Nusselt number data scattering in natural convection in porous media

Analytical solutions derived in this paper confirm the experimental and numerical results revealing widespread Nusselt number data scattering in natural convection in porous media. The weak non-linear method of solution is used to evaluate the Nusselt number in a porous layer heated from below and subject to weak boundary and domain imperfections. Little attention has been paid so far to the effect that the lower branch of the imperfect bifurcation has on the average Nusselt number. The results presented in this paper demonstrate the latter effect and explain the reason behind the scattering of data. The comparison of the results with existing experimental and numerical data confirms the findings. In addition the latter effect is shown to be essential in ones ability to control heat transfer enhancement via natural convection in porous metal foams, for example.