İNCE TABAKADA DİFÜZYON, TERMAL DALGA VE ÇİFT FAZLI-LAG ISI İLETİMİNİN KARŞILAŞTIRMALI BİR ÇALIŞMASI

Abstract

Bu çalışmada, sabit bir sıcaklığa ve yalıtılmış sınır koşullarına maruz kalan ince bir katman boyunca üç farklı ısı iletimi, difüzyon, termal dalga ve çift fazlı gecikme modu, sonlu bir eleman çözümü kullanılarak karşılaştırılmıştır. Sonlu eleman modeli, tek bir eleman için akıyı ısıtmak için gevşeme süresi ve sıcaklık gradyanı için gevşeme süresi dikkate alınarak geliştirilmiştir. Tüm elemanları birleştirdikten sonra, elde edilen cebirsel denklemlerin sayısı Python kullanılarak ince katman boyunca sıcaklık dağılımını tahmin etmek için çözülür. Çift fazlı gecikme ile tahmin edilen çözüm, tek fazlı Cattaneo – Vernotte modeli ve difüzyon Fourier modeli ile elde edilen çözüm ile karşılaştırılır. Geliştirilen model, analitik, sayısal ve deneysel çözümlerle iyi bir uyum içinde doğrulanmıştır. Her üç koşul için sıcaklık sınırları çizilmiştir ve ince katman boyunca farklı şekilde yayılma şekli açıkça gösterilmiştir. Ayrıca, çarpışmanın meydana geldiği katmanın merkezindeki sıcaklık değişimi tahmin edilir ve Fourier difüzyon modelinde sonsuz ve hem tek hem de çift fazlı gecikmede sonlu olan termal dalganın hızı, geçici olarak kararlı durum koşulu

Keywords

• çift fazlı gecikme
• CV modeli
• gevşeme süresi
• sonlu eleman modeli
• python

A COMPARATIVE STUDY OF DIFFUSION, THERMAL WAVE AND DUAL-PHASE-LAG HEAT CONDUCTION IN THIN LAYER

Abstract

In the present work, three different modes of heat conduction, diffusion, thermal wave, and dual-phase lag, across a thin layer subjected to a constant temperature and insulated boundary conditions are compared by using a finite element solution. The finite element model is developed by considering relaxation time to heat flux and relaxation time to temperature gradient for a single element. After assembling all the elements, the number of algebraic equations obtained is solved to predict the temperature distribution across the thin layer using Python. The solution predicted by the dual-phase lag is compared with that obtained by the single-phase Cattaneo–Vernotte’s model and diffusion Fourier model. The developed model is validated with analytical, numerical, and experimental solutions with good agreement. The temperature contours are plotted for all three conditions and the way it propagates differently through the thin layer is clearly shown. Further, the temperature variation at the center of the layer, at which collision occurred, is predicted and the speed of the thermal wave, infinite in the Fourier diffusion model and finite in both single and dual-phase lag, is examined under transient to steady-state condition.

Keywords

• dual-phase lag
• CV model
• relaxation time
• finite element model
• python

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