Document Type : Article

**Authors**

Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad 44000, P.O. Box 2750, Pakistan

**Abstract**

In the current examination, insightful approximations are researched for magnetohydrodynamics Carreau nanofluid having gyrotactic microorganisms over a warmed turning plate. The plate is moving with the steady uniform rakish speed. Administering conditions are gotten by utilizing certain actual presumptions as incomplete differential conditions with limit conditions. These nonlinear types of conditions are changed into coupled standard differential conditions utilizing bunch likeness change. Optimal homotopy investigation strategy (OHAM) is utilized to acquire the graphical outcomes and even qualities for the stream field factors. Graphical portrayal of speeds, temperature, fixation and thickness of gyrotactic microorganisms are examined and clarified. It is tracked down that dimensionless microorganism’s fixation develops for bioconvective Lewis number and focus distinction variable of microorganisms. It is additionally seen that dimensionless speeds diminish because of the attractive impact and Carreau liquid boundary. Contour plots and mathematical outcomes are given for neighbourhood motion boundaries like skin rubbing coefficient, Nusselt number, Sherwood number and thickness number of motile microorganisms.

**Keywords**

References:

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2. Carreau, P.J. "An analysis of the viscous behavior of polymer solutions", Can. J. Chem. Eng., 57, pp. 135- 140 (1979).

3. Khan, M., Malik, M.Y., Salahuddin, T., et al. "Numerical modeling of Carreau fluid due to variable thicked surface", Results in Physics, 7, pp. 2384-2390 (2017).

4. Bilal, S., Alshomrani, A.S., Malik, M.Y., et al. "Analysis of Carreau fluid in the presence of thermal stratification and magnetic field effect", Results in Physics, 10, pp. 118-125 (2018).

5. Irfan, M., Khan, M., and Khan, W.A. "Interaction between chemical species and generalized Fourier's law on 3D flow of Carreau fluid with variable thermal conductivity and heat sink/source: a numerical approach", Results in Physics, 10, pp. 107-117 (2018).

6. Kefayati, G.R. and Tang, H. "MHD thermosolutal natural convection and entropy generation of Carreau fluid in a heated enclosure with two inner circular cold cylinders, using LBM", International Journal of Heat and Mass Transfer, 126, pp. 508-530 (2018).

7. Choi, S.U. and Eastman, J.A. "Enhancing thermal conductivity of fluids with nanoparticles (No. ANL/MSD/CP-84938; CONF-951135-29). Argonne National Lab., IL (United States) (1995).

8. Khanafer, K. and Vafai, K. "A review on the applications of nanofluids in solar energy field", Renewable Energy, 123, pp. 398-406 (2018).

9. Munyalo, J.M. and Zhang, X. "Particle size effect on thermophysical properties of nanofluid and nanofluid based phase change materials: A review", Journal of Molecular Liquids, 265, pp. 77-87 (2018).

10. Sajid, M.U. and Ali, H.M. "Thermal conductivity of hybrid nanofluids: A critical review", International Journal of Heat and Mass Transfer, 126, pp. 211-234 (2018).

11. Rehman, K.U., Alshomrani, A.S., and Malik, M.Y. "Carreau fluid flow in a thermally stratified medium with heat generation/absorption effects", Case Studies in Thermal Engineering, 12, pp. 16-25 (2018).

12. Von Karman, T. "Uber laminare und turbulente Reibung", Z. Angew. Math. Mech., 1, pp. 233-252 (1921).

13. Hayat, T., Khan, M.I., Qayyum, S., et al. "Entropy generation for flow of Sisko fluid due to rotating disk", Journal of Molecular Liquids, 264, pp. 375-385 (2018).

14. Lai, W.C., Yin, P., and Liu, Y.H. "Investigation of flow characteristics from an inclined jet on a heated rotating disk", International Journal of Heat and Mass Transfer, 127, pp. 943-956 (2018).

15. Hassan, M., Fetecau, C., Majeed, A., et al. "Effects of iron nanoparticles' shape on convective flow of ferro fluid under highly oscillating magnetic field over stretchable rotating disk", Journal of Magnetism and Magnetic Materials, 465, pp. 531-539 (2018).

16. Lok, Y.Y., Merkin, J.H., and Pop, I. "Axisymmetric rotational stagnation-point flow impinging on a permeable stretching/shrinking rotating disk", European Journal of Mechanics-B/Fluids, 72, pp. 275-292 (2018).

17. Platt, J.R. "Bioconvection patterns in cultures of freeswimming organisms", Science, 133(3466), pp. 1766- 1767 (1961).

18. Qayyum, S., Imtiaz, M., Alsaedi, A., et al. "Analysis of radiation in a suspension of nanoparticles and gyrotactic microorganism for rotating disk of variable thickness", Chinese Journal of Physics, 56(5), pp. 2404-2423 (2018).

19. Iqbal, Z., Mehmood, Z., and Maraj, E.N. "Oblique transport of gyrotactic microorganisms and bioconvection nanoparticles with convective mass flux", Physica E: Low-dimensional Systems and Nanostructures, 88, pp. 265-271 (2017).

20. Khan, M.I., Waqas, M., Hayat, T., et al. "Behavior of stratification phenomenon in flow of Maxwell nanomaterial with motile gyrotactic microorganisms in the presence of magnetic field", International Journal of Mechanical Sciences, 131, pp. 426-434 (2017).

21. Sivaraj, R., Animasaun, I.L., Olabiyi, A.S., et al. "Gyrotactic microorganisms and thermoelectric effects on the dynamics of 29 nm CuO-water nano fluid over an upper horizontal surface of paraboloid of revolution", Multidiscipline Modeling in Materials and Structures, 14(4), pp. 695-721 (2018).

22. Marinca, V., Herisanu, N., and Nemes, I. "Optimal homotopy asymptotic method with application to thin film flow", Open Physics, 6(3), pp. 648-653 (2008).

23. Sohail, M. and Naz, R. "Modified heat and mass transmission models in the magnetohydrodynamic flow of Sutterby nanofluid in stretching cylinder", Physica A: Statistical Mechanics and Its Applications, 549, 124088 (2020).

24. Sohail, M., Naz, R., and Bilal, S. "Thermal performance of an MHD radiative Oldroyd-B nanofluid by utilizing generalized models for heat and mass fluxes in the presence of bioconvective gyrotactic microorganisms and variable thermal conductivity", Heat Transfer-Asian Research, 48(7), pp. 2659-2675 (2019).

25. Naz, R., Tariq, S., Sohail, M., et al. "Investigation of entropy generation in stratified MHD Carreau nanofluid with gyrotactic microorganisms under Von Neumann similarity transformations", The European Physical Journal Plus, 135(2), 178 (2020).

26. Danish, M., Kumar, S., and Kumar, S. "A note on the solution of singular boundary value problems arising in engineering and applied sciences: Use of OHAM", Computers and Chemical Engineering, 36, pp. 57-67 (2012).

27. Naz, R., Noor, M., Shah, Z., et al. "Entropy generation optimization in MHD pseudoplastic fluid comprising motile microorganisms with stratification effect", Alexandria Engineering Journal, 59(1), pp. 485-496 (2020).

28. Sohail, M., Ali, U., Al-Mdallal, Q., et al. "Theoretical and numerical investigation of entropy for the variable thermophysical characteristics of couple stress material: Applications to optimization", Alexandria Engineering Journal, 59(6), pp. 4365-4375 (2020).

29. Abdelsalam, S.I. and Sohail, M. "Numerical approach of variable thermophysical features of dissipated viscous nanofluid comprising gyrotactic microorganisms", Pramana, 94(1), pp. 1-12 (2020).

30. Liao, S. "An optimal homotopy-analysis approach for strongly nonlinear differential equations", Communications in Nonlinear Science and Numerical Simulation, 15(8), pp. 2003-2016 (2010).

31. Hosseinzadeh, K., Roghani, S., Asadi, A., et al. "Investigation of micropolar hybrid ferrofluid flow over a vertical plate by considering various base fluid and nanoparticle shape factor", International Journal of Numerical Methods for Heat and Fluid Flow, 31(1), pp. 402-417 (2020).

32. Hosseinzadeh, K., Roghani, S., Mogharrebi, A.R., et al. "Investigation of cross-fluid flow containing motile gyrotactic microorganisms and nanoparticles over a three-dimensional cylinder", Alexandria Engineering Journal, 59(5), pp. 3297-3307 (2020).

33. Rostami, A.K., Hosseinzadeh, K., and Ganji, D.D. "Hydrothermal analysis of ethylene glycol nanofluid in a porous enclosure with complex snow flake shaped inner wall", Waves in Random and Complex Media, pp. 1-18 (2020).

34. Das, S., Ali, A., and Jana, R.N. "Darcy-Forchheimer flow of a magneto-radiated couple stress fluid over an inclined exponentially stretching surface with Ohmic dissipation", World Journal of Engineering, 18(2), pp. 345-360 (2020). https://doi.org/10.1108/WJE-07- 2020-0258.

35. Vinoth Kanna, I., Arulprakasajothi, M., and Eliyas, S. "A detailed study of IC engines and a novel discussion with comprehensive view of alternative fuels used in petrol and diesel engines", International Journal of Ambient Energy, 42(115), pp. 1794-1802 (2019).

36. Gholinia, M., Hosseinzadeh, K., and Ganji, D.D. "Investigation of different base fluids suspend by CNTs hybrid nanoparticle over a vertical circular cylinder with sinusoidal radius", Case Studies in Thermal Engineering, 21, 100666 (2020).

37. Hosseinzadeh, K., Ganji, D.D., and Ommi, F., "Effect of SiO2 super-hydrophobic coating and self-rewetting fluid on two phase closed thermosyphon heat transfer characteristics: An experimental and numerical study", Journal of Molecular Liquids, 315, 113748 (2020).

38. Selimefendigil, F. and Oztop, H.F. "Combined effects of double rotating cones and magnetic field on the mixed convection of nanofluid in a porous 3D Ubend", International Communications in Heat and Mass Transfer, 116, 104703 (2020).

39. Selimefendigil, F. and Oztop, H.F. "Magnetohydrodynamics forced convection of nanofluid in multi-layered U-shaped vented cavity with a porous region considering wall corrugation effect", International Communications in Heat and Mass Transfer, 113, 104551 (2020).

40. Naz, R., Mabood, F., Sohail, M. et al. "Thermal and species transportation of Eyring-Powell material over a rotating disk with swimming microorganisms: applications to metallurgy", Journal of Materials Research and Technology, 9(3), May-June 2020, pp. 5577-5590 (2020).

41. Selimefendigil, F. and Oztop, H.F. "Mixed convection in a PCM filled cavity under the influence of a rotating cylinder", Solar Energy, 200, pp. 61-75 (2020).

42. Khan, R.M., Ashraf, W., Sohail, M., et al. "On behavioral response of microstructural slip on the development of magnetohydrodynamic micropolar boundary layer flow", Complexity, 2020 (2020).

43. Selimefendigil, F. and Oztop, H.F. "MHD pulsating forced convection of nanofluid over parallel plates with blocks in a channel", International Journal of Mechanical Sciences, 157, pp. 726-740 (2019).

44. Sohail, M., Nazir, U., Chu, Y.M., et al. "Computational exploration for radiative flow of Sutterby nanofluid with variable temperature-dependent thermal conductivity and diffusion coefficient", Open Physics, 18(1), pp. 1073-1083 (2020).

45. Alsabery, A.I., Selimefendigil, F., Hashim, I., et al. "Fluid-structure interaction analysis of entropy generation and mixed convection inside a cavity with flexible right wall and heated rotating cylinder", International Journal of Heat and Mass Transfer, 140, pp. 331-345 (2019).

46. Rashidi, M.M., Abelman, S., and Mehr, N.F. "Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid", International journal of Heat and Mass transfer, 62, pp. 515-525 (2013).

47. Sheikholeslami, M., Rashidi, M.M., and Ganji, D.D. "Effect of non-uniform magnetic field on forced convection heat transfer of Fe3O4-water nanofluid", Computer Methods in Applied Mechanics and Engineering, 294, pp. 299-312 (2015).

48. Rashidi, M.M., Ali, M., Freidoonimehr, N., et al. "Parametric analysis and optimization of entropy generation in unsteady MHD flow over a stretching rotating disk using artificial neural network and particle swarm optimization algorithm", Energy, 55, pp. 497- 510 (2013).

49. Rashidi, M.M., Kavyani, N., and Abelman, S. "Investigation of entropy generation in MHD and slip flow over a rotating porous disk with variable properties", International Journal of Heat and Mass Transfer, 70, pp. 892-917 (2014).

50. Sheikholeslami, M., Vajravelu, K., and Rashidi, M.M. "Forced convection heat transfer in a semi annulus under the influence of a variable magnetic field", International Journal of Heat and Mass Transfer, 92, pp. 339-348 (2016).

51. Alsaedi, A., Khan, M. I., Farooq, M., et al. "Magnetohydrodynamic (MHD) stratified bioconvective flow of nanofluid due to gyrotactic microorganisms", Advanced Powder Technology, 28(1), pp. 288-298 (2017).

52. Bibi, M., Sohail, M., and Naz, R. "Theoretical analysis of MHD Carreau liquid over a heated rotating disk under Von-Karman transformations", Multidiscipline Modeling in Materials and Structures, 16(2), pp. 390- 408 (2019).

2. Carreau, P.J. "An analysis of the viscous behavior of polymer solutions", Can. J. Chem. Eng., 57, pp. 135- 140 (1979).

3. Khan, M., Malik, M.Y., Salahuddin, T., et al. "Numerical modeling of Carreau fluid due to variable thicked surface", Results in Physics, 7, pp. 2384-2390 (2017).

4. Bilal, S., Alshomrani, A.S., Malik, M.Y., et al. "Analysis of Carreau fluid in the presence of thermal stratification and magnetic field effect", Results in Physics, 10, pp. 118-125 (2018).

5. Irfan, M., Khan, M., and Khan, W.A. "Interaction between chemical species and generalized Fourier's law on 3D flow of Carreau fluid with variable thermal conductivity and heat sink/source: a numerical approach", Results in Physics, 10, pp. 107-117 (2018).

6. Kefayati, G.R. and Tang, H. "MHD thermosolutal natural convection and entropy generation of Carreau fluid in a heated enclosure with two inner circular cold cylinders, using LBM", International Journal of Heat and Mass Transfer, 126, pp. 508-530 (2018).

7. Choi, S.U. and Eastman, J.A. "Enhancing thermal conductivity of fluids with nanoparticles (No. ANL/MSD/CP-84938; CONF-951135-29). Argonne National Lab., IL (United States) (1995).

8. Khanafer, K. and Vafai, K. "A review on the applications of nanofluids in solar energy field", Renewable Energy, 123, pp. 398-406 (2018).

9. Munyalo, J.M. and Zhang, X. "Particle size effect on thermophysical properties of nanofluid and nanofluid based phase change materials: A review", Journal of Molecular Liquids, 265, pp. 77-87 (2018).

10. Sajid, M.U. and Ali, H.M. "Thermal conductivity of hybrid nanofluids: A critical review", International Journal of Heat and Mass Transfer, 126, pp. 211-234 (2018).

11. Rehman, K.U., Alshomrani, A.S., and Malik, M.Y. "Carreau fluid flow in a thermally stratified medium with heat generation/absorption effects", Case Studies in Thermal Engineering, 12, pp. 16-25 (2018).

12. Von Karman, T. "Uber laminare und turbulente Reibung", Z. Angew. Math. Mech., 1, pp. 233-252 (1921).

13. Hayat, T., Khan, M.I., Qayyum, S., et al. "Entropy generation for flow of Sisko fluid due to rotating disk", Journal of Molecular Liquids, 264, pp. 375-385 (2018).

14. Lai, W.C., Yin, P., and Liu, Y.H. "Investigation of flow characteristics from an inclined jet on a heated rotating disk", International Journal of Heat and Mass Transfer, 127, pp. 943-956 (2018).

15. Hassan, M., Fetecau, C., Majeed, A., et al. "Effects of iron nanoparticles' shape on convective flow of ferro fluid under highly oscillating magnetic field over stretchable rotating disk", Journal of Magnetism and Magnetic Materials, 465, pp. 531-539 (2018).

16. Lok, Y.Y., Merkin, J.H., and Pop, I. "Axisymmetric rotational stagnation-point flow impinging on a permeable stretching/shrinking rotating disk", European Journal of Mechanics-B/Fluids, 72, pp. 275-292 (2018).

17. Platt, J.R. "Bioconvection patterns in cultures of freeswimming organisms", Science, 133(3466), pp. 1766- 1767 (1961).

18. Qayyum, S., Imtiaz, M., Alsaedi, A., et al. "Analysis of radiation in a suspension of nanoparticles and gyrotactic microorganism for rotating disk of variable thickness", Chinese Journal of Physics, 56(5), pp. 2404-2423 (2018).

19. Iqbal, Z., Mehmood, Z., and Maraj, E.N. "Oblique transport of gyrotactic microorganisms and bioconvection nanoparticles with convective mass flux", Physica E: Low-dimensional Systems and Nanostructures, 88, pp. 265-271 (2017).

20. Khan, M.I., Waqas, M., Hayat, T., et al. "Behavior of stratification phenomenon in flow of Maxwell nanomaterial with motile gyrotactic microorganisms in the presence of magnetic field", International Journal of Mechanical Sciences, 131, pp. 426-434 (2017).

21. Sivaraj, R., Animasaun, I.L., Olabiyi, A.S., et al. "Gyrotactic microorganisms and thermoelectric effects on the dynamics of 29 nm CuO-water nano fluid over an upper horizontal surface of paraboloid of revolution", Multidiscipline Modeling in Materials and Structures, 14(4), pp. 695-721 (2018).

22. Marinca, V., Herisanu, N., and Nemes, I. "Optimal homotopy asymptotic method with application to thin film flow", Open Physics, 6(3), pp. 648-653 (2008).

23. Sohail, M. and Naz, R. "Modified heat and mass transmission models in the magnetohydrodynamic flow of Sutterby nanofluid in stretching cylinder", Physica A: Statistical Mechanics and Its Applications, 549, 124088 (2020).

24. Sohail, M., Naz, R., and Bilal, S. "Thermal performance of an MHD radiative Oldroyd-B nanofluid by utilizing generalized models for heat and mass fluxes in the presence of bioconvective gyrotactic microorganisms and variable thermal conductivity", Heat Transfer-Asian Research, 48(7), pp. 2659-2675 (2019).

25. Naz, R., Tariq, S., Sohail, M., et al. "Investigation of entropy generation in stratified MHD Carreau nanofluid with gyrotactic microorganisms under Von Neumann similarity transformations", The European Physical Journal Plus, 135(2), 178 (2020).

26. Danish, M., Kumar, S., and Kumar, S. "A note on the solution of singular boundary value problems arising in engineering and applied sciences: Use of OHAM", Computers and Chemical Engineering, 36, pp. 57-67 (2012).

27. Naz, R., Noor, M., Shah, Z., et al. "Entropy generation optimization in MHD pseudoplastic fluid comprising motile microorganisms with stratification effect", Alexandria Engineering Journal, 59(1), pp. 485-496 (2020).

28. Sohail, M., Ali, U., Al-Mdallal, Q., et al. "Theoretical and numerical investigation of entropy for the variable thermophysical characteristics of couple stress material: Applications to optimization", Alexandria Engineering Journal, 59(6), pp. 4365-4375 (2020).

29. Abdelsalam, S.I. and Sohail, M. "Numerical approach of variable thermophysical features of dissipated viscous nanofluid comprising gyrotactic microorganisms", Pramana, 94(1), pp. 1-12 (2020).

30. Liao, S. "An optimal homotopy-analysis approach for strongly nonlinear differential equations", Communications in Nonlinear Science and Numerical Simulation, 15(8), pp. 2003-2016 (2010).

31. Hosseinzadeh, K., Roghani, S., Asadi, A., et al. "Investigation of micropolar hybrid ferrofluid flow over a vertical plate by considering various base fluid and nanoparticle shape factor", International Journal of Numerical Methods for Heat and Fluid Flow, 31(1), pp. 402-417 (2020).

32. Hosseinzadeh, K., Roghani, S., Mogharrebi, A.R., et al. "Investigation of cross-fluid flow containing motile gyrotactic microorganisms and nanoparticles over a three-dimensional cylinder", Alexandria Engineering Journal, 59(5), pp. 3297-3307 (2020).

33. Rostami, A.K., Hosseinzadeh, K., and Ganji, D.D. "Hydrothermal analysis of ethylene glycol nanofluid in a porous enclosure with complex snow flake shaped inner wall", Waves in Random and Complex Media, pp. 1-18 (2020).

34. Das, S., Ali, A., and Jana, R.N. "Darcy-Forchheimer flow of a magneto-radiated couple stress fluid over an inclined exponentially stretching surface with Ohmic dissipation", World Journal of Engineering, 18(2), pp. 345-360 (2020). https://doi.org/10.1108/WJE-07- 2020-0258.

35. Vinoth Kanna, I., Arulprakasajothi, M., and Eliyas, S. "A detailed study of IC engines and a novel discussion with comprehensive view of alternative fuels used in petrol and diesel engines", International Journal of Ambient Energy, 42(115), pp. 1794-1802 (2019).

36. Gholinia, M., Hosseinzadeh, K., and Ganji, D.D. "Investigation of different base fluids suspend by CNTs hybrid nanoparticle over a vertical circular cylinder with sinusoidal radius", Case Studies in Thermal Engineering, 21, 100666 (2020).

37. Hosseinzadeh, K., Ganji, D.D., and Ommi, F., "Effect of SiO2 super-hydrophobic coating and self-rewetting fluid on two phase closed thermosyphon heat transfer characteristics: An experimental and numerical study", Journal of Molecular Liquids, 315, 113748 (2020).

38. Selimefendigil, F. and Oztop, H.F. "Combined effects of double rotating cones and magnetic field on the mixed convection of nanofluid in a porous 3D Ubend", International Communications in Heat and Mass Transfer, 116, 104703 (2020).

39. Selimefendigil, F. and Oztop, H.F. "Magnetohydrodynamics forced convection of nanofluid in multi-layered U-shaped vented cavity with a porous region considering wall corrugation effect", International Communications in Heat and Mass Transfer, 113, 104551 (2020).

40. Naz, R., Mabood, F., Sohail, M. et al. "Thermal and species transportation of Eyring-Powell material over a rotating disk with swimming microorganisms: applications to metallurgy", Journal of Materials Research and Technology, 9(3), May-June 2020, pp. 5577-5590 (2020).

41. Selimefendigil, F. and Oztop, H.F. "Mixed convection in a PCM filled cavity under the influence of a rotating cylinder", Solar Energy, 200, pp. 61-75 (2020).

42. Khan, R.M., Ashraf, W., Sohail, M., et al. "On behavioral response of microstructural slip on the development of magnetohydrodynamic micropolar boundary layer flow", Complexity, 2020 (2020).

43. Selimefendigil, F. and Oztop, H.F. "MHD pulsating forced convection of nanofluid over parallel plates with blocks in a channel", International Journal of Mechanical Sciences, 157, pp. 726-740 (2019).

44. Sohail, M., Nazir, U., Chu, Y.M., et al. "Computational exploration for radiative flow of Sutterby nanofluid with variable temperature-dependent thermal conductivity and diffusion coefficient", Open Physics, 18(1), pp. 1073-1083 (2020).

45. Alsabery, A.I., Selimefendigil, F., Hashim, I., et al. "Fluid-structure interaction analysis of entropy generation and mixed convection inside a cavity with flexible right wall and heated rotating cylinder", International Journal of Heat and Mass Transfer, 140, pp. 331-345 (2019).

46. Rashidi, M.M., Abelman, S., and Mehr, N.F. "Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid", International journal of Heat and Mass transfer, 62, pp. 515-525 (2013).

47. Sheikholeslami, M., Rashidi, M.M., and Ganji, D.D. "Effect of non-uniform magnetic field on forced convection heat transfer of Fe3O4-water nanofluid", Computer Methods in Applied Mechanics and Engineering, 294, pp. 299-312 (2015).

48. Rashidi, M.M., Ali, M., Freidoonimehr, N., et al. "Parametric analysis and optimization of entropy generation in unsteady MHD flow over a stretching rotating disk using artificial neural network and particle swarm optimization algorithm", Energy, 55, pp. 497- 510 (2013).

49. Rashidi, M.M., Kavyani, N., and Abelman, S. "Investigation of entropy generation in MHD and slip flow over a rotating porous disk with variable properties", International Journal of Heat and Mass Transfer, 70, pp. 892-917 (2014).

50. Sheikholeslami, M., Vajravelu, K., and Rashidi, M.M. "Forced convection heat transfer in a semi annulus under the influence of a variable magnetic field", International Journal of Heat and Mass Transfer, 92, pp. 339-348 (2016).

51. Alsaedi, A., Khan, M. I., Farooq, M., et al. "Magnetohydrodynamic (MHD) stratified bioconvective flow of nanofluid due to gyrotactic microorganisms", Advanced Powder Technology, 28(1), pp. 288-298 (2017).

52. Bibi, M., Sohail, M., and Naz, R. "Theoretical analysis of MHD Carreau liquid over a heated rotating disk under Von-Karman transformations", Multidiscipline Modeling in Materials and Structures, 16(2), pp. 390- 408 (2019).

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November and December 2023Pages 2223-2234