This paper numerically investigates the effect of an externally evanescent magnetic ?eld on total entropy generation in a ?uid enclosed in a square cavity by using a control volume ?nite element method to solve the conservation equations at Prandtl number of 0·71. The values of relaxation time of the magnetic ?eld are chosen, so that the Lorentz force acts only in the transient state of entropy generation in natural convection. The total entropy generation was calculated for, ?xed value of irreversibility distribution ratio, different relaxation time varying from 0 to 1/5 and Grashof number varying from 10 4 to 10 5 . The effects of the Hartman number and the magnetic ?eld inclination angle on the evolution of total entropy generation throughout the transient regime were investigated. Results show that the application of evanescent magnetic ?eld not only suppresses the ?uctuation of the total entropy generation in the transient state, but also reduces the gap for magnetic ?eld relaxation time less than 1/10.
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