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Numerical Analysis of Natural Convection Driven Flow of a Non-Newtonian Power-Law Fluid in a Trapezoidal Enclosure with a U-Shaped Constructal

Author

Listed:
  • Sardar Bilal

    (Department of Mathematics, Air University, P.A.F Complex E-9, Islamabad 44000, Pakistan)

  • Maryam Rehman

    (Department of Mathematics, Air University, P.A.F Complex E-9, Islamabad 44000, Pakistan)

  • Samad Noeiaghdam

    (Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia
    Department of Applied Mathematics and Programming, South Ural State University, Lenin Prospect 76, 454080 Chelyabinsk, Russia)

  • Hijaz Ahmad

    (Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II 39, 00186 Roma, Italy
    Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah 64001, Iraq)

  • Ali Akgül

    (Department of Mathematics, Art and Science Faculty, Siirt University, Siirt 56100, Turkey)

Abstract

Placement of fins in enclosures has promising utilization in advanced technological processes due to their role as heat reducing/generating elements such as in conventional furnaces, economizers, gas turbines, heat exchangers, superconductive heaters and so forth. The advancement in technologies in power engineering and microelectronics requires the development of effective cooling systems. This evolution involves the utilization of fins of significantly variable geometries enclosed in cavities to increase the heat elimination from heat-generating mechanisms. Since fins are considered to play an effective role in the escalation of heat transmission, the current study is conducted to examine the transfer of heat in cavities embedding fins, as well as the effect of a range of several parameters upon the transmission of energy. The following research is supplemented with the interpretation of the thermo-physical aspects of a power-law liquid enclosed in a trapezoidal cavity embedding a U-shaped fin. The Boussinesq approximation is utilized to generate the mathematical attributes of factors describing natural convection, which are then used in the momentum equation. Furthermore, the Fourier law is applied to formulate the streaming heat inside the fluid flow region. The formulated system describing the problem is non-dimensionalized using similarity transformations. The geometry of the problem comprises a trapezoidal cavity with a non-uniformly heated U-shaped fin introduced at the center of the base of the enclosure. The boundaries of the cavity are at no-slip conditions. Non-uniform heating is provided at the walls ( l 1 and l 2 ) , curves ( c 1 , c 2 and c 3 ) and surfaces ( s 1 and s 2 ) of the fin; the upper wall is insulated whereas the base and sidewalls of the enclosure are kept cold. The solution of the non-dimensionalized equations is procured by the Galerkin finite element procedure. To acquire information regarding the change in displacement w.r.t time and temperature, supplementary quadratic interpolating functions are also observed. An amalgam meshing is constructed to elaborate the triangular and quadrilateral elements of the trapezoidal domain. Observation of significant variation in the flow configurations for a specified range of parameters is taken into consideration i.e., 0.5 ≤ n ≤ 1.5 and 10 4 ≤ R a ≤ 10 6 . Furthermore, flow structures in the form of velocity profiles, streamlines, and temperature contours are interpreted for the parameters taken into account. It is deduced from the study that ascending magnitude of ( R a ) elevates level of kinetic energy and magnitude of heat flux; however, a contrary configuration is encapsulated for the power-law index. Navier–Stokes equations constituting the phenomenon are written with the help of non-dimensionalized stream function, temperature profiles, and vortices, and the solutions are acquired using the finite element method. Furthermore, the attained outcomes are accessible through velocity and temperature profiles. It is worth highlighting the fact that the following analysis enumerates the pseudo-plastic, viscous and dilatant behavior of the fluid for different values of ( n ) . This study highlights that the momentum profile and the heat transportation increase by increasing ( R a ) and decline as the viscosity of the fluid increases. Overall, it can be seen from the current study that heat transportation increases with the insertion of a fin in the cavity. The current communication signifies the phenomenon of a power-law fluid flow filling a trapezoidal cavity enclosing a U-shaped fin. Previously, researchers have studied such phenomena mostly in Newtonian fluids, hence the present effort presents novelty regarding consideration of a power-law liquid in a trapezoidal enclosure by the placement of a U-shaped fin.

Suggested Citation

  • Sardar Bilal & Maryam Rehman & Samad Noeiaghdam & Hijaz Ahmad & Ali Akgül, 2021. "Numerical Analysis of Natural Convection Driven Flow of a Non-Newtonian Power-Law Fluid in a Trapezoidal Enclosure with a U-Shaped Constructal," Energies, MDPI, vol. 14(17), pages 1-17, August.
  • Handle: RePEc:gam:jeners:v:14:y:2021:i:17:p:5355-:d:623994
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    References listed on IDEAS

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    4. Goodarzi, Marjan & D’Orazio, Annunziata & Keshavarzi, Ahmad & Mousavi, Sayedali & Karimipour, Arash, 2018. "Develop the nano scale method of lattice Boltzmann to predict the fluid flow and heat transfer of air in the inclined lid driven cavity with a large heat source inside, Two case studies: Pure natural ," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 210-233.
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    2. Weihua Sun & Zhiyi Yu & Wenwu Zhang, 2022. "Effect of Shear-Thinning Property on the Energy Performance and Flow Field of an Axial Flow Pump," Energies, MDPI, vol. 15(7), pages 1-15, March.
    3. Muhammad Sohail Khan & Sun Mei & Shabnam & Unai Fernandez-Gamiz & Samad Noeiaghdam & Aamir Khan & Said Anwar Shah, 2022. "Electroviscous Effect of Water-Base Nanofluid Flow between Two Parallel Disks with Suction/Injection Effect," Mathematics, MDPI, vol. 10(6), pages 1-15, March.

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