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Effect of Newtonian heating on two-phase fluctuating flow of dusty fluid: Poincaré–Lighthill perturbation technique

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Abstract

This article deals with the two phase fluctuating flow of dusty fluid and heat transfer in the presence of electrically conducting dust particles induces a strong magnetic field. The flow is considered between two parallel non-conducting plates, one at rest and the other in the state of fluctuation. Heat transfers due to free convection and Newtonian heating condition (NHC). The flow is generated due to plate fluctuation. In the sequence to scrutinize methodical solutions, we have used the Poincaré–Lighthill perturbation technique (PLPT). Results are obtained and plotted in graphs. The effect of pertinent parameters on the base fluid velocity such as Grashof number, magnetic parameter, radiation parameter and dusty fluid parameter has been studied. It is noticed that the velocity of the base fluid increases with the decrease in magnetic field and the applied shear stress, i.e., decreases up to some extent but gradually increases for the large magnetic parameter.

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Data Availability Statement

This manuscript has no associated data in a data repository. [Authors’ comment: No data was needed to perform this research. This work is new and all the results are computed from the equations].

Abbreviations

u :

Velocity of the fluid \(\left( \frac{m}{s} \right)\)

v :

Velocity of the dust particle (\(m/s)\)

T :

Temperature of the fluid (\(K\)

T p :

Temperature of the dust particle (\(K)\)

ρ :

Fluid density \(\left( {\frac{Kg}{{m^{3} }}} \right)\)

υ:

Kinematic viscosity \(\left( {\frac{{m^{2} }}{s}} \right)\)

K 0 :

Stock’s resistance coefficient \(\left( {\frac{m}{{s^{2} }}} \right)\)

σ :

Electrical conductivity \(\left( \frac{S}{m} \right)\) S is Siemens.

B 0 :

Applied magnetic field \(\left( {\frac{Kg}{{s^{2} A}}} \right)\)

g :

Gravitational acceleration \(\left( {\frac{m}{{s^{2} }}} \right)\)

β T :

Coefficient of thermal expansion \(\left( \frac{1}{K} \right)\)

k :

Thermal conductivity of the base fluid \(\left( {\frac{w}{m \cdot K}} \right)\)

C s :

Specific heat capacity of the dust particle \(\left( {\frac{j}{Kg \cdot K}} \right)\)

m :

Average mass of the dust particle \(\left( {Kg} \right)\)

T ∞ :

Ambient temperature \(\left( K \right)\)

h s :

Heat transfer coefficient \( \left( \frac{1}{m} \right)\)

N :

Thermal radiation \(\left( j \right)\)

P e :

Peclet number

G r :

Grashof number

M :

Non-dimensional parameter

K 1 :

Dusty fluid parameter

K 2 :

Dusty fluid parameter

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Acknowledgements

The authors extend their appreciation to the deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number (IFP-2020-65).

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Authors and Affiliations

  1. Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia

    Ilyas Khan

  2. Department of Mathematics, City University of Science and Information Technology, Peshawar, 25000, Pakistan

    Dolat Khan & Gohar Ali

  3. Institute of Computer Sciences and Information Technology, The University of Agriculture, Peshawar, Pakistan

    Arshad Khan

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  1. Ilyas Khan
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Correspondence to Ilyas Khan.

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Khan, I., Khan, D., Ali, G. et al. Effect of Newtonian heating on two-phase fluctuating flow of dusty fluid: Poincaré–Lighthill perturbation technique. Eur. Phys. J. Plus 136, 1142 (2021). https://doi.org/10.1140/epjp/s13360-021-02101-8

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