Quantification of Uncertainty Propagation for Transient Heat Transfer in a Hollow Sphere

Uncertainty propagation and transient heat transfer for a hollow sphere are analyzed. The stochastic Biot number, stochastic linear non-dimensional initial conditions, and various boundary conditions are introduced to define uncertainty propagation influencing the temperature distribution throughout the hollow sphere. The resulting uncertainty amplitude was observed to have transient evolution in time. The uncertainty can either increase or decrease depending on the stochastic parameters. Results are presented for the variation in temperature due to uncertainties in the initial conditions and particular boundary conditions.