  We explore the transport features of a Brownian particle that walks in a
periodic ratchet potential that is coupled with a spatially varying temperature
background. Since the viscous friction of the medium decreases as the
temperature of the medium increases, any reasonable exploration regarding the
thermodynamic features of the Brownian engine should take into account the role
of temperature on the viscosity of the fluid. In this work, we study this
effect of temperature by considering a viscous friction that decreases
exponentially as the background temperature increases. Our result depicts that
the Brownian particle exhibits a fast unidirectional motion when the viscous
friction is temperature dependent than that of constant viscous friction.
Moreover the efficiency of this motor is considerably enhanced when the viscous
friction is temperature dependent. On the hand, the motor exhibits a higher
performance of the refrigerator when the viscose friction is taken to be
constant.
