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Discontinuity, Nonlinearity, and Complexity 14(4) (2025) 781--793 | DOI:10.5890/DNC.2025.12.012

M. Kalaivani$^1$, V. Ananthaswamy$^2$, S. Sivasankari$^1$

$^1$ Research Scholar, Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India

$^2$ Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India

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Abstract

The Magnetohydrodynamic Casson nanofluid with heat radiation is evaluated mathematically across an elongating or shrinking sheet within a porous substance exhibiting brownian and thermophoretic diffusion. By incorporating non-dimensional variables in the formulation, the controlling equations acquire dimensionless. The approximate analytical approach (ASM) and Modified Homotopy Analysis Methodology (MHAM) are utilized to attain the velocity, temperature and concentration explicitly in a dimensionless manner. We graphically portray the model's physical components to interpret their consequences. Furthermore, the semi-analytical expressions for the Sherwood number, Nusselt number, and dimensionless skin friction factor are assessed. Comparing the semi-analytical results with the numerical results, a great fit is confirmed.

References

1. [1]	Mabood, F., Khan, W.A., and Ismail, A.M. (2015), MHD boundary layer flow and heat transfer of nanofluids over a nonlinear stretching sheet: a numerical study, Journal of Magnetism and Magnetic Materials, 374, 569-576.

2. [2]	Rehman, K.U., Qaiser, A., Malik, M.Y., and Ali, U. (2017), Numerical communication for MHD thermally stratified dual convection flow of Casson fluid yields by stretching cylinder, Chinese Journal of Physics, 55(4), 1605-1614.

3. [3]

   Kataria, H.R. and Patel, H.R. (2019), Effects of chemical reaction and heat generation/absorption on magnetohydrodynamic (MHD) Casson fluid flow over an exponentially accelerated vertical plate embedded in porous medium with ramped wall temperature and ramped surface concentration, Propulsion and Power Research, 8(1), 35-46.

4. [4]	Mahabaleshwar, U.S., Nagaraju, K.R., Sheremet, M.A., Baleanu, D., and Lorenzini, E. (2020), Mass transpiration on Newtonian flow over a porous stretching/shrinking sheet with slip, Chinese Journal of Physics, 63, 130-137.

5. [5]	Bachok, N. and Ishak, A. (2011), Similarity solutions for the stagnation-point flow and heat transfer over a nonlinearly stretching/shrinking sheet, Sains Malaysiana, 40(11), 1297-1300.

6. [6]	Fauzi, N.F., Ahmad, S., and Pop, I. (2015), Stagnation point flow and heat transfer over a nonlinear shrinking sheet with slip effects, Alexandria Engineering Journal, 54(4), 929-934.

7. [7]	Hayat, T., Aziz, A., Muhammad, T., and Alsaedi, A. (2016), On magnetohydrodynamic three-dimensional flow of nanofluid over a convectively heated nonlinear stretching surface, International Journal of Heat and Mass Transfer, 100, 566-572.

8. [8]	Daniel, Y.S., Aziz, Z.A., Ismail, Z., and Salah, F. (2018), Effects of slip and convective conditions on MHD flow of nanofluid over a porous nonlinear stretching/shrinking sheet, Australian Journal of Mechanical Engineering, 16(3), 213-229.

9. [9]	Rana, P., Dhanai, R., and Kumar, L. (2017), Radiative nanofluid flow and heat transfer over a non-linear permeable sheet with slip conditions and variable magnetic field: Dual solutions, Ain Shams Engineering Journal, 8(3), 341-352.

10. [10]	Bakar, N.A.A., Bachok, N., Arifin, N.M., and Pop, I. (2018), Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect, Results in Physics, 9, 1335-1344.

11. [11]	Zainal, N.A., Nazar, R., Naganthran, K., and Pop, I. (2021), Heat generation/absorption effect on MHD flow of hybrid nanofluid over bidirectional exponential stretching/shrinking sheet, Chinese Journal of Physics, 69, 118-133.

12. [12]	Ph, F. (1901), Wasserbewegung durch boden, Zeitschrift des Vereines Deutscher Ingenieure, 45(50), 1781-1788.

13. [13]	Pal, D. and Mondal, H. (2014), Effects of temperature-dependent viscosity and variable thermal conductivity on MHD non-Darcy mixed convective diffusion of species over a stretching sheet, Journal of the Egyptian Mathematical Society, 22(1), 123-133.

14. [14]	Muhammad, T., Rafique, K., Asma, M., and Alghamdi, M. (2020), Darcy--Forchheimer flow over an exponentially stretching curved surface with Cattaneo--Christov double diffusion, Physica A: Statistical Mechanics and its Applications, 556, 123968.

15. [15]	Sajid, T., Sagheer, M., Hussain, S., and Bilal, M. (2018), Darcy-Forchheimer flow of Maxwell nanofluid flow with nonlinear thermal radiation and activation energy, AIP Advances, 8(3), 035102.

16. [16]	Khan, S.A., Saeed, T., Khan, M.I., Hayat, T., Khan, M.I., and Alsaedi, A. (2019), Entropy optimized CNTs based Darcy-Forchheimer nanomaterial flow between two stretchable rotating disks, International Journal of Hydrogen Energy, 44(59), 31579-31592.

17. [17]	Mallawi, F. and Ullah, M.Z. (2021), Conductivity and energy change in Carreau nanofluid flow along with magnetic dipole and Darcy-Forchheimer relation, Alexandria Engineering Journal, 60(4), 3565-3575.

18. [18]	Khan, S.A., Hayat, T., and Alsaedi, A. (2021), Irreversibility analysis in Darcy-Forchheimer flow of viscous fluid with Dufour and Soret effects via finite difference method, Case Studies in Thermal Engineering, 26, 101065.

19. [19]	Mahanthesh, B., Gireesha, B.J., Shashikumar, N.S., Hayat, T., and Alsaedi, A. (2018), Marangoni convection in Casson liquid flow due to an infinite disk with exponential space dependent heat source and cross-diffusion effects, Results in Physics, 9, 78-85.

20. [20]	Salahuddin, T., Arshad, M., Siddique, N., Alqahtani, A.S., and Malik, M.Y. (2020), Thermophysical properties and internal energy change in Casson fluid flow along with activation energy, Ain Shams Engineering Journal, 11(4), 1355-1365.

21. [21]	Alzahrani, H.A., Alsaiari, A., Madhukesh, J.K., Naveen Kumar, R., and Prasanna, B.M. (2022), Effect of thermal radiation on heat transfer in plane wall jet flow of Casson nanofluid with suction subject to a slip boundary condition, Waves in Random and Complex Media, 1-18.

22. [22]	Ganie, A.H., Mahnashi, A.M., Shafee, A., Shah, R., and Fathima, D. (2024), Comparative analysis of Casson nanofluid flow over shrinking sheet under the influence of thermal radiation, electric variable, and cross diffusions: Multiple solutions and stability analysis, IEEE Access.

23. [23]	Ragupathi, E., Prakash, D., Muthtamilselvan, M., and Al-Mdallal, Q.M. (2022), Impact of thermal nonequilibrium on flow through a rotating disk with power law index in porous media occupied by Ostwald-de-Waele nanofluid, Journal of Non-Equilibrium Thermodynamics, 47(4), 375-394.

24. [24]	Prakash, D., Ragupathi, E., Muthtamilselvan, M., Abdalla, B., and Al Mdallal, Q.M. (2021), Impact of boundary conditions of third kind on nanoliquid flow and radiative heat transfer through asymmetrical channel, Case Studies in Thermal Engineering, 28, 101488.

25. [25]	Sivasankari, S., Ananthaswamy, V., and Sivasundaram, S. (2023), A new approximate analytical method for solving some non-linear initial value problems in physical sciences, Mathematics in Engineering, Science and Aerospace (MESA), 14(1), 145.

26. [26]	Chitra, J., Ananthaswamy, V., Sivasankari, S., and Sivasundaram, S. (2023), A new approximate analytical method (ASM) for solving non-linear boundary value problem in heat transfer through porous fin, Mathematics in Engineering, Science and Aerospace (MESA), 14(1), 53.

27. [27]	Ananthaswamy, V., Sivasankari, S., and Sivasundaram, S. (2024), A new approximate analytical method (ASM) for solving some non-linear boundary value problems, Mathematics in Engineering, Science and Aerospace (MESA), 15(1), 273.

28. [28]	Subanya, R., Ananthaswamy, V., and Sivasankari, S. (2023), A new semi analytical method for solving some non-linear infinite boundary value problems in physical sciences, Communications in Mathematics and Applications, 15(4), 1739-1757. https://doi.org/10.26713/cma.v14i5.2136

29. [29]	Sivasankari, S. and Ananthaswamy, V. (2023), A mathematical study on non-linear ordinary differential equation for Magnetohydrodynamic flow of the Darcy-Forchheimer nanofluid, Computational Methods for Differential Equations, 11(4), 696-715.

30. [30]	Liao, S. and Campo, A. (2002), Analytic solutions of the temperature distribution in Blasius viscous flow problems, Journal of Fluid Mechanics, 453, 411-425.

31. [31]	Liao, S.J. (1995), An approximate solution technique not depending on small parameters: a special example, International Journal of Non-Linear Mechanics, 30(3), 371-380.

32. [32]	Liao, S.J. (1992), The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems (Doctoral dissertation, Ph.D. Thesis, Shanghai Jiao Tong University).

33. [33]	Liao, S.J. (1999), A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate, Journal of Fluid Mechanics, 385, 101-128.

34. [34]	Lone, S.A., Anwar, S., Raizah, Z., Kumam, P., Seangwattana, T., and Saeed, A. (2023), Analysis of the time-dependent magnetohydrodynamic Newtonian fluid flow over a rotating sphere with thermal radiation and chemical reaction, Heliyon, 9(7).

35. [35]	Petchiammal, G., and Ananthaswamy, V. (2024), A semi-analytical study on non-linear boundary value problem for MHD fluid flow with chemical effect, Journal of Heat and Mass Transfer Research, 11(2), 237-254.