Explicit Analytical Solutions of Linear and Nonlinear Interior Heat and Mass Transfer Equation Sets for Drying Process

2003 ◽  
Vol 125 (1) ◽  
pp. 175-178 ◽  
Author(s):  
Ruixian Cai ◽  
Na Zhang
Keyword(s):  
Analytical Solutions ◽  
Variable Coefficient ◽  
Infinite Plate ◽  
Explicit Solutions ◽  
Drying Process ◽  
Mass Transfer Equation ◽  
Mathematical Skills ◽  
One Dimensional ◽  
Linear And Nonlinear ◽  
Dimensional Variable

Some algebraic explicit analytical solutions of the unsteady one-dimensional variable coefficient partial differential equation set describing drying process of an infinite plate are derived and given. Such explicit solutions have not yet been published before. Besides their irreplaceable theoretical value, analytical solutions can also serve as benchmark to check the results of recently rapidly developing numerical calculation and study various computational methods. In addition, some mathematical skills used in this paper are special and deserve further attention.

scholarly journals l-problem of moments for one-dimensional integro-differential equations with Erdélyi-Kober operators

2019 ◽  
Vol 486 (6) ◽  
pp. 659-662
Author(s):  
Sergey S. Postnov
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Linear Equations ◽  
Integral Operators ◽  
Analytical Investigation ◽  
Explicit Solutions ◽  
One Dimensional ◽  
Problem Of Moments

Purpose: to investigate the possibility of statement of l-problem of moments for one-dimensional linear equations of three types, which contain Erdélyi-Kober differential and integral operators of fractional order. Methods: formulation of l-problem of moments for each type of investigated equations, analytical investigation and solution of problem formulated Results. Conditions derived that determine the possibility and solvability of the problem stated. In some cases an explicit solutions of l-problem of moments obtained. Conclusions. The possibility of statement of formulated l-problem of moments shown in cases that defined by conditions obtained in paper. Some analytical solutions of investigated problem obtained.

Transient convective diffusion to a uniformly accessible surface under aparent slip conditions

1991 ◽  
Vol 56 (2) ◽  
pp. 334-343
Author(s):  
Ondřej Wein
Keyword(s):  
Power Law ◽  
Analytical Solutions ◽  
Convective Diffusion ◽  
Active Surface ◽  
Velocity Profiles ◽  
One Dimensional ◽  
Slip Conditions ◽  
Accessible Surface ◽  
Diffusion Problems

Analytical solutions are given to a class of unsteady one-dimensional convective-diffusion problems assuming power-law velocity profiles close to the transport-active surface.

scholarly journals Experimental and Numerical Investigations on Conductive Drying of Phosphate Washing Waste Clay

Minerals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 482
Author(s):  
Fatiha Berroug ◽  
Yassir Bellaziz ◽  
Naaila Ouazzani ◽  
Fatima Ait Nouh ◽  
Abdessamad Hejjaj ◽  
...  
Keyword(s):  
Scale Up ◽  
Free Water ◽  
Moisture Diffusivity ◽  
Sample Thickness ◽  
Total Production ◽  
Drying Process ◽  
One Dimensional ◽  
Numerical Investigations ◽  
The World ◽  
Drying System

Morocco is the leading producer of phosphate and its derivatives in the world with a total production of 35 Mt. However, the extraction and the valorization of this mine generate huge quantities of phosphate washing waste clay (PHWWC) that constitute a main environmental and economic concern. To facilitate this waste clay storage and handling, it is necessary to decrease its moisture content that represents 80% of PHWWC. The present paper is devoted to studying the conductive drying of PHWWC. Drying experiments were conducted in a laboratory pilot. Afterwards, the experiment results were implemented in a one-dimensional numerical model of heat and mass transfer in a porous media to identify the drying parameters and performances. It was found that most of the water contained in PHWWC is free water that is removed with a constant drying rate. The volume reduction with a marked cracks phenomenon attained 65% without any significant effect of drying temperature and sample thickness. The effective moisture diffusivity of the PHWWC for a conductive drying process is ranged between 10−9 and 1.1 × 10−8 m2·s−1. The thermal efficiency of the drying system is up to 86%. The results could be used for the purpose of design and scale-up of the industrial dryer based on laboratory-scale experiments.

Simulation-based site amplification model for shallow bedrock sites in Korea

2021 ◽  
pp. 875529302098198
Author(s):  
Muhammad Aaqib ◽  
Duhee Park ◽  
Muhammad Bilal Adeel ◽  
Youssef M A Hashash ◽  
Okan Ilhan
Keyword(s):  
Linear Models ◽  
Site Response ◽  
Site Amplification ◽  
One Dimensional ◽  
Nonlinear Component ◽  
Nonlinear Site Response ◽  
Simulation Based ◽  
Linear And Nonlinear ◽  
Input Motion ◽  
Nonlinear Components

A new simulation-based site amplification model for shallow sites with thickness less than 30 m in Korea is developed. The site amplification model consists of linear and nonlinear components that are developed from one-dimensional linear and nonlinear site response analyses. A suite of measured shear wave velocity profiles is used to develop corresponding randomized profiles. A VS30 scaled linear amplification model and a model dependent on both VS30 and site period are developed. The proposed linear models compare well with the amplification equations developed for the western United States (WUS) at short periods but show a distinct curved bump between 0.1 and 0.5 s that corresponds to the range of site natural periods of shallow sites. The response at periods longer than 0.5 s is demonstrated to be lower than those of the WUS models. The functional form widely used in both WUS and central and eastern North America (CENA), for the nonlinear component of the site amplification model, is employed in this study. The slope of the proposed nonlinear component with respect to the input motion intensity is demonstrated to be higher than those of both the WUS and CENA models, particularly for soft sites with VS30 < 300 m/s and at periods shorter than 0.2 s. The nonlinear component deviates from the models for generic sites even at low ground motion intensities. The comparisons highlight the uniqueness of the amplification characteristics of shallow sites that a generic site amplification model is unable to capture.

scholarly journals New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mohamed S. Al-luhaibi
Keyword(s):  
Iterative Method ◽  
Analytical Solutions ◽  
Gas Dynamics ◽  
Time Derivative ◽  
Explicit Solutions ◽  
Fractional Partial Differential Equations ◽  
Approximate Analytical Solutions ◽  
Fractional Time Derivative ◽  
Burger's Equations ◽  
New Iterative Method

This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.

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