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Research Papers: Heat and Mass Transfer

Reflection of Generalized Magneto-Thermoelastic Waves With Two Temperatures Under Influence of Thermal Shock and Initial Stress

[+] Author and Article Information
S. M. Abo-Dahab

Mathematics Department,
Faculty of Science,
South Valley University,
Qena 83523, Egypt;
Mathematics Department,
Faculty of Science,
Taif University,
Taif 888, Saudi Arabia
e-mail: sdahb@yahoo.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 7, 2018; final manuscript received April 27, 2018; published online June 8, 2018. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 140(10), 102005 (Jun 08, 2018) (8 pages) Paper No: HT-18-1018; doi: 10.1115/1.4040258 History: Received January 07, 2018; Revised April 27, 2018

The aim of this investigation is to estimate the theory of generalized magneto-thermoelasticity to solve the problems of two-dimensional (2D) half-space under thermal shock, initial stress, and two temperatures. The governing equations are solved by using Lame's potentials method in the context of classical dynamical (CD) and Lord-Şhulman (LS) theories. The boundary conditions are as follows (i) the total normal stresses in the boundary equivalent to the initial stress; (ii) the shear stresses are vanished at the boundary; and (iii) the incidence boundary is thermal insulated. The reflection coefficients have been obtained for two incident p- and SV-waves. The results obtained for the incident waves calculated numerically by using appropriate metal and presented graphically. Comparisons have been made with the results obtained from the presence and absence of magnetic field and initial stress.

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Figures

Grahic Jump Location
Fig. 1

Geometry of the problem

Grahic Jump Location
Fig. 2

For incident p-wave: variation of the magnitudes of waves' amplitudes with respect to θ with varies values of relaxation time τ0=0.4___,0.5….,0.7−−

Grahic Jump Location
Fig. 3

For incident p-wave: variation of the magnitudes of waves' amplitudes with respect to θ with varies values of relaxation time H=104___,2×104….,2×106−−

Grahic Jump Location
Fig. 4

For incident p-wave: variation of the magnitudes of waves' amplitudes with respect to θ with varies values of relaxation time P=3×1011___,4×1011….,5×1011−−,6×1011−.−

Grahic Jump Location
Fig. 5

For incident SV-wave: variation of the magnitudes of waves' amplitudes with respect to θ with varies values of relaxation time τ0=0.4___,0.5….,0.7−−

Grahic Jump Location
Fig. 6

For incident SV-wave: variation of the magnitudes of waves' amplitudes with respect to θ with varies values of relaxation time H=104___,2×104….,2×106−−

Grahic Jump Location
Fig. 7

For incident SV-wave: variation of the magnitudes of waves' amplitudes with respect to θ with varies values of relaxation time P=3×1011___,4×1011….,5×1011−−,6×1011−.−

Grahic Jump Location
Fig. 8

A comparison between the magnitudes of waves' amplitudes |zi|, i=1,2,3 with respect to θ (a) p-wave incidence and (b) SV-wave incidence

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