Darcy's law may not he applicable for flows through highly permeable porous mediums. It is important to understand the limits of Darcy's law for flow and heat transfer through porous media. Therefore the entrance length and hydrodynamic boundary layer developing in conduits will be a function of Darcy's number and Reynolds number. In the following work, the dependence of entrance length on the Darcy and Reynolds number is correlated as a function of the controlling parameters. Also, heat transfer and thermal boundary-layer developments along the conduit are presented. The results of laminar flow in pipes are presented. Also, the effect of thermal conductivity and other controlling parameters on the rate of heat transfer are discussed for conduits filled completely or partially with porous media.