CAS Wavelet Based Numerical Technique for the Solution of Dusty Tangent Hyperbolic Fluid Flow with Magnetic Dipole Effect, Quadratic Convection and Entropy Generation

Document Type : Research Paper

Authors
S.C. Shiralashetti 1
Priyanka I. Kulkarni 1
Savita I. Hanaji 2
1 Department of Mathematics, Karnatak University, Dharwad, 580003, Karnataka, India
2 KLE Technological University, Dr. M. S. Sheshgiri College of Engineering and Technology, Udyambag, Belagavi, 590008, Karnataka, India
10.22055/jacm.2024.46918.4625
Abstract
This paper presents the CAS wavelet based numerical technique for the solution of non-linear system of differential equations arising in the analysis of an unsteady dusty tangent hyperbolic fluid flow over a stretching sheet through porous medium with magnetic dipole effect, quadratic convection, non-linear radiation, convective boundary and entropy generation. Initially, the proposed method is implemented on the test problem having the exact solution. The results obtained are very close to the exact solution in comparison with the Runge-Kutta Fehlberg 4th – 5th order method. The considered dusty fluid problem is solved by using the proposed technique. The solutions obtained for certain fixed parameters are compared and found to be coinciding with the solutions given in the literature. The comparisons and convergence analysis validate the method. The flow behaviour of dusty tangent hyperbolic fluid is analysed and the impact of various factors on the velocity and thermal profile of the fluid are studied. It is inferred that the Weissenberg number, power law index and Ferro-hydrodynamic interaction parameter declines the velocity and improves the temperature. Opposite behaviour is observed for mixed convection and quadratic convection parameters. The temperature increases for the Biot number. The Weissenberg number declines the entropy generation and enhances the Bejan number. A reverse trend is noticed for Brinkman number. CAS wavelet based numerical technique is simple, reliable, highly accurate, efficient and effective tool to solve the non-linear system of differential equations arising in dusty fluid flow problems.
Keywords
CAS wavelets
Operational matrix
Dusty tangent hyperbolic fluid
Magnetic dipole
Entropy generation
Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Saffman, P.G., On the stability of laminar flow of a dusty gas, Journal of Fluid Mechanics, 13, 1962, 120-128.
[2] Shiralashetti, S.C., Kulkarni, P.I., Hanaji, S.I., Chelyshkov wavelet-based numerical technique for the solution of Darcy–Forchheimer flow of Erying–Powell radiated dusty fluid over a stretching sheet with Cattaneo–Christov heat flux, Numerical Heat Transfer, Part B: Fundamentals, 2024, doi: 10.1080/10407790.2024.2346933.
[3] Sulochana, C., Prakash, J., Sandeep, N., Unsteady MHD flow of a dusty nanofluid past a vertical stretching surface with non-uniform heat source/sink, International Journal of Science and Engineering, 10(1), 2016, 1-9.
[4] Almaneea, A., Computational investigation on transport of heat energy by flow of dusty Carreau fluid with nanoparticles using finite element method, Ain Shams Engineering Journal, 15, 2024, 102377.
[5] Dey, D., Makinde, O.D., Chutia, B., Hydromagnetic flow of dusty fluid with heat and mass transfer past a stretching curved surface in a porous medium, Latin American Applied Research - An International Journal, 52(3), 2022, 201-206.
[6] Upadhya, S.M., Mahesha, Raju, C.S.K., Shehzad, S.A., Abbasi, F.M., Flow of Eyring-Powell dusty fluid in a deferment of aluminium and ferrous oxide nanoparticles with and Cattaneo-Christov heat flux, Powder Technology, 340, 2018, 68-76.
[7] Krishnamurthy, M.R., Gireesha, B.J., Gorla, R.S.R., Prasannakumara, B.C., Suspended particle effect on slip flow and melting heat transfer of nanofluid over a stretching sheet embedded in a porous medium in the presence of nonlinear thermal radiation, Journal of Nanofluids, 5(4), 2016, 502-510.
[8] Akbar, N.S., Nadeem, S., Haq, R.U., Khan, Z.H., Numerical solutions of magneto hydrodynamic boundary layer flow of tangent hyperbolic fluid flow towards a stretching sheet with magnetic field, Indian Journal of Physics, 87(11), 2013, 1121-1124.
[9] Ullah, Z., Zaman, G., Ishak, A., Magnetohydrodynamic tangent hyperbolic fluid flow past a stretching sheet, Chinese Journal of Physics, 66, 2020, 258-268.
[10] Sreenivasulu, P., Vasu, B., Poornima, T., Reddy, N.B., Inclined Lorentzian force effect on tangent hyperbolic radiative slip flow imbedded carbon nanotubes: Lie group analysis, Journal of Computational & Applied Research in Mechanical Engineering, 10(1), 2020, 85-99.
[11] Zeb, S., Khan, S., Ullah, Z., Yousaf, M., Khan, I., Alshammari, N., Alam, N., Hamadneh, N. N., Lie group analysis of double diffusive MHD tangent hyperbolic fluid flow over a stretching sheet, Mathematical Problems in Engineering, 2022, 2022, 9919073.
[12] Moatimid, G.M., Mohamed, M.A.A., Gaber, A.A., Mostafa, D.M., Numerical analysis for tangent-hyperbolic micropolar nanofluid flow over an extending layer through a permeable medium, Scientific Reports, 13, 2023, 13522.
[13] Andersson, H.I., Valnes, O.A., Flow of a heated ferrofluid over a stretching sheet in the presence of a magnetic dipole, Acta Mechanica, 128, 1998, 39-47.
[14] Majeed, A., Zeeshan, A., Ellahi, R., Chemical reaction and heat transfer on boundary layer Maxwell Ferro-fluid flow under magnetic dipole with Soret and suction effects, Engineering Science and Technology, 20, 2017, 1122-1128.
[15] Nidhi, Kumar, L, Magnetic dipole and mixed convective effect on boundary layer flow of ferromagnetic micropolar hybrid nanofluid, Journal of Nanofluids, 13, 2024, 435-445.
[16] Kamis, N.I. Jiann, L.Y. Shafie, S. Rawi, N.A., Numerical simulation of convection hybrid ferrofluid with magnetic dipole effect on an inclined stretching sheet, Alexandria Engineering Journal, 76, 2023, 19-33.
[17] Tijani, Y.O., Adeosun, A.T., Ogunseye, H.A., Niranjan, H., Magnetic dipole dynamics on Reiner–Philippoff boundary layer flow, Numerical Heat Transfer, Part A: Applications, 85(10), 2023, 1691-1705.
[18] Imtiaz, M., Khan, M. I., Akermi, M., Hejazi, H. A., Understanding the impact of magnetic dipole and variable viscosity on nanofluid flow characteristics over a stretching surface, Journal of Magnetism and Magnetic Materials, 589, 2024, 171613.
[19] Goren, S.L., On free convection in water at 40 C, Chemical Engineering Science, 21(6-7), 1966, 515-518.
[20] Obalalu, A.M., Alfwzan, W.F., Memon, M.A., Darvesh, A., Adegbite, P., Hendy, A.S., Ali, M.R., Energy optimization of quadratic thermal convection on two-phase boundary layer flow across a moving vertical flat plate, Case Studies in Thermal Engineering, 55, 2024, 104073.
[21] Abbas, M. Khan, N., Hashmi, M.S., Alhefthi, R.K., Rezapour, S., Inc, M., Thermal Marangoni convection in two-phase quadratic convective flow of dusty MHD trihybrid nanofluid with non-linear heat source, Case Studies in Thermal Engineering, 57, 2024, 104190.
[22] Jiann, L.Y., Zin, N.A.M., Rawi, N.A., Ilias, M.R., Shafie, S., Comparative study of quadratic mixed convection MHD Carreau fluid flow on cylinder and flat plate with mass transition, Arabian Journal for Science and Engineering, 49, 2024, 1977-2000.
[23] Imran, M., Basit. M.A., Yasmin, S., Khan, S.A., Elagan, S.K., Akgül, A., Hassan, A.M., A proceeding to numerical study of mathematical model of bioconvective Maxwell nanofluid flow through a porous stretching surface with nield/convective boundary constraints, Scientific Reports, 14(1), 2024, 1873.
[24] Venkatesh, N., Raju, R.S., Anil Kumar, M., Dharmendar Reddy, Y., A numerical study on MHD Maxwell fluid with nanoparticles over a stretching surface: Impacts of thermal radiation, convective boundary condition and induced magnetic field, Numerical Heat Transfer, Part A: Applications, 2024, doi: 10.1080/10407782.2024.2338259.
[25] Shah, S.A.G.A., Hassan, A., Karamti, H., Alhushaybari, A., Eldin, S.M., Galal, A.M., Effect of thermal radiation on convective heat transfer in MHD boundary layer Carreau fluid with chemical reaction, Scientific Reports, 13, 2023, 4117
[26] Raje, A., Bhise, A.A., Kulkarni, A., Entropy analysis of the MHD Jeffrey fluid flow in an inclined porous pipe with convective boundaries, International Journal of Thermofluids, 17, 2023, 100275.
[27] Bejan, A., A study of entropy generation in fundamental convective heat transfer, Journal of Heat Transfer, 101(4), 1979, 718-725.
[28] Reddy, M.V., Vajravelu, K., Ajithkumar, M., Sucharitha, G., Lakshminarayana, P., Analysis of entropy generation and activation energy on a convective MHD Carreau–Yasuda nanofluid flow over a sheet, Modern Physics Letters B, 38(28), 2024, 2450266.
[29] Wang, J., Farooq, U., Waqas, H., Muhammad, T., Khan, S.A., Hendy, A.S., Ali, M.R., Numerical solution of entropy generation in nanofluid flow through a surface with thermal radiation applications, Case Studies in Thermal Engineering, 54, 2024, 103967.
[30] Hayat, T., Yaqoob, R., Qayyum, S., Alsaedi, A., Entropy generation optimization in nanofluid flow by variable thicked sheet, Physica A: Statistical Mechanics and Its Applications, 551(1), 2020, 124022.
[31] Shiralashetti, S.C., Harishkumar, E., Haar wavelet matrices for the numerical solution of system of ordinary differential equations, Malaya Journal of Matematik, S(1), 2020, 144-147.
[32] Shiralashetti, S.C., Badiger, P., Haar wavelet algebraic multigrid method for the numerical solution of squeeze film lubrication problem of porous journal bearings with couple stress fluid, Palestine Journal of Mathematics, 12(2), 2023, 578-596.
[33] Shiralashetti, S.C., Badiger, P., Chebyshev wavelets approach for the squeeze film lubrication of long porous journal bearings with couple stress fluids, Malaya Journal of Matematik, S(1), 2020, 138-143.
[34] Shiralashetti, S.C., Harishkumar E., Hanaji, S., Legendre wavelet operational matrix method for the analysis of thermal radiation effect on natural convection of a vertical palte embedded in a saturated porous medium, International Journal of Ambient Energy, 44(1), 2023, 1512-1521.
[35] Lal, S., Kumari, P., Approximation of functions with bounded derivative and solution of Riccati differential equations by Jacobi wavelet operational matrix, Applied Mathematics and Computation, 394, 2021, 125834.
[36] Manohara, G., Kumbinarasaiah, S., Numerical solution of a modified epidemiological model of computer viruses by using Fibonacci wavelets, The Journal of Analysis, 32, 2024, 529-554.
[37] Yousefi, S., Banifatemi, A., Numerical solution of Fredholm integral equations by using CAS wavelets, Applied Mathematics and Computation, 183(1), 2006, 458-463.
[38] Danfu, H., Xufeng, S., Numerical solution of integro-differential equations by using CAS wavelet operational matrix of integration, Applied Mathematics and Computation, 194(2), 2007, 460-466.
[39] Yi, M., Huang J., CAS wavelet method for solving the fractional integro-differential equation with a weakly singular kernel, International Journal of Computer Mathematics, 92(8), 2014, 1715-1728.
[40] Saeedi, H., Moghadam, M.M., Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets, Communications in Nonlinear Science and Numerical Simulation, 16(3), 2011, 1216-1226.
[41] Shamooshaky, M.M., Assari, P., Adibi, H., CAS wavelet method for the numerical solution of boundary integral equations with logarithmic singular kernels, International Journal of Mathematical Modelling Computations, 4(4), 2024, 377-387.
[42] Saeed, U., A wavelet method for solving Caputo–Hadamard fractional differential equation, Engineering Computations, 39(2), 2022, 650-671.
[43] Saeed, U., A generalized CAS wavelet method for solving ψ-Caputo fractional differential equations, Engineering Computations, 40(6), 2023, 1351-1370.
[44] Shiralashetti, S.C., Lamani, L., CAS wavelets stochastic operational matrix of integration and its application for solving stochastic Itô-volterra integral equations, Jordan Journal of Mathematics and Statistics, 14(3), 2021, 555-580
[45] Bliliana, B., Roslinda, N., Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation, European Journal of Scientific Research, 33(4), 2009, 710-717.
[46] Burden, R.L., Faires, J.D., Numerical Analysis, 9th Edition, Cengage Learning, Brooks/Cole, USA, 2011.
[47] Borhanifar A., Khader M.M., Jacobi operational matrix and its application for solving systems of ODEs, Differential Equations and Dynamical Systems, 24(4), 2016, 459-473.
Journal of Applied and Computational Mechanics
Volume 11, Issue 3
Summer 2025
Pages 585-610