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Mathematical modeling of mixed convective MHD Falkner-Skan squeezed Sutterby multiphase flow with non-Fourier heat flux theory and porosity

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Abstract

In a wide variety of mechanical and industrial applications, e.g., space cooling, nuclear reactor cooling, medicinal utilizations (magnetic drug targeting), energy generation, and heat conduction in tissues, the heat transfer phenomenon is involved. Fourier’s law of heat conduction has been used as the foundation for predicting the heat transfer behavior in a variety of real-world contexts. This model’s production of a parabolic energy expression, which means that an initial disturbance would immediately affect the system under investigation, is one of its main drawbacks. Therefore, numerous researchers worked on such problem to resolve this issue. At last, this problem was resolved by Cattaneo by adding relaxation time for heat flux in Fourier’s law, which was defined as the time required to establish steady heat conduction once a temperature gradient is imposed. Christov offered a material invariant version of Cattaneo’s model by taking into account the upper-connected derivative of the Oldroyd model. Nowadays, both models are combinedly known as the Cattaneo-Christov (CC) model. In this attempt, the mixed convective MHD Falkner-Skan Sutterby nanofluid flow is addressed towards a wedge surface in the presence of the variable external magnetic field. The CC model is incorporated instead of Fourier’s law for the examination of heat transfer features in the energy expression. A two-phase nanofluid model is utilized for the implementation of nano-concept. The nonlinear system of equations is tackled through the bvp4c technique in the MATLAB software 2016. The influence of pertinent flow parameters is discussed and displayed through different sketches. Major and important results are summarized in the conclusion section. Furthermore, in both cases of wall-through flow (i.e., suction and injection effects), the porosity parameters increase the flow speed, and decrease the heat transport and the influence of drag forces.

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Abbreviations

K :

permeability variable

S :

suction/injection parameter

λ :

mixed convective parameter

Pr :

Prandtl number

f′ :

dimensionless velocity

θ :

dimensionless temperature field

τ :

the ratio of effective heat capacity

\(Re_{x}^{{1\over{2}}}C_{\rm{f}}\) :

skin friction coefficient

\(Re_{x}^{-{1\over{2}}}Nu_{x}\) :

Nusselt number

U e :

free stream velocity

u, v :

velocity components, m · s−1

β T :

thermal coefficient expansion, \({1\over{k}}\)

g :

acceleration, m · s−2

σ :

electrical conductivity, s3 · m2 · kg−1

B 0 :

constant magnetic field, A−1 · kg · s−2

μ :

dynamic viscosity, kg · (m · s)−1

ν :

kinematic viscosity, m2 · s−1

α :

thermal diffusivity, m2 · s−1

k :

thermal conductivity, kg · m · K−1·s−3

ρ f :

density of fluid, kg · m−3

T :

temperature of the fluid, K

T w :

wall temperature, K

T ∞ :

ambient temperature, K

T f :

surface heat, K.

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Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Large Group Research Project (No. RGP2/19/44).

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Shandong Technology and Business University, Yantai, Shandong Province, 264005, China

    Shuguang Li

  2. Department of Mechanics and Engineering Science, Peking University, Bei**g, 100871, China

    M. I. Khan

  3. Department of Mechanical Engineering, Lebanese American University, Beirut, 11020, Lebanon

    M. I. Khan

  4. Department of Mathematical Sciences, Federal Urdu University of Arts, Sciences & Technology, Gulshan-e-Iqbal, Karachi, 75300, Pakistan

    F. Ali

  5. Faculty of Chemical Engineering, New Uzbekistan University, Tashkent, 100070, Uzbekistan

    S. S. Abdullaev

  6. Department of Science and Innovation, Tashkent State Pedagogical University named after Nizami, Tashkent, 100070, Uzbekistan

    S. S. Abdullaev

  7. Department of Physics, Faculty of Science and Arts, Mohayel Aser, King Khalid University, Abha, 61421, Saudi Arabia

    S. Saadaoui

  8. State Key Laboratory of Turbulence and Complex System, Collaborative Innovative Center for Advanced Aero-Engines, Peking University, Bei**g, 100871, China

    Habibullah

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  1. Shuguang Li
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Correspondence to M. I. Khan.

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Li, S., Khan, M.I., Ali, F. et al. Mathematical modeling of mixed convective MHD Falkner-Skan squeezed Sutterby multiphase flow with non-Fourier heat flux theory and porosity. Appl. Math. Mech.-Engl. Ed. 44, 2005–2018 (2023). https://doi.org/10.1007/s10483-023-3044-5

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  • DOI: https://doi.org/10.1007/s10483-023-3044-5

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