The Diffusive Stresses Arising from A Locally Generalized Advection-Diffusion Process

Year 2019, , 837 - 848, 31.01.2019

Derya Avcı

https://doi.org/10.29130/dubited.499773

Abstract

In this paper, one and two-dimensional Cauchy problems based on an advection-diffusion equation with
Conformable derivative are analysed. This constitutive equation is a natural result of the description of the
diffusion coefficient and velocity field with temporally dependent power functions. The main aim of the
present study is to find the analytical solutions of the revealed one and two-dimensional Cauchy problems.
For this purpose, the fractional Laplace and the exponential Fourier integral transformations have been
applied to obtain the analytical solutions. Correspondingly, the diffusive stresses have been computed by
using some basic principles of classical elasticity theory. Some comparative interpretations have been made
with the Caputo fractional advection-diffusion model to demonstrate the effect of the conformable derivative
on the diffusion. 

Keywords

: Diffusive stresses, Conformable derivative, Integral transforms

Lokal Olarak Genelleştirilmiş Adveksiyon-Difüzyon Sürecinden Kaynaklanan Difüzif Gerilmeler

Abstract

Bu çalışmada, uyumlu türevli bir adveksiyon-difüzyon denklemine dayanan bir ve iki-boyutlu Cauchy
problemleri analiz edilmiştir. Bu kurucu denklem, zamana bağlı kuvvet fonksiyonlarıyla ifade edilen difüzyon
katsayısı ve hız alanı tanımlamalarının doğal bir sonucudur. Bu çalışmanın temel amacı, ortaya konan bir ve iki
boyutlu Cauchy problemlerinin analitik çözümlerini bulmaktır. Bu amaçla analitik çözümleri elde etmek için
kesirli Laplace ve üstel Fourier integral dönüşümleri uygulanmıştır. Buna bağlı olarak yayılma gerilmeleri klasik
elastisite teorisinin bazı temel prensipleri kullanılarak hesaplanmıştır. Uyumlu türev operatörünün difüzyon
üzerindeki etkisini göstermek için Caputo türevli kesirli adveksiyon-difüzyon modeli göz önüne alınarak bazı
karşılaştırmalı yorumlar yapılmıştır.

Keywords

Difüzif gerilmeler, Uyumlu türev, İntegral dönüşümler

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