In this work, we study the effect of the magnetic field, rotation, thermal field, and the initial stress and also voids on the reflection of P -wave with one relaxation time. The formulation is applied to generalization, the Lord-Shulman theory with one relaxation time. The electromagneto-thermoelastic interactions in perfectly conducting plane is subjected to a uniform axial magnetic field with voids and rotation. It is shown that there exist four plane waves; P 1 -, P 2 -, P 3 -and P 4 -. In addition, the reflection coefficients from insulated stress-free surface for the incident P -wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of magnetic field, initial stress, rotation, thermal relaxation time and voids parameters and displayed graphically. In the case of neglecting the effect of the magnetic field, and made clear the impact of other variables on the reflection coefficients, which is considered a special case of this study and displayed graphically.

The present paper studied the reflection of thermo-microstretch waves under the generalized thermoelasticity theory which is employed to study the reflection of plane harmonic waves from a semi-infinite elastic solid under the effect of the electromagnetic field, initial stress, and gravity. The formulation is applied under the thermoelasticity theory with three-phase lag, and the reflection coefficient ratio variations with the angle of incidence under different conditions are obtained. Numerical results obtained from the present study are presented graphically and discussed. It is observed that the initial stress, gravitation, and electromagnetic field exert some influence in the thermo-microstretch medium due to reflection of P-waves.

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Purpose The purpose of this paper is to predict the effects of magnetic field, heat and mass transfer and rotation on the peristaltic flow of an incompressible Newtonian fluid in a channel with compliant walls. The whole system is in a rotating frame of reference. Design/methodology/approach The governing equations of two-dimensional fluid have been simplified under long wavelength and low Reynolds number approximation. The solutions are carried out for the stream function, temperature, concentration field, velocity and heat transfer coefficient. Findings The results indicate that the effects of permeability, magnetic field and rotation are very pronounced in the phenomena. Impacts of various involved parameters appearing in the solutions are carefully analyzed. Originality/value The effect of the concentration distribution, heat and mass transfer and rotation on the wave frame is analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. A comparison was made with the results obtained in the presence and absence of rotation, magnetic field and heat and mass transfer.

The present research paper illustrates how noninteger derivative order analysis affects the reflection of partial thermal expansion waves under the generalized theory of plane harmonic wave reflection from a semivacuum elastic solid material with both gravity and magnetic field in the three-phase lag model (3PHL). The main goal for this study is investigating the fractional order impact and the applications related to the orders, especially in biology, medicine, and bioinformatics, besides the integer order considering an external effect, such as electromagnetic, gravity, and phase lags in a microstretch medium. The problem fractional form was formulated, and the boundary conditions were applied. The results were displayed graphically, considering the 3PHL model with magnetic field, gravity, and relaxation time. These findings were an explicit comparison of the effect of the plane wave reflection amplitude with integer derivative order analysis and noninteger derivative order analysis. The fractional order was compared to the correspondence integer order that indicated to the difference between them and agreement with the applications in biology, medicine, and other related topics. This phenomenon has more applications in relation to the biology and biomathematics problems.