A closed form solution of dual phase lag heat conduction problem with time periodic boundary conditions

[+] Author and Article Information
Pranay Biswas

Ph.D. Scholar, Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai-400076, Mumbai, Maharashtra, INDIA

Suneet Singh

Professor, Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai-400076, Mumbai, Maharashtra, INDIA

Hitesh Bindra

Professor, Department of Mechanical and Nuclear Engineering, Kansas State University, 3002 Rathbone Hall, 1701B Platt St., Manhattan, KS 66506, USA

1Corresponding author.

ASME doi:10.1115/1.4042491 History: Received July 04, 2018; Revised December 28, 2018


The Laplace transform (LT) is widely used methodology for analytical solutions of dual phase lag (DPL) heat conduction problems with consistent DPL boundary conditions (BCs). However, the inversion of LT requires a series summation with large number of terms for reasonably converged solution, thereby, increasing computational cost. In the present work, an alternative approach is proposed for this inversion which is valid only for time-periodic BCs. In this approach, an approximate convolution integral is used to get an analytical closed-form solution for sinusoidal BCs (which is obviously free of numerical inversion or series summation). The ease of implementation and simplicity of the proposed alternative LT approach is demonstrated through illustrative examples for different kind of sinusoidal BCs. It is noted that the solution has very small error only during the very short initial transient and is (almost) exact for longer time. Moreover, it is seen from the illustrative examples that for high frequency periodic BCs the Fourier and DPL model give quite different results, however, for low frequency BCs the results are almost identical. For non-sinusoidal periodic function as BCs, Fourier series expansion of the function in time can be obtained and then present approach can be used for each term of the series. An illustrative example with a triangular periodic wave as one of the BC is solved and the error with different number of terms in the expansion is shown. It is observed quite accurate solutions can be obtained with a fewer number of terms.

Copyright (c) 2019 by ASME
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In