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The flow and heat transfer characteristics of Maxwell fluid in a pipe under pulsating pressure gradient were studied.The goving equations were made dimensionless.The Rubin boundary condition was adopted.The flow field was solved theoretically and the temperature field was obtained using finite volume method.A general model suitable for various fluctuating characteristics and physical parameters was established.The Deborah number (De) was used to characterize the fluidity of the fluid.The influence of De on flow and temperature fields was evaluated.The Nusselt number and start-up process of Maxwell fluid were studied.Results showed that the influence of De on flow field was greater than that on temperature field.The effect of De on Nusselt number was irregular and related to the oscillation parameters.The over-shooting amplitude and oscillation time of axis center velocity in start-up flow grow larger with De.