The Laplace transform (LT) is a 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 this 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 nonsinusoidal 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 that quite accurate solutions can be obtained with a fewer number of terms.
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A Closed Form Solution of Dual-Phase Lag Heat Conduction Problem With Time Periodic Boundary Conditions
Pranay Biswas,
Pranay Biswas
Department of Energy Science and Engineering,
Indian Institute of Technology Bombay,
Powai,
Mumbai, Maharashtra 400076, India
e-mail: pranaybiswas@iitb.ac.in
Indian Institute of Technology Bombay,
Powai,
Mumbai, Maharashtra 400076, India
e-mail: pranaybiswas@iitb.ac.in
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Suneet Singh,
Suneet Singh
Department of Energy Science and Engineering,
Indian Institute of Technology Bombay,
Powai,
Mumbai, Maharashtra 400076, India
e-mail: suneet.singh@iitb.ac.in
Indian Institute of Technology Bombay,
Powai,
Mumbai, Maharashtra 400076, India
e-mail: suneet.singh@iitb.ac.in
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Hitesh Bindra
Hitesh Bindra
Department of Mechanical and Nuclear
Engineering,
Kansas State University,
3002 Rathbone Hall, 1701B Platt Street,
Manhattan, KS 66506
e-mail: hbindra@ksu.edu
Engineering,
Kansas State University,
3002 Rathbone Hall, 1701B Platt Street,
Manhattan, KS 66506
e-mail: hbindra@ksu.edu
Search for other works by this author on:
Pranay Biswas
Department of Energy Science and Engineering,
Indian Institute of Technology Bombay,
Powai,
Mumbai, Maharashtra 400076, India
e-mail: pranaybiswas@iitb.ac.in
Indian Institute of Technology Bombay,
Powai,
Mumbai, Maharashtra 400076, India
e-mail: pranaybiswas@iitb.ac.in
Suneet Singh
Department of Energy Science and Engineering,
Indian Institute of Technology Bombay,
Powai,
Mumbai, Maharashtra 400076, India
e-mail: suneet.singh@iitb.ac.in
Indian Institute of Technology Bombay,
Powai,
Mumbai, Maharashtra 400076, India
e-mail: suneet.singh@iitb.ac.in
Hitesh Bindra
Department of Mechanical and Nuclear
Engineering,
Kansas State University,
3002 Rathbone Hall, 1701B Platt Street,
Manhattan, KS 66506
e-mail: hbindra@ksu.edu
Engineering,
Kansas State University,
3002 Rathbone Hall, 1701B Platt Street,
Manhattan, KS 66506
e-mail: hbindra@ksu.edu
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 4, 2018; final manuscript received December 28, 2018; published online February 4, 2019. Assoc. Editor: George S. Dulikravich.
J. Heat Transfer. Mar 2019, 141(3): 031302 (12 pages)
Published Online: February 4, 2019
Article history
Received:
July 4, 2018
Revised:
December 28, 2018
Citation
Biswas, P., Singh, S., and Bindra, H. (February 4, 2019). "A Closed Form Solution of Dual-Phase Lag Heat Conduction Problem With Time Periodic Boundary Conditions." ASME. J. Heat Transfer. March 2019; 141(3): 031302. https://doi.org/10.1115/1.4042491
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