We present an analysis of a n-dimensional vacuum Einstein field equations i
n which four-dimensional space-time is described by a Friedmann-Robertson-W
alker (FRW) metric and that of extra dimensions by a Kasner-type Euclidean
metric. The field equations are interpreted as four-dimensional Einstein eq
uations with effective matter properties. The effective matter is then trea
ted as a viscous fluid. We consider the theories of imperfect fluid given b
y Eckart, truncated Israel-Stewart, and full Israel-Stewart theories, and o
btain cosmological solutions for a flat model of the universe. The imperfec
t fluid assumption admits here power law inflation for the three-physical s
pace in some cases.