The phenomena of conjugate unsteady heat transfer from a solid spheric
al particle in a convective environment is numerically investigated fo
r Reynolds numbers in the range from 0.1 to 100. The flow and energy e
quations for both dispersed and continuous phases are solved using a C
hebyshev-Legendre spectral method. This work is an extension of the pr
evious effort of simulating flow around a sphere using spectral method
[2] to include heat transfer. General findings indicate that quasi-st
eady analysis underestimates the overall heat transfer rate significan
tly at very early time stages, however the extent of underprediction b
ecomes less as time progresses. The underprediction of the quasi-stead
y assumption becomes larger as Reynolds number increases for a fixed P
randtl number.