## THERMAL SCIENCE

International Scientific Journal

### TICKHONOV BASED WELL-CONDITION ASYMPTOTIC WAVEFORM EVALUATION FOR DUAL-PHASE-LAG HEAT CONDUCTION

**ABSTRACT**

The Tickhonov based well condition asymptotic waveform evaluation (TWCAWE) is presented here to study the non-Fourier heat conduction problems with various boundary conditions. In this paper, a novel TWCAWE method is proposed to overwhelm ill-conditioning of the asymptotic waveform evaluation (AWE) technique for thermal analysis and also presented for time-reliant problems. The TWCAWE method is capable to evade the instability of AWE and also efficaciously approximates the initial high frequency and delay similar as well-established numerical method, such as Runge-Kutta (R-K). Furthermore, TWCAWE method is found 1.2 times faster than the AWE and also 4 times faster than the traditional R-K method.

**KEYWORDS**

PAPER SUBMITTED: 2014-04-10

PAPER REVISED: 2014-06-24

PAPER ACCEPTED: 2014-08-19

PUBLISHED ONLINE: 2014-09-06

**THERMAL SCIENCE** YEAR

**2016**, VOLUME

**20**, ISSUE

**Issue 6**, PAGES [1891 - 1902]

- Burke, G. J., et al., Using model-based parameter estimation to increase the efficiency of computing electromagnetic transfer functions, IEEE Transaction Magazine, 25 (1989), 4, pp. 2807- 2809
- Pillage, L. T., Rohrer, R. A., Asymptotic waveform evaluation for timing analysis, IEEE Transaction Computer-Aided Design, 9 (1990), 4, pp. 352-366
- Loh, J. S., et al., Fast transient thermal analysis of Fourier and non-Fourier heat conduction, Int. J. Heat Mass Transfer, 50 (2007), 21, pp. 4400-4408
- Lanczos, C., An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, United States Governm. Press Office, 1950
- Slone, R. D., Well-Conditioned Asymptotic Waveform Evaluation for Finite Element, IEEE Transaction on Antennas and Propagation, 51 (2003), 9, pp. 2442-2447
- Lenzi, M. S., et al., A fast frequency sweep approach using Pade approximations for solving Helmoltz finite element models, Journal of Sound and Vibration, 32 (2013), 8, pp. 1897-1917
- Baumeister, K. J., Hamill, T. D., Hyperbolic heat conduction equation - a solution for the semiinfinite body problem-I, J. Heat Transfer, 9 (1969), 4, pp. 543-548
- Baumeister, K. J., Hamill, T. D., Hyperbolic heat conduction equation - a solution for the semiinfinite body problem-II, J. Heat Transfer, 9 (1971), 3, pp. 126-127
- Tang, D. W., Araki, N., Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance, Int. J. Heat Mass Transfer, 39 (1996), 8, pp. 1585-1590
- Tang, D. W., Araki, N., Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance-II. Another form of solution, Int. J. Heat Mass Transfer, 39 (1996), 15, pp. 3305- 3308
- Tang, D.W., Araki, N., Analytical solution of non-Fourier temperature response in a finite medium under laser-pulse heating. Heat Mass Transfer 31 (1996), 5, pp. 359-363
- Tang, D.W., Araki, N., Non-Fourier heat conduction behavior in finite mediums under pulse surface heating, Mater. Sci. Eng., 29 (2000), 2, pp. 173-178
- Liu, P., et al., Fast thermal simulation for runtime temperature tracking and management, IEEE transaction on computer -aided design of integrated circuits and systems, 25 (2006), 12, pp. 2882- 2893
- Rana, S., Kanesan, J., Reza, A. W., Ramiah, H., Well-Condition Asymptotic Waveform Evaluation Method for Heat Conduction Problem, Advanced Materials Research, 845 (2014), pp. 209-215
- Rana, S., Kanesan, J., Reza, A. W., Ramiah, H., Fast Transient Thermal Analysis of Non-Fourier Heat Conduction Using Tikhonov Well-Conditioned Asymptotic Waveform Evaluation, The Scientific World Journal, 2014 (2014), Article ID 671619, 7 pages
- Mishra, S. C., Sahai, H., Analysis of non- Fourier conduction and radiation in cylindrical medium using lattice Boltzmann method and finite volume method, Int. J. Heat Mass Transfer, 61 (2013), 1, pp. 41-55
- Neumaier, A., Solving ill-conditioned and singular linear system, a tutorial on regularization, Siam Review, 40 (1998), 3, pp. 636-666
- Gheorghe, B., et al., FEM Analysis of Brushless DC Servomotor with Fractional Number of Slots per Pole, Advances in Electrical and Computer Engineering, 14 (2014), 1, pp. 103-108
- Mosallanejad, A., et al., Investigation and Calculation of Magnetic Field in Tubular Linear Reluctance Motor Using FEM, Advances in Electrical and Computer Engineering, 10 (2010), 4, pp. 34-48
- Adrian M., et al., FEM-based Analysis of a Hybrid Synchronous Generator with Skewed Stator Slots, Advances in Electrical and Computer Engineering,11 (2011), 4, pp. 9-14
- Yevgeny, S., The Practical Stability of the Linear Systems with the Phase Space Variable Measurability, Advances in Electrical and Computer Engineering, 7 (2011), 1, pp. 50-53
- Lefteriu, S., et al., On a fast frequency sweep approach for the Helmholtz FE problem via model reduction, Noise and Vibration, 38 (2012), 8,pp. 1-12
- Quintanilla, R., Racke, R., A note on stability in dual-phase -lag heat conduction, Int. J. Heat Mass Transfer, 49 (2006), 7, pp. 1209-1213