An asymptotic and numerical investigation was conducted for the cooling pro
cess, by a forced laminar flow, of a small strip with a non-uniform heat so
urce. The nondimensional temperature distribution in the strip has been obt
ained as a function of the following parameters: (a) the intensity and dist
ribution of the internal heat sources, (b) the aspect ratio of the strip, (
c) the longitudinal heat conductance of the strip and (d) the Prandtl numbe
r of the fluid. Both the thermally thin as the thick wall approximations we
re considered in this paper. The total thermal energy or averaged temperatu
re of the strip is found to decrease as the influence of the longitudinal h
eat conduction effects in the strip decreases in the thermally thin wall re
gime. After reaching a minimum, it increases again in the thermally thick w
all regime.