A numerical study is conducted to analyze the conjugate heat transfer characteristics of oscillating flow in a parallel-plate channel. An oscillating pressure gradient which varies sinusoidally with time is imposed to generate oscillating flow, and a sinusoidal temperature distribution along the external wall is applied as a boundary condition. Time-dependent energy equations of the fluid and the solid are solved numerically using a spectral method. A parametric study is conducted to quantify the effects of the non uniformity of the velocity over the cross-section and wall conduction on heat transfer. For the condition of Re > 1 and Pe > 1, the results show that the Nusselt number increases as the kinetic Reynolds number increases with a fixed Peclet number. The Peclet number was previously known to be the only parameter governing heat transfer in oscillating flow, but the kinetic Reynolds number also plays an important role in heat transfer process. If the non-uniformity of the velocity over the cross-section is not properly accounted for, the Nusselt number will be significantly overestimated, except when Pe < 1, where heat transfer is governed by conduction. A new correlations of the Nusselt number, which take into account the effect of the velocity non-uniformity, are proposed. To visualize the effect of non-uniformity of the velocity on heat transfer as well as the interplay between transverse conduction and axial advection, time-averaged heatlines are also proposed. Finally, the dimensionless thermal thickness, a dimensionless parameter defined by the product of the ratio of the wall thickness to the half-channel width (b/a) and the ratio of thermal conductivity of the fluid to that of the solid (k(f)k(s)), is proposed to quantify the effect of wall conduction. It is revealed that wall conduction can be safely neglected when the dimensionless thermal thickness is less than 0.01. As the dimensionless thermal thickness increases from 0.01, the effective thermal conductivity is shown to be significantly decreased. (C) 2017 Elsevier Ltd. All rights reserved.