Abstract: A solution methodology without using integral
transformation is proposed to develop analytical solutions for
transient heat conduction in nonuniform hollow cylinders with
time-dependent boundary condition at the outer surface. It is shown
that if the thermal conductivity and the specific heat of the medium
are in arbitrary polynomial function forms, the closed solutions of the
system can be developed. The influence of physical properties on the
temperature distribution of the system is studied. A numerical
example is given to illustrate the efficiency and the accuracy of the
solution methodology.
Abstract: An alternative approach is proposed to develop the analytic solution for one dimensional heat conduction with one mixed type boundary condition and general time-dependent heat transfer coefficient. In this study, the physic meaning of the solution procedure is revealed. It is shown that the shifting function takes the physic meaning of the reciprocal of Biot function in the initial time. Numerical results show the accuracy of this study. Comparing with those given in the existing literature, the difference is less than 0.3%.