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Spectral quasi-linearization and irreversibility analysis of magnetized cross fluid flow through a microchannel with two different heat sources and Newton boundary conditions

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Abstract

Fluid flow in a microchannel with heat transport effects can be seen in various applications such as micro heat collectors, mechanical–electromechanical systems, electronic device cooling, micro-air vehicles, and micro-heat exchanger systems. However, little is known about the consequence of internal heat source modulations on the flow of fluids in a microchannel. Therefore, in this work, the heat transfer of a magnetized cross fluid is carried out in a micro-channel subjected to two different heat source modulations. Entropy production analysis is also performed. The mathematical model consists of a cross fluid model. In addition, the effects of Joule heating, external magnetism, and the boundary conditions of Newton's heating are also examined. Determinant equations are constructed under steady-state conditions and parameterized using dimensionless variables. The numerical spectral quasi-linearization (SQLM) method was developed to interpret the Bejan number, entropy production, temperature, and velocity profiles. It is established that the power-law index of the cross fluid reduces the magnitude of the entropy production, velocity, and thermal field in the entire microchannel region. Furthermore, a larger Weissenberg number is capable of producing greater entropy, velocity, and thermal fields throughout the microchannel region. The variation in temperature distribution is more noticeable for the ESHS aspect than the THS aspect. The values of the pressure gradient parameter and the Eckert number must be kept high for maximum heat transport of the cross fluid. The entropy production of the cross fluid increases significantly with the physical aspects of Joule heating and convection heating in the system.

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Abbreviations

\(T_{1}\) :

Ambient temperature

\(Be\) :

Bejan number

\(Bi\) :

Biot number

\(h\) :

Channel width

\(E_{0}\) :

The characteristic entropy generation rate

\(L\) :

Characteristic temperature ratio

\(m\) :

Exponential index

\(h_{1} ,h_{2}\) :

Convective heat transfer coefficients

\(N_{v}\) :

Dissipative irreversibility

\(Ec\) :

Eckert number

\(Ns\) :

Entropy generation rate

\(T\) :

Fluid temperature

\(Q_{E}\) :

ESHS parameter

\(Q_{t}\) :

ESHS parameter

\(B_{0}\) :

Magnetic field strength

\({\mathbb{Q}}_{E}\) :

Coefficient of exponential heat source

\(N_{h}\) :

Heat transfer irreversibility

\(T_{2}\) :

Hot fluid temperature

\(\Gamma\) :

Material fluid parameter

\(Pr\) :

Prandtl number

\(p\) :

Pressure

\({\mathbb{Q}}_{T}\) :

Coefficient of thermal heat source

\(Re\) :

Reynolds number

\(cp\) :

Specific heat

\(k\) :

Thermal conductivity

\(n\) :

Power-law index

\(u\) :

Velocity component

\(f\) :

Dimensionless velocity component

\(\sigma\) :

Electric conductivity

\(\rho\) :

Fluid density

\(v_{0}\) :

Velocity of suction/injection

\(\mu\) :

Dynamic viscosity

\(\eta\) :

Dimensionless space variable

\(\theta\) :

Dimensionless temperature

2 :

Lower plate

1 :

Upper plate

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia for funding this work through research groups program under grant number R.G.P-1/128/42.

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Authors and Affiliations

  1. Department of Mechanical and Maintenance Engineering, German Jordanian University, Amman, 11180, Jordan

    Wael Al-Kouz

  2. Department of Mathematics, Government City College, Nayapul, Hyderabad, 500002, India

    C. Srinivas Reddy

  3. Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Saudi Arabia

    M. S. Alqarni

  4. Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia

    M. S. Alqarni

  5. Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, Karnataka, India

    B. Mahanthesh

Authors
  1. Wael Al-Kouz
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  2. C. Srinivas Reddy
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  4. B. Mahanthesh
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Correspondence to Wael Al-Kouz.

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Al-Kouz, W., Reddy, C.S., Alqarni, M.S. et al. Spectral quasi-linearization and irreversibility analysis of magnetized cross fluid flow through a microchannel with two different heat sources and Newton boundary conditions. Eur. Phys. J. Plus 136, 645 (2021). https://doi.org/10.1140/epjp/s13360-021-01625-3

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