This paper presents an analytical solution of the hyperbolic heat conduction equation for a moving finite medium under the effect of a time-dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by g(x,t) = I(t) (1 – R)μe−μx while the finite body has an insulated boundary. The solution is obtained by the Laplace transforms method, and the discussion of solutions for two time characteristics of heat source capacities (instantaneous and exponential) is presented. The effect of the dimensionless medium velocity on the temperature profiles is examined in detail. It is found that there exists clear phase shifts in connection with the dimensionless velocity U in the spatial temperature distributions: the temperature curves with negative U values lag behind the reference curves with zero U, while the ones with positive U values precedes the reference curves. It is also found that the phase differences are the sole products of U, with increasing U predicting larger phase differences.
Analytical Solution of the Hyperbolic Heat Conduction Equation for a Moving Finite Medium Under the Effect of Time Dependent Laser Heat Source
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 9, 2012; final manuscript received July 4, 2012; published online October 8, 2012. Assoc. Editor: Robert D. Tzou.
- Views Icon Views
- Share Icon Share
- Cite Icon Cite
- Search Site
Al-khairy, R. T. (October 8, 2012). "Analytical Solution of the Hyperbolic Heat Conduction Equation for a Moving Finite Medium Under the Effect of Time Dependent Laser Heat Source." ASME. J. Heat Transfer. December 2012; 134(12): 122402. https://doi.org/10.1115/1.4007139
Download citation file:
- Ris (Zotero)
- Reference Manager