AbstractNatural convection flow and heat transfer induced by a pulsating point heat source, embedded in an unbounded fluid‐saturated porous medium is studied analytically. Solutions for both the velocity and temperature fields are obtained in the form of series expansions in the Rayleigh number based on the permeability of the porous medium and the mean heat generation rate from the source. All discussions are based on the assumption that the flow is governed by Darcy's law and that the thermal Rayleigh number is small. The fluctuating part shows the evolution of different wave patterns. The interaction of the first harmonic fields induce second‐order mean components in the velocity and temperature fields. Analytical expressions are obtained for the second‐order mean in both the velocity and temperature f