Using conformal mapping techniques, superposition and analytic continuation, we derive analytic solutions to the problem of a screw dislocation interacting with a parabolic elastic inhomogeneity. The screw dislocation can be located anywhere either in the surrounding matrix or in the parabolic inhomogeneity or simply on the parabolic interface itself. We obtain explicit expressions for the two analytic functions in the image plane characterizing the elastic fields describing displacement and stresses in the two-phase composite. Using the Peach-Koehler formula, we also obtain the image force acting on the screw dislocation. The analytic function defined in the parabolic inhomogeneity in the physical plane can be interpreted in terms of real and image screw dislocations for any location of the real screw dislocation.
{"title":"A screw dislocation located outside, inside or on the interface of a parabolic elastic inhomogeneity","authors":"X. Wang, P. Schiavone","doi":"10.24423/AOM.3758","DOIUrl":"https://doi.org/10.24423/AOM.3758","url":null,"abstract":"Using conformal mapping techniques, superposition and analytic continuation, we derive analytic solutions to the problem of a screw dislocation interacting with a parabolic elastic inhomogeneity. The screw dislocation can be located anywhere either in the surrounding matrix or in the parabolic inhomogeneity or simply on the parabolic interface itself. We obtain explicit expressions for the two analytic functions in the image plane characterizing the elastic fields describing displacement and stresses in the two-phase composite. Using the Peach-Koehler formula, we also obtain the image force acting on the screw dislocation. The analytic function defined in the parabolic inhomogeneity in the physical plane can be interpreted in terms of real and image screw dislocations for any location of the real screw dislocation.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44541684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For studying mechanism of sediment transport in river flows, open channel flow is a prototype. Flow has always three components of velocity for all types of channel geometry and for a time independent uniform flow along streamwise or main flow direction, all the components of velocity are functions of lateral and vertical coordinates. The present study investigates the two dimensional distribution of streamwise (or longitudinal) velocity starting from the Reynolds averaged Navier–Stokes equation for a turbulent open channel flow which is steady and uniform along the main flow direction. Secondary flows both along the vertically upward direction and along the lateral direction are considered which are also taken as functions of lateral and vertical coordinates. Inclusion of the secondary current brings the effect of dip phenomenon in the model. The resulting second order partial differential equation is solved numerically. The model is validated for all the cross-sectional, transverse and centreline velocity distribution by comparing with existing relevant set of experimental data and also with an existing model. Comparison results show good agreement with data as well as with the previous model proving the efficiency of the model. It is found that the transverse velocity distribution depends on the formation of circular vortex in the cross-sectional plane and becomes periodic as the number of circular vortex increases for increasing aspect ratios.
{"title":"Numerical study on two dimensional distribution of streamwise velocity in open channel turbulent flows with secondary current effect","authors":"S. Mohan, S. Kundu, K. Ghoshal, Jitendra Kumar","doi":"10.24423/AOM.3610","DOIUrl":"https://doi.org/10.24423/AOM.3610","url":null,"abstract":"For studying mechanism of sediment transport in river flows, open channel flow is a prototype. Flow has always three components of velocity for all types of channel geometry and for a time independent uniform flow along streamwise or main flow direction, all the components of velocity are functions of lateral and vertical coordinates. The present study investigates the two dimensional distribution of streamwise (or longitudinal) velocity starting from the Reynolds averaged Navier–Stokes equation for a turbulent open channel flow which is steady and uniform along the main flow direction. Secondary flows both along the vertically upward direction and along the lateral direction are considered which are also taken as functions of lateral and vertical coordinates. Inclusion of the secondary current brings the effect of dip phenomenon in the model. The resulting second order partial differential equation is solved numerically. The model is validated for all the cross-sectional, transverse and centreline velocity distribution by comparing with existing relevant set of experimental data and also with an existing model. Comparison results show good agreement with data as well as with the previous model proving the efficiency of the model. It is found that the transverse velocity distribution depends on the formation of circular vortex in the cross-sectional plane and becomes periodic as the number of circular vortex increases for increasing aspect ratios.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42647355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper concerns the problem of determining friction velocity in wallbounded flows affected by an adverse pressure gradient (APG). In the work of Niegodajew et al. [22] the corrected Clauser chart method (CCCM) for such flow conditions was proposed. This approach utilises the mean velocity profiles and turbulence intensity profiles to accurately estimate the friction velocity. In another work, Drozdz et al. [27] presented a modified version of the diagnostic-plot scaling (DPS) which allows for direct reconstruction of turbulence intensity profiles based on the local mean velocity profile, even when the flow is affected by a strong pressure gradient. This paper is aimed at verifying whether, when combining both of these methods (i.e. DPS and CCCM), the friction velocity can be accurately determined for APG flow conditions and one can possibly take advantage from both methods. The analysis revealed that the new approach is able to predict the friction velocity with uncertainty less than 5% for all the considered cases for the Clauser–Rotta parameter β < 17. Lastly, DPS-CCCM was also confronted with two empirical approaches (from available literature) allowing for estimation of the friction velocity under APG conditions. The performance of DPS-CCCM was found to be better than the ones of two other empirical approaches.
{"title":"Application of the diagnostic plot in estimation of the skin friction in turbulent boundary layer under an adverse pressure gradient","authors":"P. Niegodajew, A. Dróżdż, W. Elsner","doi":"10.24423/AOM.3746","DOIUrl":"https://doi.org/10.24423/AOM.3746","url":null,"abstract":"The paper concerns the problem of determining friction velocity in wallbounded flows affected by an adverse pressure gradient (APG). In the work of Niegodajew et al. [22] the corrected Clauser chart method (CCCM) for such flow conditions was proposed. This approach utilises the mean velocity profiles and turbulence intensity profiles to accurately estimate the friction velocity. In another work, Drozdz et al. [27] presented a modified version of the diagnostic-plot scaling (DPS) which allows for direct reconstruction of turbulence intensity profiles based on the local mean velocity profile, even when the flow is affected by a strong pressure gradient. This paper is aimed at verifying whether, when combining both of these methods (i.e. DPS and CCCM), the friction velocity can be accurately determined for APG flow conditions and one can possibly take advantage from both methods. The analysis revealed that the new approach is able to predict the friction velocity with uncertainty less than 5% for all the considered cases for the Clauser–Rotta parameter β < 17. Lastly, DPS-CCCM was also confronted with two empirical approaches (from available literature) allowing for estimation of the friction velocity under APG conditions. The performance of DPS-CCCM was found to be better than the ones of two other empirical approaches.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45331146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Compared to the traditional integer order viscoelastic model, a fractional order derivative viscoelastic model is shown to be advantageous. The characteristics of guided circumferential waves in an anisotropic fractional order Kelvin–Voigt viscoelastic hollow cylinder are investigated by a quadrature-free Legendre polynomial approach combining the Weyl definition of fractional order derivatives. The presented approach can obtain dispersion solutions in a stable manner from an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles of viscoelastic guided wave, which avoids a lot of numerical integration calculation in a traditional polynomial method and greatly improves the computational efficiency. Comparisons with the related studies are conducted to validate the correctness of the presented approach. The full three dimensional spectrum of an anisotropic fractional Kelvin–Voigt hollow cylinder is plotted. The influence of fractional order and material parameters on the phase velocity dispersion and attenuation curves of guided circumferential wave is discussed in detail. Moreover, the difference of the phase velocity dispersion and attenuation characteristics between the Kelvin–Voigt and hysteretic viscoelastic models is also illustrated. The presented approach along with the observed wave features should be particularly useful in non-destructive evaluations using waves in viscoelastic waveguides.
{"title":"A quadrature-free Legendre polynomial approach for the fast modelling guided circumferential wave in anisotropic fractional order viscoelastic hollow cylinders","authors":"X. Zhang, S. Liang, S. Shao, J. Yu","doi":"10.24423/AOM.3642","DOIUrl":"https://doi.org/10.24423/AOM.3642","url":null,"abstract":"Compared to the traditional integer order viscoelastic model, a fractional order derivative viscoelastic model is shown to be advantageous. The characteristics of guided circumferential waves in an anisotropic fractional order Kelvin–Voigt viscoelastic hollow cylinder are investigated by a quadrature-free Legendre polynomial approach combining the Weyl definition of fractional order derivatives. The presented approach can obtain dispersion solutions in a stable manner from an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles of viscoelastic guided wave, which avoids a lot of numerical integration calculation in a traditional polynomial method and greatly improves the computational efficiency. Comparisons with the related studies are conducted to validate the correctness of the presented approach. The full three dimensional spectrum of an anisotropic fractional Kelvin–Voigt hollow cylinder is plotted. The influence of fractional order and material parameters on the phase velocity dispersion and attenuation curves of guided circumferential wave is discussed in detail. Moreover, the difference of the phase velocity dispersion and attenuation characteristics between the Kelvin–Voigt and hysteretic viscoelastic models is also illustrated. The presented approach along with the observed wave features should be particularly useful in non-destructive evaluations using waves in viscoelastic waveguides.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41412556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The linear theory of viscoelasticity remains an important field of research like most solids and polymer materials when exposed to a vicious dynamic loading effect. This article introduces a new model for describing the behavior of thermoviscoelastic microbeams considering the effects of temperature change and the longitudinal magnetic field. The governing equations in this model are derived based on the Euler–Bernoulli beam theory, Kelvin–Voigt model of viscosity, the generalized thermoelasticity, and the classical Maxwell equations. The two ends of the microbeam are clamped and subjected to the influence of a laser pulse with a temporal intensity profile. The analytical solutions to the physical fields are evaluated using the Laplace transform and its inversion transforms are performed numerically. The thermo-viscoelastic responses of the microbeam are calculated numerically and investigated graphically. The effect of different parameters such as viscosity, laser intensity, and the magnitude of the magnetic field are studied in detail.
{"title":"Magnetothermoelastic vibrations on a viscoelastic microbeam subjected to a laser heat source","authors":"A. Abouelregal, A. Zenkour","doi":"10.24423/AOM.3597","DOIUrl":"https://doi.org/10.24423/AOM.3597","url":null,"abstract":"The linear theory of viscoelasticity remains an important field of research like most solids and polymer materials when exposed to a vicious dynamic loading effect. This article introduces a new model for describing the behavior of thermoviscoelastic microbeams considering the effects of temperature change and the longitudinal magnetic field. The governing equations in this model are derived based on the Euler–Bernoulli beam theory, Kelvin–Voigt model of viscosity, the generalized thermoelasticity, and the classical Maxwell equations. The two ends of the microbeam are clamped and subjected to the influence of a laser pulse with a temporal intensity profile. The analytical solutions to the physical fields are evaluated using the Laplace transform and its inversion transforms are performed numerically. The thermo-viscoelastic responses of the microbeam are calculated numerically and investigated graphically. The effect of different parameters such as viscosity, laser intensity, and the magnitude of the magnetic field are studied in detail.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43583323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with the numerical simulation of an instability phenomenon called Lueders bands with two regularized material models: viscoplasticity and gradient-enhanced plasticity. The models are based on large strain kinematics and temperature-dependence is incorporated. The Huber–Mises–Hencky yield condition and multi-branch hardening are employed. After a brief presentation of the constitutive description, test computations are performed using AceGen and AceFEM symbolic packages for Wolfram Mathematica. The first benchmark is a rectangular tensile plate in plane strain isothermal conditions. For the viscoplastic model, simulation results for different values of viscosity, loading duration and enforced displacement are compared. For the gradient model different internal lengths are used. Mesh sensitivity of the results and the influence of boundary conditions are also examined. Next to the Lueders-type response to a softening-hardening yield strength function, an additional softening stage leading to failure is also considered. The second example concerns a bone-shape sample under tension, for which, next to mesh sensitivity and the effect of regularization, the influence of heat conduction on simulation results is evaluated.
{"title":"Simulation of Lueders bands using regularized large strain elasto-plasticity","authors":"M. Mucha, B. Wcisło, J. Pamin","doi":"10.24423/AOM.3647","DOIUrl":"https://doi.org/10.24423/AOM.3647","url":null,"abstract":"This paper deals with the numerical simulation of an instability phenomenon called Lueders bands with two regularized material models: viscoplasticity and gradient-enhanced plasticity. The models are based on large strain kinematics and temperature-dependence is incorporated. The Huber–Mises–Hencky yield condition and multi-branch hardening are employed. After a brief presentation of the constitutive description, test computations are performed using AceGen and AceFEM symbolic packages for Wolfram Mathematica. The first benchmark is a rectangular tensile plate in plane strain isothermal conditions. For the viscoplastic model, simulation results for different values of viscosity, loading duration and enforced displacement are compared. For the gradient model different internal lengths are used. Mesh sensitivity of the results and the influence of boundary conditions are also examined. Next to the Lueders-type response to a softening-hardening yield strength function, an additional softening stage leading to failure is also considered. The second example concerns a bone-shape sample under tension, for which, next to mesh sensitivity and the effect of regularization, the influence of heat conduction on simulation results is evaluated.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45434377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper deals with minimization of the weighted average of compliances of structures, made of an elastic material of spatially varying elasticity moduli, subjected to n load variants acting non-simultaneously. The trace of the Hooke tensor is assumed as the unit cost of the design. Three versions of the free material design are discussed: designing the moduli of arbitrary anisotropy (AMD), designing the moduli of an isotropic material (IMD), designing of Young’s modulus for a fixed Poisson ratio (YMD). The problem is in all cases reduced to the Linear Constrained Problem (LCP) of Bouchitte and Fragala consisting of two mutually dual problems: stress based and strain based, the former one being characterized by the integrand of linear growth depending on the trial statically admissible stresses. The paper shows equivalence of the stress fields solving the (LCP) problem and those appearing in the optimal body subjected to subsequent load cases.
{"title":"Optimum design of elastic moduli for the multiple load problems","authors":"T. Lewiński","doi":"10.24423/AOM.3607","DOIUrl":"https://doi.org/10.24423/AOM.3607","url":null,"abstract":"The paper deals with minimization of the weighted average of compliances of structures, made of an elastic material of spatially varying elasticity moduli, subjected to n load variants acting non-simultaneously. The trace of the Hooke tensor is assumed as the unit cost of the design. Three versions of the free material design are discussed: designing the moduli of arbitrary anisotropy (AMD), designing the moduli of an isotropic material (IMD), designing of Young’s modulus for a fixed Poisson ratio (YMD). The problem is in all cases reduced to the Linear Constrained Problem (LCP) of Bouchitte and Fragala consisting of two mutually dual problems: stress based and strain based, the former one being characterized by the integrand of linear growth depending on the trial statically admissible stresses. The paper shows equivalence of the stress fields solving the (LCP) problem and those appearing in the optimal body subjected to subsequent load cases.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41915078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Using conformal mapping techniques, analytic continuation and the theory of Cauchy singular integral equations, we prove that a non-parabolic open inhomogeneity embedded in an elastic matrix subjected to a uniform remote anti-plane stress nevertheless admits an internal uniform stress field despite the presence of a finite mode III crack in its vicinity. Our analysis indicates that: (i) the internal uniform stress field is independent of the specific shape of the inhomogeneity and the presence of the finite crack; (ii) the existence of the finite crack plays a key role in the non-parabolic open shape of the inhomogeneity and in the non-uniform stresses in the surrounding matrix; (iii) the two-term asymptotic expansion at infinity of the stress field in the matrix is independent of the presence of the finite crack. Detailed numerical results are presented to demonstrate the proposed theory.
{"title":"Uniform stress field inside a non-parabolic open inhomogeneity interacting with a mode III crack","authors":"X. Wang, P. Schiavone","doi":"10.24423/AOM.3639","DOIUrl":"https://doi.org/10.24423/AOM.3639","url":null,"abstract":"Using conformal mapping techniques, analytic continuation and the theory of Cauchy singular integral equations, we prove that a non-parabolic open inhomogeneity embedded in an elastic matrix subjected to a uniform remote anti-plane stress nevertheless admits an internal uniform stress field despite the presence of a finite mode III crack in its vicinity. Our analysis indicates that: (i) the internal uniform stress field is independent of the specific shape of the inhomogeneity and the presence of the finite crack; (ii) the existence of the finite crack plays a key role in the non-parabolic open shape of the inhomogeneity and in the non-uniform stresses in the surrounding matrix; (iii) the two-term asymptotic expansion at infinity of the stress field in the matrix is independent of the presence of the finite crack. Detailed numerical results are presented to demonstrate the proposed theory.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46825901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper reviews the static equilibrium of a micropolar porous elastic material. We assume that the body under consideration is an elastic Cosserat media with voids, however, it can also be considered as an elastic microstretch solid, since the basic differential equations and mathematical formulations of boundary value problems in these two cases are actually identical. As regards the three-dimensional case, the existence and uniqueness of a weak solution of some boundary value problems are proved. The two-dimensional system of equations corresponding to a plane deformation case is written in a complex form and its general solution is presented with the use of two analytic functions of a complex variable and two solutions of the Helmholtz equations. On the basis of the constructed general representation, specific boundary value problems are solved for a circle and an infinite plane with a circular hole.
{"title":"Some boundary value problems for a micropolar porous elastic body","authors":"R. Janjgava, B. Gulua, S. Tsotniashvili","doi":"10.24423/AOM.3504","DOIUrl":"https://doi.org/10.24423/AOM.3504","url":null,"abstract":"The paper reviews the static equilibrium of a micropolar porous elastic material. We assume that the body under consideration is an elastic Cosserat media with voids, however, it can also be considered as an elastic microstretch solid, since the basic differential equations and mathematical formulations of boundary value problems in these two cases are actually identical. As regards the three-dimensional case, the existence and uniqueness of a weak solution of some boundary value problems are proved. The two-dimensional system of equations corresponding to a plane deformation case is written in a complex form and its general solution is presented with the use of two analytic functions of a complex variable and two solutions of the Helmholtz equations. On the basis of the constructed general representation, specific boundary value problems are solved for a circle and an infinite plane with a circular hole.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42238997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Caggio, Piotr Kalita, G. Łukaszewicz, K. Mizerski
We investigate the upper bound on the vertical heat transport in the fully 3D Rayleigh–Benard convection problem at the infinite Prandtl number for a micropolar fluid. We obtain a bound, given by the cube root of the Rayleigh number, with a logarithmic correction. The derived bound is compared with the optimal known one for the Newtonian fluid. It follows that the (optimal) upper bound for the micropolar fluid is less than the corresponding bound for the Newtonian fluid at the same Rayleigh number. Moreover, strong microrotational diffusion effects can entirely suppress the heat transfer. In the Newtonian limit our purely analytical findings fully agree with estimates and scaling laws obtained from previous theories significantly relying on phenomenology.
{"title":"Vertical heat transport at infinite Prandtl number for micropolar fluid","authors":"M. Caggio, Piotr Kalita, G. Łukaszewicz, K. Mizerski","doi":"10.24423/AOM.3598","DOIUrl":"https://doi.org/10.24423/AOM.3598","url":null,"abstract":"We investigate the upper bound on the vertical heat transport in the fully 3D Rayleigh–Benard convection problem at the infinite Prandtl number for a micropolar fluid. We obtain a bound, given by the cube root of the Rayleigh number, with a logarithmic correction. The derived bound is compared with the optimal known one for the Newtonian fluid. It follows that the (optimal) upper bound for the micropolar fluid is less than the corresponding bound for the Newtonian fluid at the same Rayleigh number. Moreover, strong microrotational diffusion effects can entirely suppress the heat transfer. In the Newtonian limit our purely analytical findings fully agree with estimates and scaling laws obtained from previous theories significantly relying on phenomenology.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45110804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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