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Publications (10 of 117) Show all publications
Burtseva, E., Sundhäll, M., Tossavainen, T. & Wall, P. (2024). Engineering Students’ Varying Motivation and Self-concept in Mathematics. International Journal of Engineering Education, 40(1), 97-107
Open this publication in new window or tab >>Engineering Students’ Varying Motivation and Self-concept in Mathematics
2024 (English)In: International Journal of Engineering Education, ISSN 0949-149X, Vol. 40, no 1, p. 97-107Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Tempus Publications, 2024
National Category
Learning Didactics
Research subject
Applied Mathematics; Mathematics and Science Education
Identifiers
urn:nbn:se:ltu:diva-104323 (URN)2-s2.0-85184384737 (Scopus ID)
Note

Validerad;2024;Nivå 2;2024-04-09 (hanlid)

Available from: 2024-03-04 Created: 2024-03-04 Last updated: 2024-04-09Bibliographically approved
Almqvist, A., Burtseva, E., Rajagopal, K. & Wall, P. (2023). On flow of power-law fluids between adjacent surfaces: Why is it possible to derive a Reynolds-type equation for pressure-driven flow, but not for shear-driven flow?. Applications in Engineering Science, 15, Article ID 100145.
Open this publication in new window or tab >>On flow of power-law fluids between adjacent surfaces: Why is it possible to derive a Reynolds-type equation for pressure-driven flow, but not for shear-driven flow?
2023 (English)In: Applications in Engineering Science, ISSN 2666-4968, Vol. 15, article id 100145Article in journal (Refereed) Published
Abstract [en]

Flows of incompressible Navier–Stokes (Newtonian) fluids between adjacent surfaces are encountered in numerous practical applications, such as seal leakage and bearing lubrication. In seals, the flow is primarily pressure-driven, whereas, in bearings, the dominating driving force is due to shear. The governing Navier–Stokes system of equations can be significantly simplified due to the small distance between the surfaces compared to their size. From the simplified system, it is possible to derive a single lower-dimensional equation, known as the Reynolds equation, which describes the pressure field. Once the pressure field is computed, it can be used to determine the velocity field. This computational algorithm is much simpler to implement than a direct numerical solution of the Navier–Stokes equations and is therefore widely employed by engineers. The primary objective of this article is to investigate the possibility of deriving a type of Reynolds equation also for non-Newtonian fluids, using the balance of linear momentum. By considering power-law fluids we demonstrate that it is not possible for shear-driven flows, whereas it is feasible for pressure-driven flows. Additionally, we demonstrate that in the full 3D model, a normal stress boundary condition at the inlet/outlet implies a Dirichlet condition for the pressure in the Reynolds equation associated with pressure-driven flow. Furthermore, we establish that a Dirichlet condition for the velocity at the inlet/outlet in the 3D model results in a Neumann condition for the pressure in the Reynolds equation.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Navier-Stokes equation, Reynolds equation, Poiseuille law, Lower-dimensional model, Power-law fluid, Non-Newtonian fluid
National Category
Mathematical Analysis
Research subject
Machine Elements; Applied Mathematics
Identifiers
urn:nbn:se:ltu:diva-102664 (URN)10.1016/j.apples.2023.100145 (DOI)2-s2.0-85169543467 (Scopus ID)
Funder
Swedish Research Council, DNR 2019-04293
Note

Validerad;2023;Nivå 2;2023-11-21 (joosat);

CC BY-NC-ND 4.0 License;

Available from: 2023-11-21 Created: 2023-11-21 Last updated: 2024-03-07Bibliographically approved
Almqvist, A., Burtseva, E., Rajagopal, K. & Wall, P. (2023). On lower-dimensional models of thin film flow, Part C: Derivation of a Reynolds type of equation for fluids with temperature and pressure dependent viscosity. Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, 237(3), 514-526
Open this publication in new window or tab >>On lower-dimensional models of thin film flow, Part C: Derivation of a Reynolds type of equation for fluids with temperature and pressure dependent viscosity
2023 (English)In: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 237, no 3, p. 514-526Article in journal (Refereed) Published
Abstract [en]

This paper constitutes the third part of a series of works on lower-dimensional models in lubrication. In Part A, it was shown that implicit constitutive theory must be used in the modelling of incompressible fluids with pressure-dependent viscosity and that it is not possible to obtain a lower-dimensional model for the pressure just by letting the film thickness go to zero, as in the proof of the classical Reynolds equation. In Part B, a new method for deriving lower-dimensional models of thin-film flow of fluids with pressure-dependent viscosity was presented. Here, in Part C, we also incorporate the energy equation so as to include fluids with both temperature and pressure dependent viscosity. By asymptotic analysis of this system, as the film thickness goes to zero, we derive a simplified model of the flow. We also carry out an asymptotic analysis of the boundary condition, in the case where the normal stress is specified on one part of the boundary and the velocity on the remaining part.

Place, publisher, year, edition, pages
Sage, 2023
Keywords
Reynolds equation, elastohydrodynamic lubrication (or EHL), implicit constitutive relations, lower-dimensional models, piezo-viscous fluids, thermal effects
National Category
Tribology (Interacting Surfaces including Friction, Lubrication and Wear) Mathematical Analysis
Research subject
Machine Elements; Applied Mathematics
Identifiers
urn:nbn:se:ltu:diva-94919 (URN)10.1177/13506501221135269 (DOI)000893930300001 ()2-s2.0-85144235739 (Scopus ID)
Funder
Swedish Research Council, DNR 2019-04293
Note

Validerad;2023;Nivå 2;2023-04-18 (joosat);

Licens fulltext: CC BY License

Available from: 2022-12-20 Created: 2022-12-20 Last updated: 2024-03-07Bibliographically approved
Tossavainen, T., Wall, P. & Sundhäll, M. (2022). Engineering Students’ Mathematical Self-Concept and its Dependence on Their Study Habits and Views about Mathematics. International Journal of Engineering Education, 38(5A), 1354-1365
Open this publication in new window or tab >>Engineering Students’ Mathematical Self-Concept and its Dependence on Their Study Habits and Views about Mathematics
2022 (English)In: International Journal of Engineering Education, ISSN 0949-149X, Vol. 38, no 5A, p. 1354-1365Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Tempus Publications, 2022
National Category
Other Mathematics Learning
Research subject
Mathematics Education; Applied Mathematics
Identifiers
urn:nbn:se:ltu:diva-93239 (URN)000870236400012 ()2-s2.0-85153865470 (Scopus ID)
Note

Validerad;2022;Nivå 2;2022-09-26 (sofila)

Available from: 2022-09-26 Created: 2022-09-26 Last updated: 2023-11-06Bibliographically approved
Fabricius, J., Manjate, S. & Wall, P. (2022). Error estimates for pressure-driven Hele-Shaw flow. Quarterly of Applied Mathematics, 80(3), 575-595
Open this publication in new window or tab >>Error estimates for pressure-driven Hele-Shaw flow
2022 (English)In: Quarterly of Applied Mathematics, ISSN 0033-569X, E-ISSN 1552-4485, Vol. 80, no 3, p. 575-595Article in journal (Refereed) Published
Abstract [en]

We consider Stokes flow past cylindrical obstacles in a generalized Hele-Shaw cell, i.e. a thin three-dimensional domain confined between two surfaces. The flow is assumed to be driven by an external pressure gradient, which is modeled as a normal stress condition on the lateral boundary of the cell. On the remaining part of the boundary we assume that the velocity is zero. We derive a divergence-free (volume preserving) approximation of the flow by studying its asymptotic behavior as the thickness of the domain tends to zero. The approximation is verified by error estimates for both the velocity and pressure in H1- and L2-norms, respectively.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2022
Keywords
Hele-Shaw flow, asymptotic expansions, pressure boundary condition, thin film flow, error estimates
National Category
Probability Theory and Statistics Computer Sciences
Research subject
Applied Mathematics
Identifiers
urn:nbn:se:ltu:diva-91626 (URN)10.1090/qam/1619 (DOI)000807138600001 ()2-s2.0-85131407179 (Scopus ID)
Note

Validerad;2022;Nivå 2;2022-06-20 (joosat);

Available from: 2022-06-20 Created: 2022-06-20 Last updated: 2022-06-22Bibliographically approved
Fabricius, J., Manjate, S. & Wall, P. (2022). On pressure-driven Hele–Shaw flow of power-law fluids. Applicable Analysis, 101(14), 5107-5137
Open this publication in new window or tab >>On pressure-driven Hele–Shaw flow of power-law fluids
2022 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 101, no 14, p. 5107-5137Article in journal (Refereed) Published
Abstract [en]

We analyze the asymptotic behavior of a non-Newtonian Stokes system, posed in a Hele–Shaw cell, i.e. a thin three-dimensional domain which is confined between two curved surfaces and contains a cylindrical obstacle. The fluid is assumed to be of power-law type defined by the exponent 1< p<∞. By letting the thickness of the domain tend to zero we obtain a generalized form of the Poiseuille law, i.e. the limit velocity is a nonlinear function of the limit pressure gradient. The flow is assumed to be driven by an external pressure which is applied as a normal stress along the lateral part of the boundary. On the remaining part of the boundary we impose a no-slip condition. The two-dimensional limit problem for the pressure is a generalized form of the p′-Laplace equation, 1/p+1/p'=1, with a coefficient called ‘flow factor’, which depends on the geometry as well as the power-law exponent. The boundary conditions are preserved in the limit as a Dirichlet condition for the pressure on the lateral boundary and as a Neumann condition for the pressure on the solid obstacle.

Place, publisher, year, edition, pages
Taylor & Francis, 2022
Keywords
stress boundary condition, Hele-Shaw cell, power-law fluid, p-Laplace equation, thin film flow
National Category
Mathematical Analysis
Research subject
Applied Mathematics
Identifiers
urn:nbn:se:ltu:diva-82624 (URN)10.1080/00036811.2021.1880570 (DOI)000614510000001 ()2-s2.0-85100661967 (Scopus ID)
Note

Validerad;2022;Nivå 2;2022-09-26 (hanlid)

Available from: 2021-01-24 Created: 2021-01-24 Last updated: 2022-09-26Bibliographically approved
Almqvist, A., Burtseva, E., Rajagopal, K. & Wall, P. (2021). On lower-dimensional models in lubrication, Part A: Common misinterpretations and incorrect usage of the Reynolds equation. Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, 235(8), 1692-1702
Open this publication in new window or tab >>On lower-dimensional models in lubrication, Part A: Common misinterpretations and incorrect usage of the Reynolds equation
2021 (English)In: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 235, no 8, p. 1692-1702Article in journal (Refereed) Published
Abstract [en]

Most of the problems in lubrication are studied within the context of Reynolds’ equation, which can be derived by writing the incompressible Navier-Stokes equation in a dimensionless form and neglecting terms which are small under the assumption that the lubricant film is very thin. Unfortunately, the Reynolds equation is often used even though the basic assumptions under which it is derived are not satisfied. One example is in the mathematical modelling of elastohydrodynamic lubrication (EHL). In the EHL regime, the pressure is so high that the viscosity changes by several orders of magnitude. This is taken into account by just replacing the constant viscosity in either the incompressible Navier-Stokes equation or the Reynolds equation by a viscosity-pressure relation. However, there are no available rigorous arguments which justify such an assumption. The main purpose of this two-part work is to investigate if such arguments exist or not. In Part A, we formulate a generalised form of the Navier-Stokes equation for piezo-viscous incompressible fluids. By dimensional analysis of this equation we, thereafter, show that it is not possible to obtain the Reynolds equation, where the constant viscosity is replaced with a viscosity-pressure relation, by just neglecting terms which are small under the assumption that the lubricant film is very thin. The reason is that the lone assumption that the fluid film is very thin is not enough to neglect the terms, in the generalised Navier-Stokes equation, which are related to the body forces and the inertia. However, we analysed the coefficients in front of these (remaining) terms and provided arguments for when they may be neglected. In Part B, we present an alternative method to derive a lower-dimensional model, which is based on asymptotic analysis of the generalised Navier-Stokes equation as the film thickness goes to zero.

Place, publisher, year, edition, pages
Sage Publications, 2021
Keywords
Reynolds equation, elastohydrodynamic (or EHL), implicit constitutive relations, lower-dimensional models, piezo-viscous fluids
National Category
Tribology (Interacting Surfaces including Friction, Lubrication and Wear) Mathematical Analysis
Research subject
Applied Mathematics; Machine Elements
Identifiers
urn:nbn:se:ltu:diva-81978 (URN)10.1177/1350650120973792 (DOI)000666594700016 ()2-s2.0-85097313267 (Scopus ID)
Funder
Swedish Research Council, 2019-04293
Note

Validerad;2021;Nivå 2;2021-07-05 (beamah)

Available from: 2020-12-14 Created: 2020-12-14 Last updated: 2021-07-09Bibliographically approved
Almqvist, A., Burtseva, E., Rajagopal, K. & Wall, P. (2021). On lower-dimensional models in lubrication, Part B: Derivation of a Reynolds type of equation for incompressible piezo-viscous fluids. Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, 235(8), 1703-1718
Open this publication in new window or tab >>On lower-dimensional models in lubrication, Part B: Derivation of a Reynolds type of equation for incompressible piezo-viscous fluids
2021 (English)In: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 235, no 8, p. 1703-1718Article in journal (Refereed) Published
Abstract [en]

The Reynolds equation is a lower-dimensional model for the pressure in a fluid confined between two adjacent surfaces that move relative to each other. It was originally derived under the assumption that the fluid is incompressible and has constant viscosity. In the existing literature, the lower-dimensional Reynolds equation is often employed as a model for the thin films, which lubricates interfaces in various machine components. For example, in the modelling of elastohydrodynamic lubrication (EHL) in gears and bearings, the pressure dependence of the viscosity is often considered by just replacing the constant viscosity in the Reynolds equation with a given viscosity-pressure relation. The arguments to justify this are heuristic, and in many cases, it is taken for granted that you can do so. This motivated us to make an attempt to formulate and present a rigorous derivation of a lower-dimensional model for the pressure when the fluid has pressure-dependent viscosity. The results of our study are presented in two parts. In Part A, we showed that for incompressible and piezo-viscous fluids it is not possible to obtain a lower-dimensional model for the pressure by just assuming that the film thickness is thin, as it is for incompressible fluids with constant viscosity. Here, in Part B, we present a method for deriving lower-dimensional models of thin-film flow, where the fluid has a pressure-dependent viscosity. The main idea is to rescale the generalised Navier-Stokes equation, which we obtained in Part A based on theory for implicit constitutive relations, so that we can pass to the limit as the film thickness goes to zero. If the scaling is correct, then the limit problem can be used as the dimensionally reduced model for the flow and it is possible to derive a type of Reynolds equation for the pressure.

Place, publisher, year, edition, pages
Sage Publications, 2021
Keywords
Reynolds equation, elastohydrodynamic (or EHL), implicit constitutive relations, lower-dimensional models, piezo-viscous fluids
National Category
Mathematical Analysis Tribology (Interacting Surfaces including Friction, Lubrication and Wear)
Research subject
Machine Elements; Applied Mathematics
Identifiers
urn:nbn:se:ltu:diva-81977 (URN)10.1177/1350650120973800 (DOI)000666594700017 ()2-s2.0-85097279613 (Scopus ID)
Funder
Swedish Research Council, 2019-04293
Note

Validerad;2021;Nivå 2;2021-07-05 (beamah)

Available from: 2020-12-14 Created: 2020-12-14 Last updated: 2021-07-09Bibliographically approved
Persson, L.-E., Tephnadze, G., Tutberidze, G. & Wall, P. (2021). Some New Results on the Strong Convergence of Fejér Means with Respect to Vilenkin Systems. Ukrainian Mathematical Journal, 73, 635-648
Open this publication in new window or tab >>Some New Results on the Strong Convergence of Fejér Means with Respect to Vilenkin Systems
2021 (English)In: Ukrainian Mathematical Journal, ISSN 0041-5995, E-ISSN 1573-9376, Vol. 73, p. 635-648Article in journal (Refereed) Published
Abstract [en]

We prove some new strong convergence theorems for partial sums and Fejér means with respect to the Vilenkin system.

Place, publisher, year, edition, pages
Springer, 2021
National Category
Mathematical Analysis
Research subject
Applied Mathematics
Identifiers
urn:nbn:se:ltu:diva-88278 (URN)10.1007/s11253-021-01948-5 (DOI)000717918000005 ()2-s2.0-85118264527 (Scopus ID)
Note

Validerad;2022;Nivå 2;2022-01-01 (johcin)

Available from: 2021-12-10 Created: 2021-12-10 Last updated: 2023-11-18Bibliographically approved
Persson, L.-E., Tephnadze, G., Tutberidze, G. & Wall, P. (2021). Some new resuts concering strong convergence of Fejér means with respect to Vilenkin systems. Ukrains’kyi Matematychnyi Zhurnal, 73(4), 544-555
Open this publication in new window or tab >>Some new resuts concering strong convergence of Fejér means with respect to Vilenkin systems
2021 (English)In: Ukrains’kyi Matematychnyi Zhurnal, ISSN 0041-6053, Vol. 73, no 4, p. 544-555Article in journal (Refereed) Published
Abstract [en]

We prove some new strong convergence theorems for partial sums and Fejér means with respect to the Vilenkin system.

Place, publisher, year, edition, pages
Springer, 2021
Keywords
Vilenkin system, Fejér means, martingale Hardy space, strong convergence
National Category
Mathematical Analysis
Research subject
Applied Mathematics
Identifiers
urn:nbn:se:ltu:diva-88317 (URN)10.37863/umzh.v73i4.226 (DOI)
Note

Godkänd;2021;Nivå 0;2021-12-13 (johcin)

Available from: 2021-12-13 Created: 2021-12-13 Last updated: 2021-12-17Bibliographically approved
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