that is heated convectively: An approximate solution using ADM,” Case Studies in Thermal Engineering, 60, 104683 (2024). https://doi.org/10.1016/j.csite.2024.104683
P.R. Sekhar, S. Sreedhar, S.M. Ibrahim, P.V. Kumar, and B. Omprakash, “Numerical investigation of heat radiation on MHD viscoelastic nanofluid flow over a stretching sheet with heat source and slip conditions,” Int. J. Interact Des. Manuf. 18, 2991–3000 (2024). https://doi.org/10.1007/s12008-023-01407-4
F. Ali, A. Zaib, M. Faizan, S.S. Zafar, S. Alkarni, N. Ali Shah, and J.D. Chung, “Heat and mass exchanger analysis for Ree-Eyring hybrid nanofluid through a stretching sheet utilizing the Homotopy perturbation method,” Case Studies in Thermal Engineering, 54, 104014 (2024). https://doi.org/10.1016/j.csite.2024.104014
M.T. Akolade, S.A. Agunbiade, and T.L. Oyekunle, “Onset modules of heat source and generalized Fourier’s law on Carreau fluid flow over an inclined nonlinear stretching sheet,” International Journal of Modelling and Simulation, 44(1), (2024). https://doi.org/10.1080/02286203.2022.2151964
M. Saleem, M. Hussain, and I. Mustafa, “Significance of Darcy-Forchheimer law and magnetic field on the comparison of Williamson-Casson fluid subject to an exponential stretching sheet,” 37(27), 2350315 (2023). https://doi.org/10.1142/S0217979223503150
D. Srinivasacharya, and R.S. Kumar, “An Artificial Neural Network Solution for the Casson Fluid Flow Past a Radially Stretching Sheet with Magnetic and Radiation Effect,” Mathematical Models and Computer Simulations, 15, 944-955 (2023). https://doi.org/10.1134/S2070048223050101
Y. Ouyang, Md.F.Md. Basir, K. Naganthran, and I. Pop, “Dual solutions in Maxwell ternary nanofluid flow with viscous dissipation and velocity slip past a stretching/shrinking sheet,” Alexandria Engineering Journal, 105, 437-448 (2024). https://doi.org/10.1016/j.aej.2024.07.093
M.M. Biswal, K. Swain, G.C. Dash, and S. Mishra, “Study of chemically reactive and thermally radiative Casson nanofluid flow past a stretching sheet with a heat source,” 52(1), 333-353 (2023). https://doi.org/10.1002/htj.22697
A. Eid, M.M. Khader, and A.M. Megahed, “Vieta-Lucas Collocation Technique for Examination of the Flow of Casson Fluid over a Slippery Stretching Sheet Which Is Impacted by Thermal Slip, Ohmic Dissipation, and Variable Thermal Conductivity,” Journal of Mathematics, 2023, 8723343, (2023). https://doi.org/10.1155/2023/8723343
O.D. Makinde, Z.H. Khan, R. Ahmad, and W.A. Khan, “Numerical study of unsteady hydromagnetic radiating fluid flow past a slippery stretching sheet embedded in a porous medium,” Phys. Fluids, 30, 083601 (2018). https://doi.org/10.1063/1.5046331
M.E. Rao, “The effects of thermal radiation and chemical reaction on MHD flow of a Casson fluid over and exponentially inclined stretching surface,” IOP Conf. Series: Journal of Physics: Conf. Series, 1000, 012158 (2018). https://doi.org/10.1088/1742-6596/1000/1/012158
B. Mahanthesh, B.J. Gireesha, R.S.R. Gorla, and O.D. Makinde, “Magnetohydrodynamic three-dimensional flow of nanofluids with slip and thermal radiation over a nonlinear stretching sheet: a numerical study,” Neural Comput Appl. 30, 1557–1567 (2018). https://doi.org/10.1007/s00521-016-2742-5
N. Tarakaramu, N. Sivakumar, P.V.S. Narayana, and R. Sivajothi, “Viscous Dissipation and Joule Heating Effects on 3D Magnetohydrodynamics Flow of Williamson Nanofluid in a Porous Medium Over a Stretching Surface With Melting Condition,” ASME Open J. Engineering, 2022(1), 0110331 (2022). https://doi.org/10.1115/1.4055183
K.B. Lakshmi, V. Sugunamma, N. Tarakaramu, N. Sivakumar, and R. Sivajothi, “Cross-dispersion effect on magnetohydrodynamic dissipative Casson fluid flow via curved sheet,” Heat Transfer, 51(8), 7822-7842 (2022).. https://doi.org/10.1002/htj.22668
N. Tarakaramu, P.V.S. Narayana, R. Sivajothi, K.B. Lakshmi, D.H. Babu, and B. Venkateswarlu, “Three-dimensional non-Newtonian couple stress fluid flow over a permeable stretching surface with nonlinear thermal radiation and heat source effects,” Heat Transfer, 51(6), 5348-5367 (2022). https://doi.org/10.1002/htj.22550
M. Khan, H. Sardar, and Hashim, “Heat generation/absorption and thermal radiation impacts on three-dimensional flow of Carreau fluid with convective heat transfer,” Mole. Liq. 272, 474-480 (2018). https://doi.org/10.1016/j.molliq.2018.08.088
T. Javed, and M.A. Siddiqui, “Mixed convection in micropolar nanofluid flow through entrapped triangular enclosures and linear stability analysis considering magnetic effects and heat generation/absorption,” Can. J. Phys. 97(3), 252-266 (2018). https://doi.org/10.1139/cjp-2017-0974
A.G. Madaki, R. Roslan, M.S. Rusiman, and C.S.K. Raju, “Analytical and numerical solutions of squeezing unsteady Cu and TiO2-nanofluid flow in the presence of thermal radiation and heat generation/absorption,” Alexandria Eng. J. 57(2), 1033-1040 (2017). https://doi.org/10.1016/j.aej.2017.02.011
S. Qayyum, T. Hayat, and A. Alsaedi, “Chemical reaction and heat generation/absorption aspects in MHD nonlinear convective flow of third grade nanofluid over a nonlinear stretching sheet with variable thickness,” Results Phys. 7, 2752–2761 (2017). https://doi.org/10.1016/j.rinp.2017.07.043
P.S. Reddy, A.J. Chamkha, and A.A. Mudhaf, “MHD heat and mass transfer flow of a nanofluid over an inclined vertical porous plate with radiation and heat generation/absorption,” Advanced Powder Tech. 28, 1008-1017 (2017). https://doi.org/10.1016/j.apt.2017.01.005
Ch. Ram Reddy, O. Surender, Ch. Venkata Rao, and T. Pradeepa, “A domain decomposition method for Hall and ion-slip effect son mixed convection flow of a chemically reacting Newtonian fluid between parallel plates with heat generation/absorption,” Propulsion Power Res. 6(4), 296–306 (2017). https://doi.org/10.1016/j.jppr.2017.11.001
K.U. Rehman, A.S. Alshomrani, and M.Y. Malik, “Carreau fluid flow in a thermally stratified medium with heat generation/absorption effects,” Case Studies Thermal Eng. 12, 16–25 (2018). https://doi.org/10.1016/j.csite.2018.03.001
G. Sarojamma, K. Vajravelu, and K. Sreelakshmi, “A study on entropy generation on thin film flow over an unsteady stretching sheet under the influence of magnetic field, thermocapillarity, thermal radiation and internal heat generation/absorption,” Communications Numerical Analysis, 2017(2), 141-156 (2017). http://dx.doi.org/10.5899/2017/cna-00319
I.S. Oyelakin, S. Mondal, and P. Sibanda, “Unsteady Casson nanofluid flow over a stretching sheet with thermal radiation, convective and slip boundary conditions,” Alexandria Eng. J. 55, 1025-1035 (2015). https://doi.org/10.1016/j.aej.2016.03.003
S. Nadeem, R.U. Haq, and N.S. Akbar, “MHD three-dimensional boundary layer flow of Casson nanofluid past a linearly stretching sheet with convective boundary condition,” IEEE Trans. Nanotech. 13(1), 109-115 (2014). https://doi.org/10.1109/TNANO.2013.2293735
S. Gupta, and K. Sharma, “Numerical simulation for magnetohydrodynamic three-dimensional flow of Casson nanofluid with convective boundary conditions and thermal radiation,” Eng. Comp. 34(8), 2698-2722 (2017).
K. Ahmad, and R. Nazar, “Magnetohydrodynamic three-dimensional flow and heat transfer over a stretching surface in a viscoelastic fluid,” J. Sci. Technol. 3(1), 1-14 (2011).
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