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We explore the transport features of a Brownian particle that walks in aperiodic ratchet potential that is coupled with a spatially varying temperaturebackground. Since the viscous friction of the medium decreases as thetemperature of the medium increases, any reasonable exploration regarding thethermodynamic features of the Brownian engine should take into account the roleof temperature on the viscosity of the fluid. In this work, we study thiseffect of temperature by considering a viscous friction that decreasesexponentially as the background temperature increases. Our result depicts thatthe Brownian particle exhibits a fast unidirectional motion when the viscousfriction is temperature dependent than that of constant viscous friction.Moreover the efficiency of this motor is considerably enhanced when the viscousfriction is temperature dependent. On the hand, the motor exhibits a higherperformance of the refrigerator when the viscose friction is taken to beconstant.

The effect of temperature on viscous friction and the performance of a Brownian heat engine