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The numerical simulation and sensitivity analysis of a non-Newtonian fluid flow inside a square chamber exposed to a magnetic field using the FDLBM approach

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Abstract

This paper simulated the free convective heat transfer (CHT) and generation of entropy (GOE) of a non-Newtonian fluid (NNF) in a square chamber using the FDLBM approach. The NNF is modeled by the power-law method. A magnetic field (MF) is able to take different angles which has affected the chamber. A hot square barrier exists in the middle of the chamber. The side edges of the chamber have sinusoidal temperature profiles, and the top and bottom sides are insulated. The effective studied parameters include the Hartmann number (Ha), angle of MF, exponential function index, and the aspect ratio (AR) of the hot barrier. The results of simulation disclosed that shear-thinning NNF has the highest CHT and shear-thickening NNF has the lowest GOE. Increasing the AR of the hot barrier led to an increase in the Nusselt number (Nu) and GOE and a decrease in the Bejan number (Be). Increasing the angle of the MF at small ARs with Newtonian fluid increases the Nu. Increasing the Ha from 0 to 40 in shear-thinning NNF, shear-thickening NNF, and Newtonian fluid reduced CHT by 43%, 15%, and 43%, respectively. Increasing the Ha also reduces the GOE by 27% for Newtonian fluid and 763% and 4% shear-thinning NNF and shear-thickening NNF, respectively. Eventually, a relation is proposed for the mean Nu, GOE, and Be.

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Abbreviations

\(B_{0}\) :

Strength of magnetic field

\(C\) :

Lattice speed

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

Specific heat at constant pressure

\(F\) :

External forces

\(f\) :

Density distribution functions

\(f_{{{\text{eq}}}}\) :

Equilibrium density distribution functions

\(g\) :

Internal energy distribution functions

\(g _{{{\text{eq}}}}\) :

Equilibrium internal energy distribution functions

g :

Gravity

H :

Dimensionless enclosure height

\(K\) :

The consistency coefficient

l :

Enclosure height

l 1 :

Thickness of obstacle

L :

Dimensionless thickness of obstacle

\(n\) :

Power-law index

\(Nu\) :

Nusselt number

\(P\) :

Pressure

\(Pr\) :

Prandtl number

S :

Entropy

\(T\) :

Temperature

\(t\) :

Time

\(u\) :

Velocity in x direction

\(v\) :

Velocity in y direction

\(x,y\) :

Cartesian coordinates

\(\sigma\) :

The electrical conductivity

\(\tau\) :

Shear stress

\(\zeta\) :

Discrete particle speeds

\(\Delta x\) :

Lattice spacing

\(\Delta t\) :

Time increment

\(\alpha\) :

Thermal diffusivity

\(\rho\) :

Density

\(\mu\) :

Dynamic viscosity

\(\psi\) :

Stream function value

\(\theta\) :

Angle of magnetic field

\({\text{Ave }}\) :

Average

\(C\) :

Cold

f :

Fluid

gen:

Generation

\(H\) :

Hot

\(x,y\) :

Cartesian coordinates

\(\alpha\) :

The number of the node

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Acknowledgements

This work was supported by the University of Science and Technology Beijing. Muhammad Ibrahim acknowledges the Office of China Postdoctoral Council (OCPC) for the postdoctoral international exchange program. The research was supported by the National Natural Science Foundation of China (Grant Nos. 11971142, 61673169). This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia, under grant number (KEP-17-130-41). The authors, therefore, acknowledge with thanks DSR for technical and financial support. The authors thanks of Dr.Ebrahem A. Algehyne and Murad Ullah.

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Muhammad Ibrahim

  2. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Tareq Saeed & Ahmed Mohammed Alshehri

  3. Department of Mathematics, Huzhou University, Huzhou, 313000, People’s Republic of China

    Yu-Ming Chu

  4. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, People’s Republic of China

    Yu-Ming Chu

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  1. Muhammad Ibrahim
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Ibrahim, M., Saeed, T., Alshehri, A.M. et al. The numerical simulation and sensitivity analysis of a non-Newtonian fluid flow inside a square chamber exposed to a magnetic field using the FDLBM approach. J Therm Anal Calorim 144, 2403–2421 (2021). https://doi.org/10.1007/s10973-021-10695-5

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