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An impact of MHD and radiation on Boussinesq–Stokes suspensions fluid flow past a porous flat plate with mass suction/injection

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Abstract

The present study reveals the analytical model to inquiry impact of an inclined magnetic field and radiation on Boussinesq–Stokes suspension flow over a porous flat surface in the presence of mass suction/injection and viscous dissipation. By adopting a system of nonlinear partial differential equations to model the entire physical situation, a proper similarity variable may turn the system of equations into nonlinear ordinary differential equations and is solved analytically. The impact of emerging flow parameter on velocity, temperature, and local skin friction coefficient is described comprehensively through graphs. The findings also suggest that momentum boundary layer thickness diminishes with decreases magnetic field strength in the presence of suction/injection case, and thermal boundary layer thickness accelerates with radiation and Eckert number parameter. Nonetheless, there are several applications for this research in a variety of engineering domains and technology, for instance geophysics, polymer processing, total energy consumption, electric engines, blood flow measures, pumps, and flow metres.

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Abbreviations

PDEs:

Partial differential equations

ODEs:

Ordinary differential equations

MHD:

Magnetohydrodynamic

NN:

Non-Newtonian

\(B_{0}\) :

Uniform magnetic field strength (Tesla)

\(C_{{\text{p}}}\) :

Specific heat (Jk−1 Kg−1)

\(d\) :

Constant

\({\text{Da}}^{ - 1}\) :

Inverse Darcy number \(\left( {{\mu \mathord{\left/ {\vphantom {\mu {\rho K^{*} U_{\infty }^{2} }}} \right. \kern-0pt} {\rho K^{*} U_{\infty }^{2} }}} \right)\)

\(f\) :

Non-dimensional function

\(K^{*}\) :

Permeability (N/A2)

\(k^{*}\) :

Mean absorption coefficient

\(M\) :

Magnetic field \(\left( {{{B_{0}^{2} \sigma \nu } \mathord{\left/ {\vphantom {{B_{0}^{2} \sigma \nu } {\rho U_{\infty }^{2} }}} \right. \kern-0pt} {\rho U_{\infty }^{2} }}} \right)\)

\(N_{{\text{r}}}\) :

Radiation \(\left( {16\sigma^{*} T_{\infty }^{3} /3k^{*} \kappa } \right)\)

\(\Pr\) :

Prandtl number \(\left( {{{\mu c_{{\text{p}}} } \mathord{\left/ {\vphantom {{\mu c_{{\text{p}}} } \kappa }} \right. \kern-0pt} \kappa }} \right)\)

\(q_{{\text{r}}}\) :

Radiative heat flux (Wm−2)

\(s\) :

Mass suction/injection

\(T\) :

Fluid temperature (K)

\(T_{{\text{w}}}\) :

Surface temperature (K)

\(T_{\infty }\) :

Far temperature (K)

\(u,v\) :

Velocity components of x, y directions (m s−1)

\(x,y\) :

Coordinate systems (m)

\(\mu\) :

Dynamic viscosity (Nsm−1)

\(\rho\) :

Density (kg m−3)

\(\nu\) :

Kinematic viscosity (m2 s−1)

\(\kappa_{{\text{f}}}\) :

Thermal conductivity (W m−1 K−1)

\(\sigma\) :

Electrical conductivity (S m−1)

\(\sigma^{*}\) :

Stefan–Boltzman constant (W m−1 K−1)

\(\Gamma_{1} ,\Gamma_{2}\) :

Constants

\(\beta\) :

Solution domain

References

  1. Stokes VK. Couple stress in fluids. Phys Fluids. 1966;9:1709–15.

    Article  CAS  Google Scholar 

  2. Stokes VK. Theories of fluids with microstructure. New York, NY, USA: Springer; 1984.

  3. Naduvinamani NB, Fathima ST, Hiremath PS. Effect of surface roughness on characteristics of couple stress squeeze film between anisotropic porous rectangular plates. Fluid Dyn Res. 2003;32:217–31.

    Article  Google Scholar 

  4. Naduvinamani NB, Syeda TF, Hiremath PS. Hydrodynamic lubrication of rough slider bearings with couple stress fluids. Tribol Int. 2003;36:949–59.

    Article  Google Scholar 

  5. Madasu KP, Sarkar P. Couple stress fluid past a sphere embedded in a porous medium. Arch Mech Eng. 2022;69:5–19.

    Google Scholar 

  6. Devakar M, Sreenivasu D, Shankar B. Analytical solution of couple stress fluid flows with slip boundary conditions. Alex Eng J. 2014;53:723–30.

    Article  Google Scholar 

  7. Sneha KN, Vanitha GP, Mahabaleshwar US, Laroze D. Effect of couple stress and mass transpiration on ternary hybrid nanoliquid over a stretching/shrinking sheet with heat transfer. Micromachines. 2022;13:1694.

    Article  PubMed  PubMed Central  Google Scholar 

  8. Gangadhar K, Bhargavi ND, Rao MVS, Chamkha AJ. Entropy minimization on magnetized Boussinesq couple stress fluid with non-uniform heat generation. Phys Scr. 2021;96:095205.

    Article  Google Scholar 

  9. Munivenkatappa U, Aswathanarayana DP, Reddy AS, Ramakrishna SB. Effect of couple stress fluid in an irregular Couette flow channel: an analytical approach. Biointerface Res Appl Chem. 2022;12:4686–704.

    CAS  Google Scholar 

  10. Adesanya SO, Fakoya MB. Second law analysis for couple stress fluid flow through a porous medium with constant heat flux. Entropy. 2017;19:498.

    Article  Google Scholar 

  11. Mahabaleshwar US, Sarris IE, Hill AA, Lorenzini G, Pop I. An MHD couple stress fluid due to a perforated sheet undergoing linear stretching with heat transfer. Int J Heat Mass Transf. 2017;105:157–67.

    Article  CAS  Google Scholar 

  12. Turkyilmazoglu M. Exact solution for two-dimensional laminar flow over a continuously stretching or shrinking sheet in an electrically conducting quiescent couple stress fluid. Int J Heat Mass Transf. 2014;72:1–8.

    Article  Google Scholar 

  13. Gajjela N, Nandkeolyar R. Investigating the magnetohydrodynamic flow of a couple stress dusty fluid along a stretching sheet in the presences of viscous dissipation and suction. Heat Transf. 2021;50:2709–24.

    Article  Google Scholar 

  14. Krishna MV, Chamkha AJ. Hall and ion slip effects on unsteady MHD convective rotating flow of nanofluids-applications in biomedical engineering. J Egypt Math Soc. 2020;1:28.

    Google Scholar 

  15. Soliman MS. MHD three-dimensional flow of couple stress nanofluids over a stretching sheet through a porous medium in presence of heat generation/absorption and non-linear thermal radiation. Chall Nano Micro Scale Sci Tech. 2021;9:135–50.

    Google Scholar 

  16. Mallikarjun P, Murthy RV, Mahabaleshwar US, Lorenzini G. Numerical study of mixed convective flow of a couple stress fluid in a vertical channel with first order chemical reaction and heat generation/absorption. Math Model Eng. 2019;6:175–82.

    Google Scholar 

  17. Reddy GJ, Kumar M, Kethireddy B, Chamkha AJ. Colloidal study of unsteady magnetohydrodynamic couple stress fluid flow over an isothermal vertical flat plate with entropy heat generation. J Mol Liq. 2018;252:169–79.

    Article  Google Scholar 

  18. Prasad RS, Kumar R, Prasad BG. Study of couple stresses on MHD Poiseuille flow through a porous medium past an accelerated plate. Bull Pure Appl Sci E Math Stat. 2021;40E:45–59.

    Article  Google Scholar 

  19. Mahabaleshwar US, Maranna T, Mishra MR, Hatami M, Sunden B. Radiation effect on stagnation point flow of Casson nanofluid past a stretching plate/cylinder. Sci Rep. 2024;14:1387.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Rajamani S, Reddy AS. Effects of joule heating thermal radiation on MHD pulsating flow of a couple stress hybrid nanofluid in a permeable channel. Nonlinear Anal Model Control. 2022;27:684–99.

    Google Scholar 

  21. Hayat T, Asad S, Alsaedi A. Non-uniform heat source/sink and thermal radiation effects on the stretched flow of cylinder in a thermally stratified medium. J Appl Fluid Mech. 2016;10:915–24.

    Google Scholar 

  22. Gireesh BJ, Anitha L. Entropy generation analysis in magnetohydrodynamic couple stress nanofluid flow through an oblique microchannel in a permeable medium with thermal radiation. J Nanofluids. 2023;12:996–1007.

    Article  Google Scholar 

  23. Shafiq A, Colak AB, Sindhu TN. Significance of EMHD graphene oxide(GO) water ethylene glycol nanofluid flow in a Darcy-Forchheimer medium by machine learning algorithm. Eur Phys J Plus. 2023;138:213.

    Article  CAS  Google Scholar 

  24. Shafiq A, Colak AB, Sindhu TN. Significance of bioconvective flow of MHD thixotropic nanofluid passing through a vertical surface by machine learning algorithm. Chin J Phys. 2022;80:427–44.

    Article  CAS  Google Scholar 

  25. Chamkha AJ, Ben-Nakhi A. MHD mixed convection-radiation interaction along a permeable surface immersed in a porous medium in the presence of Soret and Dufour’s effects. Heat Mass Transf. 2008;44:845–56.

    Article  Google Scholar 

  26. Krishna MV, Jyothi K, Chamkha AJ. Heat and mass transfer on MHD flow of second-grade fluid through porous medium over a semi-infinite vertical stretching sheet. J Porous Media. 2020;23:751–65.

    Article  Google Scholar 

  27. Brinkman HC. Heat effects in capillary flow. I Appl Sci Res. 1951;A2:120–4.

    Article  Google Scholar 

  28. Turkyilmazoglu M. Asymptotic suction/injection flow induced by a uniform magnetohydrodynamic free stream couple stress fluid over a flat surface. J Fluids Eng. 2022;144:031301.

    Article  CAS  Google Scholar 

  29. El Arabawy HA. Effect of suction/injection on the flow of a micropolar fluid past a continuously moving plate in the presence of radiation. Int J Heat Mass Transf. 2003;46:1471–7.

    Article  Google Scholar 

  30. Kishan N, Deepa G. Viscous dissipation effects on stagnation point flow and heat transfer of a micropolar fluid with uniform suction or blowing. Adv Appl Sci Res. 2012;3:430–9.

    Google Scholar 

  31. Mahabaleshwar US, Vishalakshi AB, Bognar GV, Mallikarjun SM. Effect of thermal radiation on the flow of a Boussinesq couple stress nanofluid over a porous nonlinear stretching sheet. Int J Appl Comput Math. 2022;8:169.

    Article  Google Scholar 

  32. Biswas N, Mahapatra PS, Manna NK. Thermal management of heating element in a ventilated enclosure. Int Commun Heat Mass Transf. 2015;66:84–92.

    Article  Google Scholar 

  33. Biswas N, Mahapatra PS, Manna NK. Mixed convection heat transfer in a grooved channel with injection. Numer Heat Transf A. 2015;68:663–85.

    Article  CAS  Google Scholar 

  34. Chakravarty A, Biswas N, Ghosh K, Manna NK, Mukhopadhyay A, Sen S. Impact of side injection on heat removal from truncated conical heat-generating porous bed: thermal non-equilibrium approach. J Therm Anal Calorim. 2021;143:3741–60.

    Article  CAS  Google Scholar 

  35. Biswas N, Manna NK, Datta P, Mahapatra PS. Analysis of heat transfer and pumping power for bottom-heated porous cavity saturated with Cu-water nanofluid. Powder Technol. 2018;326:356–69.

    Article  CAS  Google Scholar 

  36. Venkata Ramadu AC, Anantha Kumar K, Sugunamma V, Sandeep N. Influence of suction/injection on MHD Casson fluid flow over a vertical stretching surface. J Therm Anal Calorim. 2019;113:1–8.

    Google Scholar 

  37. Anantha Kumar K, Sugunamma V, Sandeep N. Influence of viscous dissipation on MHD flow of micropolar fluid flow over a slandering stretching surface with modified heat flux model. J Therm Anal Calorim. 2019;139:3661–74.

    Article  Google Scholar 

  38. Sneha KN, Mahabaleshwar US, Bhattacharyya S. An effect of thermal radiation on inclined MHD flow in hybrid nanofluids over a stretching/shrinking sheet. J Therm Anal Calorim. 2023;148:2961–75.

    Article  CAS  Google Scholar 

  39. Chamkha AJ. Non-Darcy hydromagnetic free convection from a cone and a wedge in porous media. Int Comm Heat Mass Transfer. 1996;223:875–87.

    Article  Google Scholar 

  40. Chamkha AJ. Non-Darcy fully developed mixed convection in a porous medium channel with heat generation/absorption and hydromagnetic effects. Numer Heat Transf A Appl. 1997;32:653–75.

    Article  Google Scholar 

  41. Ellahi R, Bhatti MM, Fetecau C, Vafai K. Peristaltic flow of couple stress fluid in a non-uniform rectangular duct having compliant walls. Commun Theor Phys. 2016;65:66.

    Article  CAS  Google Scholar 

  42. Cortell R. Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Phys Lett A. 2008;372:631–6.

    Article  CAS  Google Scholar 

  43. Maranna T, Mahabaleshwar US, Bognar GV, Oztop HF. Effect of radiation and injection on a Newtonian fluid flow due to porous shrinking sheet with Brinkman model. J Porous Media. 2024;27:13–34.

    Article  Google Scholar 

  44. Vishala HV, Maranna T, Mahabaleshwar US, Souayeh B. The impact of radiation and Marangoni boundary condition on fluid flow through s porous medium with Brinkman model. Math Model Fluid Dyns Nanofluids. 2024;1:138–52.

    Google Scholar 

  45. Vishalakshi AB, Mahabaleshwar US, Laroze D, Zeidan D. A study of mixed convective ternary hybrid nanofluid flow over a stretching sheet with radiation and transpiration. Spec Top Rev Porous Media. 2023;14:33–51.

    Article  Google Scholar 

  46. Sachhin SM, Mahabaleshwar US, Huang HN, Sunden B, Zeidan D. An influence of temperature jump and Navier’s slip on hybrid nanofluid flow over a permeable stretching/shrinking sheet with heat transfer and inclined MHD. Nanotechnol. 2024;35:115401.

    Article  Google Scholar 

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Acknowledgements

The author T. Maranna would like to thank the financial assistance received from Karnataka Science and Technology Society (KSTePS) under the program of Karnataka DST-Ph.D fellowship for Science and Engineering: DST/KSTePS/Ph.D.Fellowship/MP-07:2023-24.This work is also funded by the Grant NRF2022-R1A2C2002799 of the National Research Foundation of Korea. The work of the author H.-N. Huang is partially supported under the grant No. MOST 110-2115-M-029-002. Dia Zeidan also acknowledges the support provided by the German Jordanian University, Amman, Jordan.

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Authors and Affiliations

  1. Department of Studies in Mathematics, Davangere University, Shivagangothri, Davangere, 577007, India

    U. S. Mahabaleshwar & T. Maranna

  2. Department of Applied Mathematics, Tunghai University, Taichung, 407224, Taiwan

    H. N. Huang

  3. School of Mechanical Engineering, Yeungnam University, Gyeongsan, 38541, Korea

    S. W. Joo

  4. School of Electrical Engineering and Information Technology, German Jordanian University, Amman, Jordan

    Dia Zeidan

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  1. U. S. Mahabaleshwar
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Contributions

U. S. Mahabaleshwar was contributed supervision, modelling and solving the problem, formal analysis and investigation, writing–original draft, and numerical computations. T. Maranna was involved methodology, investigation and formal analysis, numerical computations, programming in mathematica, and plotting the graphical results. H.N. Huang was performed modelling and solving the problem, writing, review and editing, and validation of the results. S. W. Joo was attributed conceptualization and supporting, writing, review, and editing. Dia Zeidan was done corresponding author, supervision, validation of the results, and writing–review and editing. All the authors have contributed equally to this manuscript.

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Correspondence to Dia Zeidan.

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Mahabaleshwar, U.S., Maranna, T., Huang, H.N. et al. An impact of MHD and radiation on Boussinesq–Stokes suspensions fluid flow past a porous flat plate with mass suction/injection. J Therm Anal Calorim (2024). https://doi.org/10.1007/s10973-024-13120-9

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