Fractional time derivative on fluid flow through horizontal microchannel filled with porous material

Öz

Fractional time derivative is considered in the description of the unsteady fluid flow through a horizontal microchannel filled with porous material. The resultant governing equations were solved using the Laplace transform technique and the method of undetermined coefficient in the Laplace domain. The Riemann-sum approximation approach was then utilized to obtain the solution in the time domain. The results were then simulated and presented as line graphs utilizing MATLAB (R2015b) to study the effects of the parameters involved in the fluid flow.

Anahtar Kelimeler

• Fractional time derivative
• Pressure driven flow
• Darcy number
• Knudsen number

Gözenekli malzeme ile doldurulmuş yatay mikrokanaldan akışkan akışında kesirli zaman türevi

Öz

Kesirli zaman türevi, gözenekli malzeme ile doldurulmuş yatay bir mikrokanaldan geçen kararsız akışkan akışının tanımlanmasında dikkate alınmıştır. Elde edilen yönetici denklemler Laplace dönüşümü tekniği ve Laplace alanında belirlenmemiş katsayı yöntemi kullanılarak çözülmüştür. Riemann-toplam yaklaşımı daha sonra zaman alanında çözümü elde etmek için kullanılmıştır. Sonuçlar daha sonra simüle edilmiş ve akışkan akışına dahil olan parametrelerin etkilerini incelemek için MATLAB (R2015b) kullanılarak çizgi grafikler halinde sunulmuştur.

Anahtar Kelimeler

• Darcy numarası
• Kesirli zaman türevi
• Knudsen numarası
• Basınç tahrikli akış

Kaynakça

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