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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 20 Feb 2020 13:49:32 GMT2020-02-20T13:49:32ZParametric solution of the Rayleigh-Benard convection model by using the PGD Application to nanofluids
http://hdl.handle.net/10985/10242
Parametric solution of the Rayleigh-Benard convection model by using the PGD Application to nanofluids
AGHIGHI, Mohammad Saeid; AMMAR, Amine; METIVIER, Christel; CHINESTA, Francisco
Purpose – The purpose of this paper is to focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural thermal convection. This flow is fully determined by the dimensionless Prandtl and Rayleigh numbers. Thus, if one could precompute (off-line) the model solution for any possible choice of these two parameters the analysis of many possible scenarios could be performed on-line and in real time. Design/methodology/approach – In this paper both parameters are introduced as model extracoordinates, and then the resulting multidimensional problem solved thanks to the space-parameters separated representation involved in the proper generalized decomposition (PGD) that allows circumventing the curse of dimensionality. Thus the parametric solution will be available fast and easily. Findings – Such parametric solution could be viewed as a sort of abacus, but despite its inherent interest such calculation is at present unaffordable for nowadays computing availabilities because one must solve too many problems and of course store all the solutions related to each choice of both parameters. Originality/value – Parametric solution of coupled models by using the PGD. Model reduction of complex coupled flow models. Analysis of Rayleigh-Bernard flows involving nanofluids.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/102422015-01-01T00:00:00ZAGHIGHI, Mohammad SaeidAMMAR, AmineMETIVIER, ChristelCHINESTA, FranciscoPurpose – The purpose of this paper is to focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural thermal convection. This flow is fully determined by the dimensionless Prandtl and Rayleigh numbers. Thus, if one could precompute (off-line) the model solution for any possible choice of these two parameters the analysis of many possible scenarios could be performed on-line and in real time. Design/methodology/approach – In this paper both parameters are introduced as model extracoordinates, and then the resulting multidimensional problem solved thanks to the space-parameters separated representation involved in the proper generalized decomposition (PGD) that allows circumventing the curse of dimensionality. Thus the parametric solution will be available fast and easily. Findings – Such parametric solution could be viewed as a sort of abacus, but despite its inherent interest such calculation is at present unaffordable for nowadays computing availabilities because one must solve too many problems and of course store all the solutions related to each choice of both parameters. Originality/value – Parametric solution of coupled models by using the PGD. Model reduction of complex coupled flow models. Analysis of Rayleigh-Bernard flows involving nanofluids.Non-incremental transient solution of the Rayleigh–Bénard convection model by using the PGD
http://hdl.handle.net/10985/10265
Non-incremental transient solution of the Rayleigh–Bénard convection model by using the PGD
AGHIGHI, Mohammad Saeid; AMMAR, Amine; METIVIER, Christel; NORMANDIN, Magdeleine; CHINESTA, Francisco
This paper focuses on the non-incremental solution of transient coupled non-linear models, in particular the one related to the Rayleigh–Bénard flow problem that models natural thermal convection. For this purpose we are applying the so-called Proper Generalized Decomposition that proceeds by performing space-time separated representations of the different unknown fields involved by the flow model. This non-incremental solution strategy allows significant computational time savings and opens new perspectives for introducing some flow and/or fluid parameters as extra-coordinates.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/102652013-01-01T00:00:00ZAGHIGHI, Mohammad SaeidAMMAR, AmineMETIVIER, ChristelNORMANDIN, MagdeleineCHINESTA, FranciscoThis paper focuses on the non-incremental solution of transient coupled non-linear models, in particular the one related to the Rayleigh–Bénard flow problem that models natural thermal convection. For this purpose we are applying the so-called Proper Generalized Decomposition that proceeds by performing space-time separated representations of the different unknown fields involved by the flow model. This non-incremental solution strategy allows significant computational time savings and opens new perspectives for introducing some flow and/or fluid parameters as extra-coordinates.Rayleigh-Bénard convection of Casson fluids
http://hdl.handle.net/10985/16695
Rayleigh-Bénard convection of Casson fluids
AGHIGHI, Mohammad Saeid; AMMAR, Amine; METIVIER, Christel; GHARAGOZLU, M.
This study aims at investigating numerically the Rayleigh-Bénard Convection (RBC) in viscoplastic fluids. A Casson fluid is considered in a bidimensional square cavity heated from below. The effects of the dimensionless yield stress, the Bingham number Bn, on the heat transfer and motion is investigated in the range 5.10^3 < Ra < 10^5 for the Rayleigh number and Pr = 10, 100, 1000 for the Prandtl number. One shows that the yield stress has a stabilizing effect, reducing the convection intensity. Above a certain value of Bnmax , the convection does not occur and the heat transfer is only due to conduction. For moderate Bn values, truly unyielded regions are located in the center of the cavity; their areas grow with increasing Bingham number and invade the whole cavity at the threshold value Bnmax .
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/166952018-01-01T00:00:00ZAGHIGHI, Mohammad SaeidAMMAR, AmineMETIVIER, ChristelGHARAGOZLU, M.This study aims at investigating numerically the Rayleigh-Bénard Convection (RBC) in viscoplastic fluids. A Casson fluid is considered in a bidimensional square cavity heated from below. The effects of the dimensionless yield stress, the Bingham number Bn, on the heat transfer and motion is investigated in the range 5.10^3 < Ra < 10^5 for the Rayleigh number and Pr = 10, 100, 1000 for the Prandtl number. One shows that the yield stress has a stabilizing effect, reducing the convection intensity. Above a certain value of Bnmax , the convection does not occur and the heat transfer is only due to conduction. For moderate Bn values, truly unyielded regions are located in the center of the cavity; their areas grow with increasing Bingham number and invade the whole cavity at the threshold value Bnmax .Aspect ratio effects in Rayleigh-Bénard convection of Herschel-Bulkley fluids
http://hdl.handle.net/10985/16656
Aspect ratio effects in Rayleigh-Bénard convection of Herschel-Bulkley fluids
AGHIGHI, Mohammad Saeid; AMMAR, Amine
Purpose The purpose of this paper is to analyze two-dimensional steady-state Rayleigh–Bénard convection within rectangular enclosures in different aspect ratios filled with yield stress fluids obeying the Herschel–Bulkley model. Design/methodology/approach In this study, a numerical method based on the finite element has been developed for analyzing two-dimensional natural convection of a Herschel–Bulkley fluid. The effects of Bingham number Bn and power law index n on heat and momentum transport have been investigated for a nominal Rayleigh number range (5 × 10^3 < Ra < 10^5), three different aspect ratios (ratio of enclosure length:height AR = 1, 2, 3) and a single representative value of nominal Prandtl number (Pr = 10). Findings Results show that the mean Nusselt number Nu¯ increases with increasing Rayleigh number due to strengthening of convective transport. However, with the same nominal value of Ra, the values of Nu¯ for shear thinning fluids n < 1 are greater than shear thickening fluids n > 1. The values of Nu¯ decrease with Bingham number and for large values of Bn, Nu¯ rapidly approaches unity, which indicates that heat transfer takes place principally by thermal conduction. The effects of aspect ratios have also been investigated and results show that Nu¯ increases with increasing AR due to stronger convection effects. Originality/value This paper presents a numerical study of Rayleigh–Bérnard flows involving Herschel–Bulkley fluids for a wide range of Rayleigh numbers, Bingham numbers and power law index based on finite element method. The effects of aspect ratio on flow and heat transfer of Herschel–Bulkley fluids are also studied.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/166562017-01-01T00:00:00ZAGHIGHI, Mohammad SaeidAMMAR, AminePurpose The purpose of this paper is to analyze two-dimensional steady-state Rayleigh–Bénard convection within rectangular enclosures in different aspect ratios filled with yield stress fluids obeying the Herschel–Bulkley model. Design/methodology/approach In this study, a numerical method based on the finite element has been developed for analyzing two-dimensional natural convection of a Herschel–Bulkley fluid. The effects of Bingham number Bn and power law index n on heat and momentum transport have been investigated for a nominal Rayleigh number range (5 × 10^3 < Ra < 10^5), three different aspect ratios (ratio of enclosure length:height AR = 1, 2, 3) and a single representative value of nominal Prandtl number (Pr = 10). Findings Results show that the mean Nusselt number Nu¯ increases with increasing Rayleigh number due to strengthening of convective transport. However, with the same nominal value of Ra, the values of Nu¯ for shear thinning fluids n < 1 are greater than shear thickening fluids n > 1. The values of Nu¯ decrease with Bingham number and for large values of Bn, Nu¯ rapidly approaches unity, which indicates that heat transfer takes place principally by thermal conduction. The effects of aspect ratios have also been investigated and results show that Nu¯ increases with increasing AR due to stronger convection effects. Originality/value This paper presents a numerical study of Rayleigh–Bérnard flows involving Herschel–Bulkley fluids for a wide range of Rayleigh numbers, Bingham numbers and power law index based on finite element method. The effects of aspect ratio on flow and heat transfer of Herschel–Bulkley fluids are also studied.