Due to ramp type heating, this chapter depicts the thermoelastic diffusion beam in modified couple stress theory. To address the problem in non-dimensional form, the Euler-Bernoulli beam theory, Laplace transform technique, and eigenvalue approach are used. The basic equations are written in the form of a vector-matrix differential equation, which is solved using the eigenvalue approach, using Euler-Bernoulli beam theory and the Laplace transform technique. Displacement, lateral deflection, temperature, axial tension, chemical potential, and concentration components are converted. To recover the solutions in the physical domain, a numerical inversion technique was used. With the help of MATLAB software, the analytical results were numerically determined. Mathematical modelling is done with copper substance. For various time values, numerically simulated results for displacement, lateral deflection, temperature, axial stress, chemical potential, and concentration are graphically presented. For various time values, comparisons have been done. In the problem, certain specific instances are discussed.
Author (S) Details
Department of Mathematics, Maharaja Lakshman Sen Memorial College, Sundernagar, Mandi, Himachal Pradesh, India.
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