scholarly journals Heat Transfer and Computational Simulations on the Drying Process of a Kiln

2005 ◽  
Author(s):  
Almon Chai ◽  
Andrew Rigit ◽  
Ha How Ung
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Energy Conservation ◽  
Large Scale ◽  
Lumped Parameter Model ◽  
Difference Approximation ◽  
Drying Process ◽  
Ceramic Tiles ◽  
Partial Differential ◽  
Central Difference

In this paper, the analytical and computational results are presented for a large-scale ceramic-tiles drying kiln. A lumped-parameter model was initially derived for the drying process of the kiln. This has led to the development of mathematical models for the energy conservation and convective heat and mass transfer drying process. Diffusion on the boundary layers of the tiles was also derived based on the basis of moisture isotherm, drying curve and different temperature profiles. This also takes into consideration the internal moisture transportation. The developed partial differential equations were discretized using the central-difference approximation method, which were further verified by a computational fluid-dynamics solver and the Gauss-Siedel iterative method. The modelling and simulations performed on the partial differential equations give possible auxiliary energy conservation and improvement on the drying process of the kiln.

scholarly journals Introduction: Big data and partial differential equations

2017 ◽  
Vol 28 (6) ◽  
pp. 877-885 ◽  
Author(s):  
YVES VAN GENNIP ◽  
CAROLA-BIBIANE SCHÖNLIEB
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Large Scale ◽  
Data Science ◽  
Applied Mathematics ◽  
Mathematical Finance ◽  
Energy Functional ◽  
Continuous Change ◽  
Opinion Formation ◽  
Partial Differential

Partial differential equations (PDEs) are expressions involving an unknown function in many independent variables and their partial derivatives up to a certain order. Since PDEs express continuous change, they have long been used to formulate a myriad of dynamical physical and biological phenomena: heat flow, optics, electrostatics and -dynamics, elasticity, fluid flow and many more. Many of these PDEs can be derived in a variational way, i.e. via minimization of an ‘energy’ functional. In this globalised and technologically advanced age, PDEs are also extensively used for modelling social situations (e.g. models for opinion formation, mathematical finance, crowd motion) and tasks in engineering (such as models for semiconductors, networks, and signal and image processing tasks). In particular, in recent years, there has been increasing interest from applied analysts in applying the models and techniques from variational methods and PDEs to tackle problems in data science. This issue of the European Journal of Applied Mathematics highlights some recent developments in this young and growing area. It gives a taste of endeavours in this realm in two exemplary contributions on PDEs on graphs [1, 2] and one on probabilistic domain decomposition for numerically solving large-scale PDEs [3].

scholarly journals Using analog computers in today's largest computational challenges

2021 ◽  
Vol 19 ◽  
pp. 105-116
Author(s):  
Sven Köppel ◽  
Bernd Ulmann ◽  
Lars Heimann ◽  
Dirk Killat
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Energy Efficient ◽  
Large Scale ◽  
Scientific Computing ◽  
Analog Computer ◽  
Partial Differential ◽  
Technology Platform

Abstract. Analog computers can be revived as a feasible technology platform for low precision, energy efficient and fast computing. We justify this statement by measuring the performance of a modern analog computer and comparing it with that of traditional digital processors. General statements are made about the solution of ordinary and partial differential equations. Computational fluid dynamics are discussed as an example of large scale scientific computing applications. Several models are proposed which demonstrate the benefits of analog and digital-analog hybrid computing.

scholarly journals Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Mehnaz Shakeel ◽  
Iltaf Hussain ◽  
Hijaz Ahmad ◽  
Imtiaz Ahmad ◽  
Phatiphat Thounthong ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Caputo Derivative ◽  
Time Derivative ◽  
Order Derivative ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Central Difference ◽  
Definition Of

In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and complex geometries. Time derivative is approximated by Caputo derivative for the values of α ∈ 0 , 1 and α ∈ 1 , 2 . Forward difference scheme is applied to approximate the 1st order derivative appearing in the definition of Caputo derivative for α ∈ 0 , 1 , whereas central difference scheme is used for the 2nd order derivative in the definition of Caputo derivative for α ∈ 1 , 2 . Numerical problems are given to judge the behaviour of the proposed method for both the cases of α . Error norms are used to asses the accuracy of the method. Both uniform and nonuniform nodes are considered. Numerical simulation is carried out for irregular domain as well. Results are also compared with the existing methods in the literature.

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