Temperature characteristics of heat exchange due to thermal conductivity of three hollow cylinders in their contact planes

For the case where a system of three hollow cylinders, having contact along their ends, are heated the problem on the determination of the thermal characteristics in the contact planes is solved analytically. Numerical calculations and the construction of plots of the temperature variation, thermal fluxes, and the heating and stabilization times in the contact planes are carried out on the basis of the formulas so obtained.Notation _j = (T_j–T₀)/(T₀–T_c) dimensionless temperature - T₀ initial temperature - T_c temperature of the medium - T_j temperature at an arbitrary point of the j-th cylinder - Fo_j a_jt/R₁² - K_a a₂/a₁ - d R₂/R₁ - b R₁/l - _j, a_j thermal and thermiometric conductivities, respectively - R₂, R₁ respectively, the outer and inner radii of the cylinders - t time - X, Z dimensionless cylindrical coordinatesTranslated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 80–84, July, 1972.