In this work, we studied the problem of thermoelastic diffusion beams on the basis of modified couple stress theory under the effects of two temperature and laser pulse. The Euler-Bernoulli beam theory and the Laplace transform technique are applied to solve the basic equations of thermoelastic diffusion in the non-dimensional form. The transformed components of displacement, lateral deflection, axial stress, temperature change, concentration, and chemical potential are calculated mathematically to solve the problem. Copper material is used to prepare the mathematical model. The general algorithm of the inverse Laplace transform technique has been calculated numerically. MATLAB software is used to find the results numerically and depict them graphically. The effects of two temperature, laser pulse, and couple stress are presented graphically on the physical quantities. Particular cases are also discussed in the present problem. Laser pulse has many applications in Heat treatment, cutting of plastics, glasses, ceramics, semiconductors and metals, surgery, Lithography, and welding.

The problem of thermoelastic nanoscale beam based on a modified couple stress theory with diffusion subjected to ramp type heating is investigated. The Laplace transform technique and eigen value approach are applied to solve the equations which are written in the dimensionless form. The expressions for displacement, lateral deflection, temperature change, mass concentration, axial stress and chemical potential are derived in the transformed domain. A general algorithm of the inverse Laplace transform is developed to compute the results numerically. The mathematical model is prepared for Copper material. The resulting quantities are depicted graphically to show the effects of time. Some particular cases of interest are also deduced from the present problem.