Stresses in long cylinder due to rotating line source of heat.

An Analysis of Unsteady Thermal Stresses in Rolls of CCP under a Rotating Heat Source

“…Applying the Laplace transforms to eqs. (1)(2)(3)(4)(5), and performing the inverse Laplace transform with the theorem of residue, the temperature T\ can be expressed…”

“…Rotating velocity of the roll, however, is pretty slow, so these treatments are not suitable for the analysis of thermal stress problem of the roll. Recently Hetnarsky [2] has improved the concept of the Jaeger's analysis [3] of temperature problems of a solid circular cylinder under a moving heat source and extended to the thermal stresses. His result, however, was considered for a solid circular cylinder and for.…”

Thermal-Stress Problems in Industry. 1: On Thermoelastic Distortion in Machining Metals

“…This approach is not applicable to the present problem because the result is appropriate only in the region neighboring the cutting position. Hetnarski [5) has analyzed unsteady heat conduction and thermal stresses, but his result was obtained for the plane problem. A similar problem was later treated by Pal [61.…”

“…2, in which thermal expansion in the axial direction is prevented by the reactions at the ends so that a compressive strain is produced in the bar. The amount of longitudinal compressive strain at the section z due to complete restraint in the axial direction may be calculated from the condition(5) where Tm is the mean temperature in the radial direction and is given byI JR Tm = 1TR22T1Tr dr o Substituting Eq. (3) into the above integral, we obtain T m' Once T m is determined, the final form of €z may be determined entirely from Eq.…”

Effect of Heat Generation on Quasi- Static Thermal Stresses in a Solid Sphere

“…Carslaw and Jeager [5] studied the use of sources and sinks in cases of variable temperature in a sphere, Ozisik [6] discussed many homogeneous and non homogeneous heat conduction boundary value problems with heat sources, Cheung et al [7] studied the transient problem in a sphere with local heating, Takeuti et al [8] studied the transient thermal stresses of a hollow sphere due to rotating heat source, Hetnarski [9] discussed the stresses in a long cylinder due to rotating line source, Nasser M. EI-Maghraby [10,11] deal with problems of thermoelasticity with heat sources. Deshmukh et al [12] studied the determination of displacement and thermal stresses in a thin hollow circular disk due to internal heat generation and integral transform is used to solve the heat distribution and stresses are obtained in a Bessel's functions.…”