Document Type : Article

**Authors**

Department of Mathematics, Capital University of Science and Technology, 44000, Islamabad,Pakistan

**Abstract**

In the present study, MHD Casson nanofluid under the influence of exponential temperature dependent thermal conductivity and variable viscosity past a stretching surface has been scrutinize. After the application of the similarity transformations, the governing partial differential equations of the modelled problem are converted into ordinary differential equations and solution is achieved with the assistance of the shooting method. The solution obtained with the help of shooting technique is used to analyze the distribution of mass and heat flux over sheet. The influence of various governing parameters on the dimensionless velocity, temperature and concentration distribution have been analyzed and discussed in detail. The simulations of the presented model show that the surface drag is upsurged as each of the Casson parameter and temperature dependent thermal conductivity parameter is boosted whereas the rate of heat transfer is diminished. It is also observed that an increment in the temperature near the surface is noted against the thermal conductivity parameter whereas an opposite trend is observed away from the surface.

**Keywords**

References:

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10. Hsiao, K.L. "To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau nanofluid with parameters control method", Energy, 130, pp. 486- 499 (2017).

11. Hsiao, K.L. "Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet", Applied Thermal Engineering, 98, pp. 850-861 (2016).

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25. Hsiao, K.L. "Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects", Applied Thermal Engineering, 112, pp. 1281-1288 (2017).

26. Naz, R., Noor, M., Hayat, T., et al. "Dynamism of magnetohydrodynamic Cross nanofluid with particulars of entropy generation and gyrotactic motile microorganisms", International Communications in Heat and Mass Transfer, 110, p. 104431 (2020).

27. Atif, S.M., Hussain, S., and Sagheer, M. "Heat and mass transfer analysis of time-dependent tangent hyperbolic nanofluid

ow past a wedge," Physics Letters A, 283(11), pp. 1187-1198 (2019).

28. Sheikholeslami, M., Farshad, S.A., Ebrahimpour, et al. "Recent progress on at plate solar collectors and photovoltaic systems in the presence of nanofluid: A review", Journal of Cleaner Production, 293, p. 126119 (2021).

29. Shah, S., Atif, S.M., and Kamran, A. "Radiation and slip effects on MHD Maxwell nanofluid flow over an inclined surface with chemical reaction", Heat Transfer, 50(4), pp. 4062-4085 (2021).

30. Hsiao, K.L. "Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature", International Journal of Heat and Mass Transfer, 112, pp. 983-990, (2017).

31. Atif, S.M., Hussain, S., and Sagheer, M. "Effect of thermal radiation and variable thermal conductivity on magnetohydrodynamics squeezed flow of Carreau fluid over a sensor surface", Journal of Nanofluid, 8, pp. 806-816 2019.

32. Akmal, N., Sagheer, M., Hussain, S., et al. "Study of micropolar nanofluids with power-law spin gradient viscosity model by the Keller box method", Canadian Journal of Physics, 8(4), pp. 16-27 (2020).

33. Shah, S., Hussain, S., and Sagheer, M. "Thermal stratification effects on mixed convective Maxwell fluid flow with variable thermal conductivity and homogeneous/ heterogeneous reactions", Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40, pp. 452-463 (2018).

34. Atif, S.M., Hussain, S., and Sagheer, M. "Effect of viscous dissipation and Joule heating on MHD radiative tangent hyperbolic nanofluid with convective and slip conditions", Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(4), pp. 189- 206 (2019).

35. Atif, S.M., Abbas, M., Rashid, U., et al. "Stagnation point flow of EMHD micropolar nanofluid with mixed convection and slip boundary", Complexity, 2021 (2021).

36. Bestman, A.R. "Natural convection boundary layer with suction and mass transfer in a porous medium", International Journal of Energy Research, 14(4), pp. 389-396 (1990).

37. Nisar, Z., Hayat, T., Alsaedi, A., et al. "Significance of activation energy in radiative peristaltic transport of Eyring Powell nanofluid", International Communications in Heat and Mass Transfer, 116, p. 104655(2020).

38. Azam, M., Xu, T., Shakoor, A., et al. "Effects of Arrhenius activation energy in development of covalent bonding in axisymmetric flow of radiative Cross nanofluid", International Communications in Heat and Mass Transfer, 113, p. 104547 (2020).

39. Reddy, S.R.R., Reddy, P.B.A., and Bhattacharyya, K. "Effect of nonlinear thermal radiation on 3D magneto slip flow of Eyring-Powell nanofluid flow over a slendering sheet with binary chemical reaction and Arrhenius activation energy", Advanced Powder Technology, 30(12), pp. 3203-3213 (2019).

40. Jangilis, S., Adesanya, S.O., and Ogunseye, H.A. "Couple stress fluid flow with variable properties: a second law analysis", Mathematical Methods in Applied Science, 42, pp. 85-98 (2019).

41. Na, T.Y., Computational Methods in Engineering Boundary Value Problems, 145, Academic Press (1979).

42. Nadeem, S., Haq, R.U., and Akbar, N.S. "MHD three dimensional boundary layer flow of Casson nanofluid past a linearly stretching sheet with convective boundary condition", IEEE Transactions on Nanotechnology, 13(1), pp. 109-115 (2014).

43. Ahmad, K. and Nazar, R. "Magnetohydrodynamic three dimensional flow and heat transfer over a stretching surface in a viscoelastic fluid", Journal of Science and Technology, 3 (2011).

44. Ullah, I., Khan, I., and Shafie, S. "MHD natural convection flow of Casson nanofluid over nonlinearly stretching sheet through porous medium with chemical reaction and thermal radiation", Nanoscale Research Letters, 3, pp. 527-539 (2016).

2. Azam, M., Xu, T., and Khan, M. "Numerical simulation for variable thermal properties and heat source/sink in flow of Cross nanofluid over a moving cylinder", International Communications in Heat and Mass Transfer, 118, p. 104832 (2020).

3. Das, R.K., Sokhal, G.S., and Sehgal, S.S. "A numerical study on the performance of water based copper oxide nanofluids in compact channel", Materials Today: Proceedings (2020).

4. Jusoh, R., Nazar, R., and Pop, I. "Dual solutions of magnetohydrodynamic stagnation point flow and heat transfer of viscoelastic nanofluid over a permeable stretching/shrinking sheet with thermal radiation", Journal of Physics: Conference Series, 890(1), 012063 (2017).

5. Rasheed, H.U., Islam, S., Noor, S., et al. " Impact of magneto hydro dynamics on stagnation point slip flow due to nonlinearly propagating sheet with nonuniform thermal reservoir", Mathematical Problems in Engineering, 2020 (2020).

6. Pal, D. and Mandal, G. "Magnetohydrodynamic stagnation point flow of Sisko nanofluid over a stretching sheet with suction", Propulsion and Power Research, 9(4), pp. 408-422 (2020).

7. Abbasi, A., Farooq, W., and Riaz, I. "Stagnation point flow of Maxwell nanofluid containing gyrotactic microorganism impinging obliquely on a convective surface", Heat Transfer, 49(5), pp. 2977-2999. (2020).

8. Lund, L.A., Omar, Z., Khan, I., et al. "Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis", Scientific Reports, 10(1), pp. 1-13 (2020).

9. Sheikholeslami, M., Farshad, S.A., and Said, Z. "Analyzing entropy and thermal behavior of nanomaterial through solar collector involving new tapes", International Communications in Heat and Mass Transfer, 123, p. 105190 (2021).

10. Hsiao, K.L. "To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau nanofluid with parameters control method", Energy, 130, pp. 486- 499 (2017).

11. Hsiao, K.L. "Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet", Applied Thermal Engineering, 98, pp. 850-861 (2016).

12. Chakraborty, S. and Panigrahi, P.K. "Stability of nanofluid: A review", Applied Thermal Engineering, p. 115259 (2020).

13. Khan, M.I., Hafeez, M.U., Hayat, T., et al. "Magneto rotating flow of hybrid nanofluid with entropy generation",Computer Methods and Programs in Biomedicine, 183, p. 105093 (2020).

14. Izadi, A., Siavashi, M., Rasam, H., et al. "MHD enhanced nanofluid mediated heat transfer in porous metal for CPU cooling", Applied Thermal Engineering, 168, p. 114843 (2020).

15. Atif, S.M., Hussain, S. and Sagheer, M. "MHD micropolar nanofluid with non Fourier and non Fick's law", International ommunications in Heat and Mass Transfer, 122, p. 105114 (2021).

16. Sheikholeslami, M. and Farshad, S.A. "Investigation of solar collector system with turbulator considering hybrid nanoparticles", Renewable Energy, 171, pp. 1128-1158 (2021).

17. Atif, S.M., Hussain, S., and Sagheer, M. "Effect of thermal radiation on MHD micropolar Carreau nanofluid with viscous dissipation, Joule heating, and internal heating", Scientia Iranica, 26(6), pp. 3875- 3888 (2019).

18. Aneja, M., Chandra, A., and Sharma, S. "Natural convection in a partially heated porous cavity to Casson fluid", International Communications in Heat and Mass Transfer, 114, p. 104555 (2020).

19. Alwawi, F.A., Alkasasbeh, H.T., Rashad, A.M., et al. "MHD natural convection of sodium alginate Casson nanofluid over a solid sphere", Results in Physics, 16, pp. 102818 (2020).

20. Salehi, F. "Effect of common and new gums on the quality, physical, and textural properties of bakery products: A review", Journal of Texture Studies, 51(2), pp. 361-370 (2020).

21. Hamid, A. "Terrific effects of Ohmic-viscous dissipation on Casson nanofluid flow over a vertical thin needle: buoyancy assisting & opposing flow", Journal of Materials Research and Technology, 9(5), pp. 11220-11230 (2020).

22. Naqvi, S.M.R.S., Muhammad, T., and Asma, M. "Hydromagnetic flow of Casson nanofluid over a porous stretching cylinder with newtonian heat and mass conditions", Physica A: Statistical Mechanics and Its Applications, p. 123988 (2020).

23. Kamran, A., Hussain, S., Sagheer, M., et al. "A numerical study of magnetohydrodynamics flow in Casson nanofluid combined with Joule heating and slip boundary conditions", Results in Physics, 7, pp. 3037-3048 (2017).

24. Ren, Z., Lei, Z., Li, C., et al. "New study and development on electromagnetic field technology in metallurgical processes", Acta Metallurgica Sinica, 56(4), pp. 583-600, (2020).

25. Hsiao, K.L. "Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects", Applied Thermal Engineering, 112, pp. 1281-1288 (2017).

26. Naz, R., Noor, M., Hayat, T., et al. "Dynamism of magnetohydrodynamic Cross nanofluid with particulars of entropy generation and gyrotactic motile microorganisms", International Communications in Heat and Mass Transfer, 110, p. 104431 (2020).

27. Atif, S.M., Hussain, S., and Sagheer, M. "Heat and mass transfer analysis of time-dependent tangent hyperbolic nanofluid

ow past a wedge," Physics Letters A, 283(11), pp. 1187-1198 (2019).

28. Sheikholeslami, M., Farshad, S.A., Ebrahimpour, et al. "Recent progress on at plate solar collectors and photovoltaic systems in the presence of nanofluid: A review", Journal of Cleaner Production, 293, p. 126119 (2021).

29. Shah, S., Atif, S.M., and Kamran, A. "Radiation and slip effects on MHD Maxwell nanofluid flow over an inclined surface with chemical reaction", Heat Transfer, 50(4), pp. 4062-4085 (2021).

30. Hsiao, K.L. "Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature", International Journal of Heat and Mass Transfer, 112, pp. 983-990, (2017).

31. Atif, S.M., Hussain, S., and Sagheer, M. "Effect of thermal radiation and variable thermal conductivity on magnetohydrodynamics squeezed flow of Carreau fluid over a sensor surface", Journal of Nanofluid, 8, pp. 806-816 2019.

32. Akmal, N., Sagheer, M., Hussain, S., et al. "Study of micropolar nanofluids with power-law spin gradient viscosity model by the Keller box method", Canadian Journal of Physics, 8(4), pp. 16-27 (2020).

33. Shah, S., Hussain, S., and Sagheer, M. "Thermal stratification effects on mixed convective Maxwell fluid flow with variable thermal conductivity and homogeneous/ heterogeneous reactions", Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40, pp. 452-463 (2018).

34. Atif, S.M., Hussain, S., and Sagheer, M. "Effect of viscous dissipation and Joule heating on MHD radiative tangent hyperbolic nanofluid with convective and slip conditions", Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(4), pp. 189- 206 (2019).

35. Atif, S.M., Abbas, M., Rashid, U., et al. "Stagnation point flow of EMHD micropolar nanofluid with mixed convection and slip boundary", Complexity, 2021 (2021).

36. Bestman, A.R. "Natural convection boundary layer with suction and mass transfer in a porous medium", International Journal of Energy Research, 14(4), pp. 389-396 (1990).

37. Nisar, Z., Hayat, T., Alsaedi, A., et al. "Significance of activation energy in radiative peristaltic transport of Eyring Powell nanofluid", International Communications in Heat and Mass Transfer, 116, p. 104655(2020).

38. Azam, M., Xu, T., Shakoor, A., et al. "Effects of Arrhenius activation energy in development of covalent bonding in axisymmetric flow of radiative Cross nanofluid", International Communications in Heat and Mass Transfer, 113, p. 104547 (2020).

39. Reddy, S.R.R., Reddy, P.B.A., and Bhattacharyya, K. "Effect of nonlinear thermal radiation on 3D magneto slip flow of Eyring-Powell nanofluid flow over a slendering sheet with binary chemical reaction and Arrhenius activation energy", Advanced Powder Technology, 30(12), pp. 3203-3213 (2019).

40. Jangilis, S., Adesanya, S.O., and Ogunseye, H.A. "Couple stress fluid flow with variable properties: a second law analysis", Mathematical Methods in Applied Science, 42, pp. 85-98 (2019).

41. Na, T.Y., Computational Methods in Engineering Boundary Value Problems, 145, Academic Press (1979).

42. Nadeem, S., Haq, R.U., and Akbar, N.S. "MHD three dimensional boundary layer flow of Casson nanofluid past a linearly stretching sheet with convective boundary condition", IEEE Transactions on Nanotechnology, 13(1), pp. 109-115 (2014).

43. Ahmad, K. and Nazar, R. "Magnetohydrodynamic three dimensional flow and heat transfer over a stretching surface in a viscoelastic fluid", Journal of Science and Technology, 3 (2011).

44. Ullah, I., Khan, I., and Shafie, S. "MHD natural convection flow of Casson nanofluid over nonlinearly stretching sheet through porous medium with chemical reaction and thermal radiation", Nanoscale Research Letters, 3, pp. 527-539 (2016).

Transactions on Nanotechnology (F)

November and December 2022Pages 3570-3581