For small Biot numbers (the relative strength between h and k),
Bib0.001, the public have learned from the literature [5] that the temperature
inside a solid object,which is suddenly immersed in a fluid flow at a
different temperature, can be safely assumed to be uniform. In other
words, T is a function of time only, not a function of space. This assumption
allows the adoption of the well-known lumped-capacitance model,
which greatly simplifies the analysis. Very few textbooks or literature papers,
however, have clearly pointed out that such an assumption is valid
only for temperature variables, and that actually surface heat fluxes at a
fewinitial time steps are strong functions of x, as showninFig. 1. Relevant
data used to compute this example with the traditional implicit method
are given below