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Modeling of thermal and solute transport within a Maxwell fluid in contact with a porous rotating disc

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Abstract

In the last few years, there has been much interest in nanofluids on a global scale because of their thermal implications in engineering and biological sciences. A growing number of researchers are looking into the possibility of suspending organized nanoparticles in one base fluid to further boost the thermal performance of conventional ordinary fluids, even though the performance of nanofluids is well-known and has shown promising results in heat transport phenomena. The development of global manufacturing is aided by the non-Newtonian fluid model, which enhances product performance and captures fluid flow dynamics. Therefore, the current study scrutinizes the three-dimensional (3D) rotating disc near a stagnation point flow of Maxwell nanofluid over a porous medium. The Maxwell nanofluid is selected as the operational fluid since it is indicated that this model accurately captures the behavior of viscoelastic fluids and is successful in modeling polymeric liquids. The considerable terms are convective heat, heat source/sink, and chemical species which have been implemented frequently in the present exploration. The thermophoresis and Brownian motion of the nanoparticles are monitored using a novel modification of Buongiorno's nanofluid model. The nature of Maxwell nanofluid is described by this model. The systems of modeled equations have been rendered into the set of ODEs and are derived via Von Kaman’s similarity transformations. A numerical approach, namely bvp4c in Matlab is used to compute the solution of the set of ODEs. The main implications of the rapidly growing parameters versus relevant domains are examined using graphical and tabular illustrations. The effects of different factors on the solution profiles are also discussed. The data obtained demonstrate that the radial velocity and angular velocity are reduced through the Deborah number parameter, while both velocities are significantly upswing with enlarging the rotational parameter for the respective phenomenon of suction and injection parameter. Additionally, it is renowned that the rotation of the disc causes a drop in the radial velocity and increases the angular velocity via the uplift of the Darcy parameter. It is also discovered that temperature and concentration profiles display diverse behavior for porous medium factors.

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Data availability

All the data have been included in the form of graphs and tables in this manuscript.

Abbreviations

\(c,b\) :

Constants

\(u,v,w\) :

Velocity components

\(r,\varphi ,z\) :

Cylindrical coordinates

\({\text{Re}}\) :

Reynolds number

\(\omega_1\) :

Angular velocity

\(u_{\text{e}}\) :

Free stream velocity

\(\lambda_1\) :

Deborah number

\(\lambda_2\) :

Porous medium

\(K\) :

Permeability parameter

\(\varepsilon\) :

Velocity ratio parameter

\(Fr\) :

Darcy Forchheimer parameter

\(\Pr\) :

Prandtl number

\(Nt\) :

Thermophoresis parameter

\(Nb\) :

Brownian motion parameter

\(\Upsilon\) :

Heat source/sink parameter

\(Sc\) :

Schmidt number

\(Cr\) :

Chemical reaction constant

\(S\) :

Suction/injection parameter

\(Bi\) :

Biot number

\(D_{\text{B}}\) :

Brownian diffusion coefficient

\(D_{\text{T}}\) :

Thermophoresis parameter

\(F,G,H\) :

Dimensionless velocity component

\(\Theta\) :

Dimensionless temperature

\(\phi\) :

Dimensionless concentration

\(\zeta\) :

Pseudo-similarity variable

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

Temperature of the hot fluid

\(T_\infty\) :

Ambient temperature

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

Concentration at the wall surface of the disc

\(C_\infty\) :

Ambient concentration

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

Specific heat at constant pressure

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

Skin friction

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

Local Nusselt number

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

Local Sherwood number

\(\beta_1\) :

Relaxation time of fluid

\(k\) :

Thermal conductivity

\(Q_\circ\) :

Volumetric rate of heat generation/absorption

\(\rho\) :

Density of the fluid

\(\upsilon\) :

Kinematic viscosity

\(k_1\) :

Chemical reaction rate constant

\(\tau\) :

Ratio of heat capacity to the base fluid

\(\psi\) :

Stream Function

\(\alpha_{\text{m}}\) :

Thermal diffusivity

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Acknowledgements

This research has been funded by Scientific Research Deanship at University of Hail—Saudi Arabia through project number RG-23 082.

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Authors and Affiliations

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

    Muhammad Faizan & Aurang Zaib

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

    Umair Khan & Anuar Ishak

  3. Department of Mathematics, Faculty of Science, Sakarya University, Serdivan/Sakarya, 54050, Turkey

    Umair Khan

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

    Umair Khan

  5. Department of Civil Engineering, College of Engineering, University of Hail, Hail, Saudi Arabia

    Hatem Gasmi & Ahmed Al-Naghi

  6. LR14ES03 Laboratoire d’Ingé Nierie Géotechnique, Ecole Nationale d’Ingé Nieurs de Tunis, Université de Tunis El Manar, 1002, Tunis, Tunisia

    Hatem Gasmi & Hatem Karoui

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  1. Muhammad Faizan
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Correspondence to Umair Khan.

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Faizan, M., Zaib, A., Khan, U. et al. Modeling of thermal and solute transport within a Maxwell fluid in contact with a porous rotating disc. Eur. Phys. J. Spec. Top. (2024). https://doi.org/10.1140/epjs/s11734-024-01135-0

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