6 research outputs found

    Some remarks on the model of rigid heat conductor with memory: unbounded heat relaxation function

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    The model of rigid linear heat conductor with memory is reconsidered focussing the interest on the heat relaxation function. Thus, the definitions of heat flux and thermal work are revised to understand where changes are required when the heat flux relaxation function kk is assumed to be unbounded at the initial time t=0t=0. That is, it is represented by a regular integrable function, namely k∈L1(R+)k\in L^1(\R^+), but its time derivative is not integrable, that is k˙∉L1(R+)\dot k\notin L^1(\R^+). Notably, also under these relaxed assumptions on kk, whenever the heat flux is the same also the related thermal work is the same. Thus, also in the case under investigation, the notion of equivalence is introduced and its physical relevance is pointed out

    Some remarks on the model of rigid heat conductor with memory: unbounded heat relaxation function

    Get PDF
    The model of rigid linear heat conductor with memory is reconsidered focussing the interest on the heat relaxation function. Thus, the definitions of heat flux and thermal work are revised to understand where changes are required when the heat flux relaxation function kk is assumed to be unbounded at the initial time t=0t=0. That is, it is represented by a regular integrable function, namely k∈L1(R+)k\in L^1(\R^+), but its time derivative is not integrable, that is k˙∉L1(R+)\dot k\notin L^1(\R^+). Notably, also under these relaxed assumptions on kk, whenever the heat flux is the same also the related thermal work is the same. Thus, also in the case under investigation, the notion of equivalence is introduced and its physical relevance is pointed out

    Joule Heat Parameter Effects on Unsteady MHD flow Over a Stretching Sheet with Viscous Dissipation and Heat source

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    In the present investigation, we studied the effects of heat source and Joule heating parameter on unsteady magneto-hydro-dynamic and heat transfer of a fluid flow over a radiating stretching sheet. The governing partial differential equations of nonlinear with boundary conditions are solved numerically by implicit finite difference method with Gauss Seidel iteration scheme. The obtained numerical solutions of velocity and temperature profiles are discussed and represented graphically. The effects of various parameters on the velocity and temperature profiles are shown graphically and numerical values of physical quantities such as the skin friction coefficient and the local Nusselt number are presented in tabular form

    ALGEBRAIC AND NUMERICAL EXPLORATION OF FREE ENERGIES FOR MATERIALS WITH MEMORY

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    Abstract. We study the forms of a range of free energy functionals for materials with memory for two types of strain history, namely sinusoidal and ex- ponential behaviours. The work deals with discrete spectrum materials, which are those with relaxation functions given by sums of decaying exponentials

    Mathematical modelling of wet paper pressing

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    The aim of this project is to reduce energy costs in paper production by optimising the process in the press section of a paper machine. In this press section water is squeezed as it passes through the press nip. In a modern press section the moisture content of the sheet after three or four presses will be in the range 47 - 55%. The excess water left in the web is to be removed afterwards in the dryer section of the paper machine by very expensive and energy consuming vaporisation. Even small improvements in the press performance will considerable reduce the construction and operational costs of the dryer. The best option for more effective pressing is heating the web during the pressing process. The possibilities of detailed experimental studies under industrial conditions are limited, due to the very small time and spatial scales of the process. Therefore there is a great need for mathematical, computational models that describe heat transfer and mechanical processes during and immediately after contact of the paper web with the press nip. After validation with experimental data such models serve on industrial levels to optimise the pressing conditions. Initially, the research will concentrate on models for "hot pressing", where temperatures up to 100°C are introduced to decrease the water viscosity. At a later stage of the project the attention will be shifted towards "impulse pressing", where press rolls are heated up to 300°C and very rapid evaporation will take place near the press nip. This process is still experimental and implementation in an industrial environment is not expected before the year 2005. The research in this proposal aims at improving the modelling of these processes, the development of fast numerical techniques to make the models operational on workstations and PCs, and validation of models by comparisons with experimental data from TNO. At the end of the 4 year period a validated, operational model will be available for hot pressing. At the same time, in co-operation with TNO-TPD, an experimental model will be developed for impulse pressin
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