---

Journal of Vibration Testing and System Dynamics 9(3) (2025) 249--260 | DOI:10.5890/JVTSD.2025.09.004

P. Priyadharshini, V. Karpagam

Department of Mathematics, PSG College of Arts and Science, Coimbatore-641014, Tamil Nadu, India

Download Full Text PDF

 

Abstract

The primary intent of this work is to explore the radiation effects of an unstable MHD Williamson bio-fluid (Blood) over a wedge that interacts with thermophoresis diffusion and Brownian motion. Apply similarity transformation to convert the essential prerequisites of partial differential equations (PDEs) into ordinary differential equations (ODEs). The results of these ODEs have a significant impact on the BVP4C approach from the MATLAB package computational structures. The graphs and tabular data provided the various values for physical quantities found and discussed in detail. Furthermore, to estimate Machine Learning (ML) under Multiple Linear Regression (MLR) and validate Linear Support Vector Machine (SVM) to anticipate the physical quantities for current numerical discoveries. Drug delivery systems for therapeutic and diagnostic approaches for cancer treatment are possible advantages of these results. An additional benefit is that the outcomes showed acceptable congruence with the tangible findings of recent research and enlargements for future investigators.

References

1. [1]	Inoue, S. and Kabaya, M. (1989), Biological activities caused by far-infrared radiation, International Journal of Biometeorology, 33, 145–150.

2. [2]	Kobu, Y. (1999), Effects of infrared radiation on intraosseous blood flow and oxygen tension in rat tibia, The Kobe Journal of Medical Sciences, 45, 27–39.

3. [3]	Nishimoto, C., Ishiura, Y., Kuniasu, K., and Koga, T. (2006), Effects of ultrasonic radiation on cutaneous blood flow in the paw of decerebrated rats, Kawasaki Journal of Medical Welfare, 12, 13–18.

4. [4]	Misra, J.C., Sinha, A., and Shit, G.C. (2010), Flow of a biomagnetic viscoelastic fluid: application to the estimation of blood flow in arteries during electromagnetic hyperthermia, a therapeutic procedure for cancer treatment, Applied Mathematics and Mechanics, 31, 1405–1420.

5. [5]	Mandal, P.K. (2005), An unsteady analysis of non-Newtonian blood flow through tapered arteries with stenosis, International Journal of Non-Linear Mechanics, 40, 51–164.

6. [6]	Valencia, A. and Villanueva, M. (2006), Unsteady flow and mass transfer in models of stenotic arteries considering fluid-structure interaction, International Communications in Heat and Mass Transfer, 33, 966–75.

7. [7]	Bali, R. and Awasthi, U. (2007), Effect of a magnetic field on the resistance to blood flow through the stenotic artery, Applied Mathematics and Computation, 188, 1635–1641.

8. [8]	Habibi, M.R. and Ghasemi, M. (2011), Numerical study of magnetic nano-particles concentration in biofluid (blood) under the influence of high gradient magnetic field, Journal of Magnetism and Magnetic Materials, 323, 32–38.

9. [9]	Akbar, N.S., Nadeem, S., and Lee, C. (2012), Influence of heat transfer and chemical reactions on Williamson fluid model for blood flow through a tapered artery with a stenosis, Asian Journal of Chemistry, 24, 2433-2441.

10. [10]	Reddy, S.R.R., Reddy, P.B.A., and Suneetha, S. (2018), Magnetohydrodynamic flow of blood in a permeable inclined stretching viscous dissipation, non-uniform heat source/sink, and chemical reaction, Frontiers in Heat and Mass Transfer, 10, 22.

11. [11]	Falkner, V.M. and Skan, S.W. (1931), Some approximate solutions of the boundary-layer for flow past a stretching boundary, SIAM Journal of Applied Mathematics, 46, 1350–8.

12. [12]	Kuo, B.L. (2003), Application of the differential transformation method to the solutions of Falkner-Skan wedge flow, Acta Mechanica, 164, 161–74.

13. [13]	Chamkha, A.J., Mujtaba, M., Quadri, A., and Issa, C. (2003), Thermal radiation effects on MHD forced convection flow adjacent to a non-isothermal wedge in the presence of heat source or sink, Heat and Mass Transfer, 39, 305–12.

14. [14]	Hsiao, K.L. (2011), MHD mixed convection for viscoelastic fluid past a porous wedge, International Journal of Non-Linear Mechanics, 46, 1–8.

15. [15]	Alam, M.S., Islam, T., and Rahman, M.M. (2015), Unsteady hydromagnetic forced convective heat transfer flow of a micropolar fluid along a porous wedge with convective surface boundary condition, International Journal of Heat and Technology, 33(2), 115-122.

16. [16]	Williamson, R.V. (1929), The flow of pseudo-plastic materials, Industrial and Engineering Chemistry, 21, 11.

17. [17]	Cramer, S.D. and Marchello, J.M. (1968), Numerical evaluation of models describing non-Newtonian behavior, American Institute of Chemical Engineers Journal, 14, 980.

18. [18]	Sreenadh, S., Goverdhan, P., and Ravi Kumar, Y.V.K. (2014), Effect of slip and heat transfer on the Peristaltic pumping of a Williamson fluid in an inclined channel, International Journal of Applied Science and Engineering, 12(2), 143–155.

19. [19]	Kumaran, G. and Sandeep, N. (2017), Thermophoresis and Brownian moment effects on the parabolic flow of MHD Casson and Williamson fluids with cross-diffusion, Journal of Molecular Liquids, 233, 262-269.

20. [20]	Makinde, O.D., Mabood, F., and Ibrahim, M.S. (2018), Chemically reacting on MHD boundary-layer flow of nanofluids over a nonlinear stretching sheet with heat source/sink and thermal radiation, Thermal Science, 22(1B), 495-506.

21. [21]	Amanulla, C.H., Nagendra, N., and Reddy, M.S., (2018), Numerical simulation of slip influence on the flow of an MHD Williamson fluid over a vertical convective surface, Nonlinear Engineering, 7(4), 309-321.

22. [22]	Ahmed, K. and Akbar, T. (2021), Numerical investigation of magnetohydrodynamics Williamson nanofluid flow over an exponentially stretching surface, Advances in Mechanical Engineering, 13(5), p.16878140211019875.

23. [23]

    Wakif, A. (2020), A novel numerical procedure for simulating steady MHD convective flows of radiative Casson fluids over a horizontal stretching sheet with irregular geometry under the combined influence of temperature-dependent viscosity and thermal conductivity, Mathematical Problems in Engineering, 20, p.1675350.

24. [24]	Tuz Zohra, F., Uddin, M.J., Basir, M.F., and Ismail, A.I.M. (2020), Magnetohydrodynamic bio-nano-convective slip flow with Stefan blowing effects over a rotating disc, Proceedings of the Institution of Mechanical Engineers, 234, 83–97.

25. [25]	Huang, J.Z. and Peters, D. ( 2019), Entire flow field modeling including wake region through improved finite-state method, Journal of Vibration Testing and System Dynamics, 3(4), 453-468.

26. [26]	Sun, Y.H., Luo, Z., Wei, K., Wang, Y., and Han, G.X. (2021), Numerical analysis of fluid-structure interaction of fire doors in cross-passages of subway tunnels, Journal of Vibration Testing and System Dynamics, 5(1), 19-32.

27. [27]

    Basha, H.T. and Sivaraj, R. (2021), Numerical simulation of blood nanofluid flow over three different geometries using gyrotactic microorganisms: applications to the flow in a circulatory system, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235(2), 441–460.

28. [28]	Kuo, B.L. (2003), Application of the differential transformation method to the solutions of Falkner-Skan wedge flow, Acta Mechanica, 164, 161-174.

29. [29]	Ishaq, A., Nazar, R., and Pop, I. (2006), Moving wedge and flat plate in a micropolar fluid, International Journal of Engineering Science, 44, 1225-1236.

30. [30]	Hamid, A. and Khan, M. (2018), Numerical investigation on heat transfer performance in time-dependent flow of Williamson fluid past a wedge-shaped geometry, Results in Physics, 9, 479-485.

31. [31]	Subbarayudu, K., Suneetha, S., and Bala Anki Reddy, P. (2020), The assessment of the time-dependent flow of Williamson fluid with radiative blood flow against a wedge,Propulsion and Power Research, 9(1), 87–99.

32. [32]	Khan, M., Malik, M.Y., Salahuddin, T., and Hussian, A. (2018), Heat and mass transfer of Williamson nanofluid flow yield by an inclined Lorentz force over a nonlinear stretching sheet, Results in Physics, 8, 862-868.

33. [33]	Khan, M. and Hamid, A. (2017), Influence of nonlinear thermal radiation on the 2D unsteady flow of a Williamson fluid with heat source/sink, Results in Physics, 7, 3968-3975.

34. [34]	Khan, W.A. and Gorla, R.S.R. (2012), Heat and mass transfer in non-Newtonian nanofluids over a non-isothermal stretching wall, Journal of Nanomaterials, Nanoengineering and Nanosystems, 225(4), 155-163.

35. [35]	Alam, M.S., Islam, T., and Rahman, M.M. (2015), Unsteady hydromagnetic forced convective heat transfer flow of a micropolar fluid along a porous wedge with convective surface boundary condition, International Journal of Heat and Technology, 33(2), 115-122.

36. [36]	Shampine, L.F., Gladwell, I., and Thompson, S. (2003), Solving ODEs with Matlab, Cambridge University Press.

37. [37]	Shampine, L.F., Kierzenka, J., and Reichelt, M.W. (2000), Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c, Tutorial Notes, 1–27.

38. [38]	Umair, K., Aurang, Z., Sakhinah, A.B., Anuar, I., Dumitru, B., Sayed, E.L., and Sherif, M. (2022), Computational simulation of cross-flow of Williamson fluid over a porous shrinking/stretching surface comprising hybrid nanofluid and thermal radiation. AIMS Mathematics, 7(4), 6489–6515.

39. [39]	Chu, Y.M., Khan, U., Shafiq, A., and Zaib, A. (2021), Numerical simulations of time-dependent micro-rotation blood flow induced by a curved moving surface through conduction of gold particles with non-uniform heat sink/source, Arabian Journal for Science and Engineering, 46, 2413–2427.

40. [40]	Spall, R.E. and Yu, W.B. (2013), Imbedded dual-number automatic differentiation for computational fluid dynamics sensitivity analysis, Journal of Fluids Engineering, 135, 14501.

41. [41]

    Melito, G.M., Müller, T.S., Badeli, V., Ellermann, K., Brenn, G., and Reinbacher-Köstinger, A. (2021), Sensitivity analysis study on the effect of the fluid mechanics assumptions for the computation of electrical conductivity of flowing human blood, Reliability Engineering and System Safety, 213, 107663.

42. [42]	Priyadharshini, P., Vanitha Archana, M., Ameer Ahammad, N., Raju, C.S.K., Yook, S.J., and Nehad Ali Shah, (2022), Machine learning regression using gradient descent for MHD flow: Metallurgy process, International Communications in Heat and Mass Transfer, 138, 106307.

43. [43]	Priyadharshini, P., and Vanitha Archana, M. (2023), Augmentation of magnetohydrodynamic nanofluid flow through a Permeable stretching sheet employing Machine learning algorithm, Examples and Counterexamples, 3, 100093.

44. [44]

    Dinesh Kumar, M., Ameer Ahammad, N., Raju, C.S.K., Yook, S.J., Shah, N.A., and Sayed, M. (2023), Response surface methodology optimization of dynamical solutions of Lie group analysis for nonlinear radiated magnetized unsteady wedge: Machine learning approach (gradient descent), Alexandria Engineering Journal, 74, 29–50.

45. [45]	Priyadharshini, P., Karpagam, V., Shah, N.A., and Alshehri, M.H. (2023), Bio- Convection effects of MHD Williamson fluid flow over a symmetrically stretching sheet: Machine learning, MDPI Symmetry, 15(9), 1684.