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Two-Phase Numerical Simulation for the Heat and Mass Transfer Evaluation Across a Vertical Deformable Sheet with Significant Impact of Solar Radiation and Heat Source/Sink

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Abstract

The growing need for industrial development, limited availability of non-renewable energy resources, minimizing energy consumption, and ecosystem concerns has prompted researchers to explore the practical applications of two-phase nanofluid materials processing and electromagnetic energy emitted via the sun. Therefore, using two-phase nanofluids in solar thermal technology systems can enhance system performance by improving heat absorption and transfer efficiency. Owing to its usage, this study examines the magnetized two-phase nanofluid flow on a two-dimensional laminar mixed convective boundary layer with the impact of multiple slips. The flow contains an electrically conducting non-Newtonian nanofluid over a deformable (stretching/shrinking) sheet with a solar radiation effect. Also, the study utilizes a nonlinear Roseland diffusion flux approximation to incorporate the solar radiation effect, which is valid for nanofluid media with high optical density. This work utilizes similarity variables to simplify the partial derivative model into ordinary differential equations. These equations are then solved using the wavelets and Chebyshev wavelets scheme with the help of MATHEMATICA 11.3 software. According to the findings, the nanoparticle volume fraction is increased for high electrical conductivity (M = 2) and decreased for the electrically non-conducting case (M = 0).

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Abbreviations

\({\overline{U} }_{{\text{e}}}\) :

External velocity

\(\tau\) :

Nanoparticle heat capacity

\(k\) :

Thermal conductivity

\(\sigma\) :

\

Electric conductivity

\({\sigma }_{0}\) :

Electric conductivity

\({B}_{0}\) :

Constant magnetic field

\({k}_{{\text{p}}}\) :

Permeability

\({E}_{1}\) :

Solutal slip

\({\beta }_{0}\) :

Thermal expansion coefficient

\({\overline{u} }_{{\text{slip}}}\) :

Velocity slip

\({\text{Ec}}\) :

Eckert number

\({N}_{{\text{r}}}\) :

Buoyancy ratio

\(\xi\) :

Stretching or Shrinking sheet parameter

\(b\) :

Thermal slip parameter

\({\text{Tr}}\) :

Excess wall temperature

\({\text{Nt}}\) :

Thermophoresis parameter

\(a\) :

Velocity slip parameter

\(\xi >0\) :

Stretching sheet

\(\xi =0\) :

Static sheet

\({\alpha }^{*}\) :

Thermal diffusivity

\({\rho }_{f}\) :

Density

\({\rho }_{f\infty }\) :

Ambient fluid density

\({\vartheta }_{{\text{f}}}\) :

Kinematic Casson fluid

\(B\left(\overline{x }\right)\) :

Magnetic field

\({\rho }_{p}\) :

Density of nanoparticle

\(g\) :

Acceleration due to gravity

\({D}_{1}\) :

Thermal slip factor

\({D}_{{\text{B}}}\) :

Brownian diffusion

\({D}_{{\text{T}}}\) :

Thermophoresis diffusion

\({\text{Ra}}\) :

Rayleigh number

\({\text{Da}}\) :

Darcy number

\(c\) :

Mass slip parameter

\({\text{Pr}}\) :

Prandtl number

\({\text{Rd}}\) :

Thermal radiation

\({\text{Le}}\) :

Lewis number

\(\xi\) :

Shrinking sheet parameter

\(\xi <0\) :

Shrinking sheet

MBL:

Momentum boundary layer

TBL:

Thermal boundary layer

CBL:

Concentrations boundary layer

NFs:

Nanofluid

CF:

Casson fluid

NPs:

Nanoparticles

MHD:

Magnetohydrodynamics

MRI:

Magnetic resonance imaging

NNF:

Non-Newtonian fluid

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Acknowledgements

The authors extend their appreciation to the research unit at King Khalid University for funding this work through Project number 495 and the authors acknowledge the Research Center for Advanced Materials Science (RCAMS) at King Khalid University, Saudi Arabia for their valuable technical support.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Augustine University Ilara-Epe, Lagos, Nigeria

    A. M. Obalalu

  2. Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria

    M. O. Oni

  3. Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM, 43600, Bangi, Selangor, Malaysia

    Umair Khan

  4. Department of Computer Science and Mathematics, Lebanese American University, Byblos, 1401, Lebanon

    Umair Khan

  5. Department of Mathematics and Social Sciences, Sukkur IBA University, Sukkur, Sindh, 65200, Pakistan

    Umair Khan

  6. Department of Mathematics, Faculty of Science, University of Gujrat, Sub-Campus, Mandi Bahauddin, 50400, Pakistan

    Amir Abbas

  7. Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia

    Taseer Muhammad

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

    Aurang Zaib

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  1. A. M. Obalalu
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Correspondence to Aurang Zaib.

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Obalalu, A.M., Oni, M.O., Khan, U. et al. Two-Phase Numerical Simulation for the Heat and Mass Transfer Evaluation Across a Vertical Deformable Sheet with Significant Impact of Solar Radiation and Heat Source/Sink. Arab J Sci Eng (2023). https://doi.org/10.1007/s13369-023-08585-z

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