Mathematical modelling of thermoelastic problem in a circular sector disk subject to heat generation

The present paper deals with the determination of temperature, displacement and thermal stresses in a circular sector disk defined as 0 ≤ r ≤ a , 0 ≤ φ ≤ φ0 < 2π, 0 ≤ z ≤ h under an unsteady-state temperature field, due to internal heat generation within it. The time dependent heat flux f1(φ, z , t ) is applied on the fixed circular edge (r = a ). For time t > 0, the boundary surfaces at (φ = 0), (φ = φ0), (z = 0) and (z = h) are maintained at a prescribed temperatures f2(r, z , t ), f3(r, z , t ), f4(r,φ, t ) and f5(r,φ, t ) respectively, while the entire volume is subjected to internal energy generation given by the function g (r,φ, z , t ). The governing heat conduction equation has been solved by using finite Hankel transform and the generalized finite Fourier transform technique. As a special case mathematical model is constructed for pure aluminium circular sector disk considered. The results are obtained in series form in terms of Bessel’s functions. These have been computed numerically and illustrated graphically. MSC: 35B07 • 35G30 • 35K05 • 44A10