# Effects of Hall Current and Rotation on Magneto-Micropolar Generalized Thermoelasticity Due to Ramp-Type Heating

Abstract: In this work, a two dimensional problem in magnetic micropolar generalized thermoelastic medium, in the presence of a transverse magnetic field -taking into consideration the effect of Hall current- subjected to ramp-type heating, is investigated. The entire elastic medium is rotating with a uniform angular velocity. Laplace-Fourier transform technique is used to solve the problem. The transformed components of normal strain, normal stress, tangential couple stress, temperature distribution, and the current density components are obtained. The integral transforms have been inverted by using a numerical technique. Hall current effects and effect of rotation have been depicted graphically on the resulting quantities.

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### Cites background from "Effects of Hall Current and Rotatio..."

...Particular cases (i) If we consider the medium to be isotropic, i.e., c11 = λ + 2μ = c33, c12 = c13 = λ, c44 = μ, β1 = β3= β , α1 = α3 = α, K1 = K3 = K, without two temperatures, i.e., a1 = a3 = 0, and consider the generalized heat conduction equation, then results are similar as derived by Zakaria [33]....

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...[33] M. Zakaria, Effect of Hall current on generalized magnetothermoelasticity micropolar solid subjected to ramp-type heating, Int....

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...Authors, such as Zakaria [32, 33], Salem [34], Kumar andDevi [35], and Sarkar and Lahiri [36], have considered the effect of Hall current for 2D problems in micropolar thermoelasticity....

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...[32] M. Zakaria, Effects of Hall current and rotation on magnetomicropolar generalized thermoelasticity due to ramp-type heating, Int....

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9 citations

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##### References

2,848 citations

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...The first is due to Lord and Shulman[7], who obtained a wave-type heat equation by postulating a new law of heat conduction to replace the classical Fourier’s law....

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...In this work, we introduced a new model of the equations of the generalized magneto micropolar thermoelasticity in the presence of transverse magnetic field, taking into consideration the effects of Hall current and rotation, is applied to both generalizations, Lord–Shulman theory and Green–Lindsay theory, as well as to the coupled theory....

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...27 (1956) 240–253 [7] H. Lord, Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech....

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### "Effects of Hall Current and Rotatio..." refers background in this paper

...Biot[6] introduced the theory of coupled thermoelasticity to overcome the first shortcoming....

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1,228 citations

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### "Effects of Hall Current and Rotatio..." refers background in this paper

...C Eringen, Nonlinear theory of micro-elastic Solids II....

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...Purdue University, (1965) [5] A. C. Eringen, Linear theory of micropolar elasticity, J. Mech....

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...REFERENCES [1] A. C. Eringen, E. S. Suhubi, Non-linear theory of mi- cro-elastic Solids I. Int....

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