Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem

Fractional pennes' bioheat equation: theoretical and numerical studies

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Modelling integral viscoelastic flows in OpenFOAM

[Excerpt] A large number of constitutive equations were developed for viscoelastic fluids, some empirical and other with strong physical foundations. The currently available macroscopic constitutive equations can be divided in two main types: differential and integral. Some of the constitutive equations, e.g. Maxwell are available both in differential and integral types. However, relevant in tegral models, like K - BKZ, just possesses the integral form. (...)

Improvign mixing processes with the help of numerical tools

In several industrial applications, highly complex behaviour materials are used together with intricate mixing processes, which difficult the achievement of the desired properties for the produced materials. This is the case of the well-known dispersion of nano-sized fillers in a melt polymer matrix, used to improve the nanocomposite mechanical and/or electrical properties. This mixing is usually performed in twin-screw extruders, that promote complex flow patterns, and, since an in loco analysis of the material evolution and mixing is difficult to perform, numerical tools can be very useful to predict the evolution and behaviour of the material. This work presents a numerical based study to improve the understanding of mixing processes. Initial numerical studies were performed with generalized Newtonian fluids, but, due to the null relaxation time that characterize this type of fluids, the assumption of viscoelastic behavior was required. Therefore, the polymer melt was rheologically characterized, and, a six mode Phan-Thien-Tanner and Giesekus models were used to fit the rheological data. These viscoelastic rheological models were used to model the process. The conclusions obtained in this work provide additional and useful data to correlate the type and intensity of the deformation history promoted to the polymer nanocomposite and the quality of the mixing obtained.

Spatio-temporal modelling of environmental data

Programa Doutoral em Matemática e Aplicações.

Numerical modeling and assessment of the thermal environment in an industrial premise of automotive components

Dissertação de mestrado em Engenharia Industrial

Structural analysis of the timber structure of Ica Cathedral, Peru

Dissertação de mestrado em Structural Analysis of Monuments and Historical Constructions

Numerical simulation of the reflow soldering process

Dissertação de mestrado integrado em Mechanical Engineering

Dynamic modelling and analysis of hydraulic forces in radial blood pumps

Dissertação de mestrado integrado em Biomedical Engineering Biomaterials, Biomechanics and Rehabilitation

Numerical and experimental analysis of full scale arches reinforced with GFRP materials

In this contribution, original limit analysis numerical results are presented dealing with some reinforced masonry arches tested at the University of Minho-UMinho, PT. Twelve in-scale circular masonry arches were considered, reinforced in various ways at the intrados or at the extrados. GFRP reinforcements were applied either on undamaged or on previously damaged elements, in order to assess the role of external reinforcements even in repairing interventions. The experimental results were critically discussed at the light of limit analysis predictions, based on a 3D FE heterogeneous upper bound approach. Satisfactory agreement was found between experimental evidences and the numerical results, in terms of failure mechanisms and peak load.

Modelling tyre-road noise with data mining techniques

The research aimed to establish tyre-road noise models by using a Data Mining approach that allowed to build a predictive model and assess the importance of the tested input variables. The data modelling took into account three learning algorithms and three metrics to define the best predictive model. The variables tested included basic properties of pavement surfaces, macrotexture, megatexture, and uneven- ness and, for the first time, damping. Also, the importance of those variables was measured by using a sensitivity analysis procedure. Two types of models were set: one with basic variables and another with complex variables, such as megatexture and damping, all as a function of vehicles speed. More detailed models were additionally set by the speed level. As a result, several models with very good tyre-road noise predictive capacity were achieved. The most relevant variables were Speed, Temperature, Aggregate size, Mean Profile Depth, and Damping, which had the highest importance, even though influenced by speed. Megatexture and IRI had the lowest importance. The applicability of the models developed in this work is relevant for trucks tyre-noise prediction, represented by the AVON V4 test tyre, at the early stage of road pavements use. Therefore, the obtained models are highly useful for the design of pavements and for noise prediction by road authorities and contractors.

Assessment of the mechanical performance of recycled unbound materials for pavement subbase layers

The cyclic load triaxial test is a laboratory test that allows studying the mechanical behaviour of unbound granular materials used in base/subbase layers of road pavements. The resilient modulus and permanent strains are required as inputs in structural pavement design. This paper presents some results obtained for recycled materials (crushed concrete aggregate and blended crushed waste aggregate), with a view to promoting their use in pavement structures. Results relating to a reference material (limestone) are also presented, for comparison. All the test results discussed in this paper were obtained in variable cyclic radial pressure (VCP) tests. The tests performed (VCP) aim to study the influence of water content on the resilient modulus of recycled materials, as well as on the resistance to permanent deformation. Using the experimental data as a basis, further modelling work was carried out to establish the stresses developing in base/capping layers in typical Belgian road pavements. These numerical results allow to propose some simplifications of the stress paths applied in the testing procedures and to establish a new test protocol that also considers compaction during construction works. The results of this research work provide an excellent set of findings for the mechanical characterization of unbound base materials through the cyclic triaxial test, and contribute to a better understanding and correct application of recycled materials under geotechnical engineering background