An analytical solution is obtained for forced convection in a circular tube occupied by a core-sheath-layered saturated porous medium with counterflow produced by pulsating pressure gradients. The case of the constant heat-flux boundary conditions is considered, and the Brinkman model is employed for the porous medium. A perturbation approach is used to obtain analytical expressions for the velocity, temperature distribution, and transient Nusselt number for convection produced by an applied pressure gradient that fluctuates with small amplitude harmonically in time about a non-zero mean. It is shown that the fluctuating part of the Nusselt number alters in magnitude and phase as the dimensionless frequency increases. The magnitude increases from zero, goes through a peak, and then decreases to zero. The height of the peak depends on the values of various parameters. The phase (relative to that of the steady component) decreases from pi/2 to -pi/2 as the frequency increases.