Steady Natural Convection of Non-Newtonian Power-Law Fluid in a Trapezoidal Enclosure

Sojoudi, Atta; Saha, Suvash C.; Gu, Yuantong; Hossain, Md. Anwar

doi:10.1155/2013/653108

Cited by 18 publications

(6 citation statements)

References 16 publications

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“…From graphical structures total agreement is accomplished. In addition, tabular values of average Nusselt number against (n) are compared with previous work published by Khezzar et al [30] and Sojoudi et al [33]. From the data it is also depicted that the average Nusselt number magnitudes are in complete agreement with each other.…”

Section: Results Validationsupporting

confidence: 53%

“…Ternik and Rudolf [32] simulated results for hydrodynamic and thermal fields for the power-law rheological model coupled with Boussinesq approximation by incorporating the finite volume method. Sajoudi et al [33] performed delineated convection in a trapezoidal enclosure saturated with quiescent power-law liquid by keeping top and bottom surfaces adiabatic. Turan et al [34] manipulated the influence of the aspect ratio of heaters placed on walls of a rectangular enclosure on steady state simulations of laminar natural convective flow.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Study of Natural Convection of Power Law Fluid in a Square Cavity Fitted with a Uniformly Heated T-Fin

et al. 2022

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Flow of a liquid in an enclosure with heat transfer has drawn special focus of researchers due to the abundant thermal engineering applications. So, the aim of present communication is to explore thermal characteristics of natural convective power-law liquid flow in a square enclosure rooted with a T-shaped fin. The formulation of the problem is executed in the form of partial differential expressions by incorporating the rheological relation of the power-law fluid. The lower wall of the enclosure along with the fin is uniformly heated and vertical walls are prescribed with cold temperature. For effective heat transfer within the cavity the upper boundary is considered thermally insulated. A finite element based commercial software known as COMSOL is used for simulations and discretization of differential equations and is executed incorporating a weak formulation. Domain discretization is performed by dividing it into triangular and rectangular elements at different refinement levels. A grid independence test is accomplished for quantities of engineering interest like local and average Nusselt numbers to attain accuracy and validity in results. Variation in the momentum and thermal distributions against pertinent parameters is analyzed through stream lines and isothermal contour plots. Measurement of the heat flux coefficient along with the calculation of kinetic energy against involved parameters is displayed through graphs and tables. After the comprehensive overview of attained results it is deduced that kinetic energy elevates against the upsurging magnitude of the Rayleigh number, whereas contrary behavior is encapsulated versus power-law index n. Elevation in the Nusselt number for the shear thinning case i.e., n=0.5 adheres as compared to Newtonian i.e., n=1 and shear thickening cases i.e., n=1.5. It is perceived that by the upsurging power-law index viscosity augmentations and circulation zones increases. Heat is transferred quickly against Rayleigh number (Ra) due to production of temperature difference in flow domain.

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Section: Results Validationsupporting

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Numerical Study of Natural Convection of Power Law Fluid in a Square Cavity Fitted with a Uniformly Heated T-Fin

et al. 2022

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“…Распределения линий тока, полученные в работе [Khezzar et al, 2012] (а), настоящие результаты (б) при Ra = 10 5 , Pr = 10 2 , n = 1.0 и 1. Нуссельта на изотермической стенке полости, полученных в данном исследовании и авторами работ [Khezzar et al, 2012;Sojoudi et al, 2013]. Результаты данного сравнения приведены в таблице 1.…”

Section: математическая модельunclassified

Numerical modeling of the natural convection of a non-Newtonian fluid in a closed cavity

Loenko¹,

Sheremet²

2020

CRM

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In this paper, a time-dependent natural convective heat transfer in a closed square cavity filled with non-Newtonian fluid was considered in the presence of an isothermal energy source located on the lower wall of the region under consideration. The vertical boundaries were kept at constant low temperature, while the horizontal walls were completely insulated. The behavior of a non-Newtonian fluid was described by the Ostwald de Ville power law. The process under study was described by transient partial differential equations using dimensionless non-primitive variables "stream function-vorticity-temperature". This method allows excluding the pressure field from the number of unknown parameters, while the non-dimensionalization allows generalizing the obtained results to a variety of physical formulations. The considered mathematical model with the corresponding boundary conditions was solved on the basis of the finite difference method. The algebraic equation for the stream function was solved by the method of successive lower relaxation. Discrete analogs of the vorticity equation and energy equation were solved by the Thomas algorithm. The developed numerical algorithm was tested in detail on a class of model problems and good agreement with other authors was achieved. Also during the study, the mesh sensitivity analysis was performed that allows choosing the optimal mesh. As a result of numerical simulation of unsteady natural convection of a non-Newtonian power-law fluid in a closed square cavity with a local isothermal energy source, the influence of governing parameters was analyzed including the impact of the Rayleigh number in the range 10 4-10 6 , power-law index n = 0.6-1.4, and also the position of the heating element on the flow structure and heat transfer performance inside the cavity. The analysis was carried out on the basis of the obtained distributions of streamlines and isotherms in the cavity, as well as on the basis of the dependences of the average Nusselt number. As a result, it was established that pseudoplastic fluids (n < 1) intensify heat removal from the heater surface. The increase in the Rayleigh number and the central location of the heating element also correspond to the effective cooling of the heat source.

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“…Figure 3 shows the comparison of streamlines at Ra = 10 5 , Pr = 100, n = 1.0 and 1.4, obtained using the developed in-house computational code and numerical data of Khezzar et al [33]. As a result of this validation study, an analysis was obtained for the values of the average Nusselt number at the left isothermal wall of the cavity in comparison with the results [33,34]. Table 1 shows the obtained comparison for the average Nusselt number.…”

Section: Of 12mentioning

confidence: 99%

Natural Convection of Non-Newtonian Power-Law Fluid in a Square Cavity with a Heat-Generating Element

2019

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Development of modern technology in microelectronics and power engineering necessitates the creation of effective cooling systems. This is made possible by the use of the special fins technology within the cavity or special heat transfer liquids in order to intensify the heat removal from the heat-generating elements. The present work is devoted to the mathematical modeling of thermogravitational convection of a non-Newtonian fluid in a closed square cavity with a local source of internal volumetric heat generation. The behavior of the fluid is described by the Ostwald-de Waele power law model. The defining Navier–Stokes equations written using the dimensionless stream function, vorticity and temperature are solved using the finite difference method. The effects of the Rayleigh number, power-law index, and thermal conductivity ratio on heat transfer and the flow structure are studied. The obtained results are presented in the form of isolines of the stream function and temperature, as well as the dependences of the average Nusselt number and average temperature on the governing parameters.

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Steady Natural Convection of Non-Newtonian Power-Law Fluid in a Trapezoidal Enclosure

Cited by 18 publications

References 16 publications

Numerical Study of Natural Convection of Power Law Fluid in a Square Cavity Fitted with a Uniformly Heated T-Fin

Numerical Study of Natural Convection of Power Law Fluid in a Square Cavity Fitted with a Uniformly Heated T-Fin

Numerical modeling of the natural convection of a non-Newtonian fluid in a closed cavity

Natural Convection of Non-Newtonian Power-Law Fluid in a Square Cavity with a Heat-Generating Element

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