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Heating transients and response function for a hollow cylinder. (English) Zbl 0844.73003

Heat transfer for a hollow cylinder governed by the equation \(T(t) = T^e(t) - \int^t_0 R(t - \tau) {dT^e \over d \tau} d \tau\) is considered, where \(T\) is the hollow cylinder temperature, \(T^e\) is the external temperature, and \(R\) is the time response function of the material of the cylinder. The temperature distribution \(T = T(r,t)\) in the hollow cylinder is the solution of the boundary value problem \({\partial^2 T \over \partial r^2} + {1 \over r} {\partial T \over \partial r} - {1 \over \chi} {\partial T \over \partial t} = 0\), \(0 < a \leq r \leq b\), \({\partial T \over \partial r} |_{r = a} = 0\), \({\partial T \over \partial r} |_{r = b} = h[T(b,t) - T^e (t)]\), \(\chi\) and \(h\) are constants.
The time response function is given, and the solution of the above problem with \(T^e (t) = T_0 \sin wt\) is written down.

MSC:

74A15 Thermodynamics in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
35K05 Heat equation

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