Abstract




 
   

IJE TRANSACTIONS C: Aspects Vol. 27, No. 6 (June 2014) 971-978   

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  ANALYTICAL ANALYSIS OF THE DUAL-PHASE-LAG HEAT TRANSFER EQUATION IN A FINITE SLAB WITH PERIODIC SURFACE HEAT FLUX (RESEARCH NOTE)
 
H. Askarizadeh and H. Ahmadikia
 
( Received: October 19, 2013 – Accepted: December 12, 2013 )
 
 

Abstract    This work uses the dual-phase-lag (DPL) model of heat conduction to demonstrate the effect of temperature gradient relaxation time on the result of non-Fourier hyperbolic conduction in a finite slab subjected to a periodic thermal disturbance. DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. For the first time, the analytical solution of DPL model of heat conduction equation is obtained adopting Laplace transform method and inversion theorem. The temperature profiles at the front and rear surfaces of the slab are calculated for various temperature gradient relaxation time. The phase and amplitude difference between the front and the rear surface are calculated numerically as a function of the temperature gradient relaxation time, which are reported previously as a function of the heat flux relaxation time. The results demonstrate that increasing on the temperature gradient relaxation time leads to the lower phase difference and upper amplitude difference between the temperature responses of the front and rear surfaces.

 

Keywords    Dual-Phase-Lag, Finite Medium, Temperature Gradient Relaxation Time, Analytical Solution

 

چکیده    در این مطالعه از مدل تأخیر فاز دوگانه معادله هدایت گرما برای تعیین اثر زمان آسایش حرارتی گرادیان دما روی نتایج هدایت گرمای غیر فوریه هذلولوی در یک ورق محدودی که در معرض اغتشاش گرمایی نوسانی قرار گرفته، استفاده شده است. مدل تأخیر فاز دوگانه ویژگی­های موج گونه­ای و پخش گونه­ای هدایت گرما را ترکیب می­کند که مدل هذلولوی قادر به این کار نیست. برای اولین بار حل تحلیلی مدل تأخیر فاز دوگانه معادله هدایت گرما با استفاده از روش تبدیل لاپلاس و تئوری وارونه سازی به دست آمده است. پروفیل­های توزیع دما در سطح و پشت ورق برای زمان­های مختلف آسایش حرارتی گرادیان دما به دست آمده­اند. اختلاف فاز و دامنه بین پاسخ­های دمایی سطح و پشت به عنوان تابعی از زمان آسایش حرارتی گرادیان دما که قبلاً به عنوان تابعی از زمان آسایش حرارتی شار گرما ارائه شده­اند، به صورت عددی محاسبه شده­اند. نتایج نشان می­دهند که افزایش زمان آسایش حرارتی گرادیان دما باعث کاهش اختلاف فاز و افزایش اختلاف دامنه بین پاسخ­های دمایی سطح و پشت می­شود..

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