Solution of coupled thermoelasticity Sample Clauses

Solution of coupled thermoelasticity. The governing Equations (2.11) and (2.12) are a system of second order linear par- tial differential equations (PDE) with nonconstant (radius dependent) coefficients subjected to the nonhomogeneous initial and boundary conditions. These equations can be solved using the analytical method based on the finite Xxxxxx transform, which can change the partial differential equations into solvable ordinary differen- tial equations. To this end, first, the principle of superposition can be used to sim- plify the coupled initial-boundary value problem (IBVP) into simpler sub-IBVPs. Therefore, using the principle of superposition, the heat conduction Equation (2.11) along with the corresponding boundary and initial conditions (2.14) in terms of the nondimensional parameters (without the hat sign for convenience), can be decom- posed into two following sub-IBVPs ∂ 2T1 + 1 ∂ T1 − T˙ − t T¨ = 0 ∂ r2 r ∂ r k11 ∂ T1 ∂ r r=a + k12T1(a, t) = f1 (t) , k21 ∂ T1 ∂ r r=b + k22 T1(b, t) = f2 (t) (2.19) T1(r, 0) = 0 , T˙1(r, 0) = 0
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Solution of coupled thermoelasticity. The governing Equations (2.11) and (2.12) are a system of second order linear par- tial differential equations (PDE) with nonconstant (radius dependent) coefficients subjected to the nonhomogeneous initial and boundary conditions. These equations can be solved using the analytical method based on the finite Xxxxxx transform, which can change the partial differential equations into solvable ordinary differen- tial equations. To this end, first, the principle of superposition can be used to sim- plify the coupled initial-boundary value problem (IBVP) into simpler sub-IBVPs.

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