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In the present investigation, an oscillating motion of unsteady Burger's fluid in a circular cylinder was modeled with different pressure waveforms. Three different waveforms are considered: the case of a trapezoidal, triangular and sinusoidal waveform. Analytical solutions of velocity and temperature distribution are obtained for an oscillating laminar flow, which can be used to analyze the effects of flow type on the heat transfer performance. The limiting cases have been considered to examine the heat transfer performance of four different non-Newtonian fluids. Results show that the heat transfer of the oscillating flow depends on the fluid material parameter, Prandtl number, amplitude oscillating waveform and radial coordinate. The trapezoidal and sinusoidal waveforms of oscillating motion can result in a higher heat transfer performance.