Download Laser Pulse Heating of Surfaces and Thermal Stress Analysis by Bekir S. Yilbas, Ahmad Y. Al-Dweik, Nasser Al-Aqeeli, PDF

By Bekir S. Yilbas, Ahmad Y. Al-Dweik, Nasser Al-Aqeeli, Hussain M. Al-Qahtani

This e-book introduces laser pulse heating and thermal tension research in fabrics floor. Analytical temperature remedies and rigidity built within the floor sector also are explored. The booklet may help the reader research the laser triggered tension within the irradiated quarter and provides suggestions for the tension box. designated thermal tension research in numerous laser pulse heating events and diverse boundary stipulations also are awarded. Written for floor engineers.

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Example text

Therefore, during the time interval s\ cx0 the step function in Eq. 133 is set to zero (u ¼ 0) or else it is set to 1. 133 is used to compute the dimensionless stress distribution for zero stress gradient at the surface. 3 Time Exponentially Varying Laser Pulse Heating Since the laser power intensity varies with time, temporal variation of the pulse intensity is incorporated in the stress analysis. In addition, the laser pulse intensity distribution can be resembled through employing a time exponentially varying pulse intensity profile.

86 is given lightly. The initial and boundary conditions are: and At the surface x ¼ 0 ! oT ox ! ¼0 x¼0 ð2:88Þ and at x ¼ 1 ! Tðt; 1Þ ¼ 0 The solution of Eq. , with respect to t, the Laplace transformation of Eq. 86 yields: Ã o2 T I1 d Àdx 1 Â e þ ¼ sT À Tðx; 0Þ 2 ox ks a ð2:89Þ where T ¼ Tðx; sÞ. Using the initial condition, Tðx; 0Þ ¼ 0; Eq. 87 yields: o2 T I1 d Àdx e À q2 T ¼ À ox2 ks ð2:90Þ where q2 ¼ as . 89 has a solution: T ¼ Aeqx þ BeÀqx þ I1 ad À Á eÀdx ks s À ad2 ð2:91Þ where A and B are the constants and they are calculated through the boundary conditions.

16 is used to formulate thermal stress distribution in the substrate material. In order to solve the momentum equation (Eq. 16) it is necessary to establish the initial conditions for stress and temperature fields. In this case, the substrate material is assumed to be free from stresses initially (at time = 0) and as the time extends to infinity, the stress free state must apply in the substrate. The same initial condition for the temperature is applied as in Eq. 198 provided that as time approaches infinity, the temperature in the substrate material reduces to zero.

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