of channel 28 a the somewhat heated fluid may then pass through a transfer channel 48 to a back row channel 32 a where the cooling demand is somewhat reduced due to the increased distance from the heated surface 42 a after being further heated in channel 32 a the now spent cooling fluid may pass into the hot combustion fluid gas path 41 through outlet 54 the various inlets outlets and transfer channels may be formed by processes well known in the art such as by using fugitive materials during lay up of the wall fibers or by mechanical removal of material from the wall such as by drilling fig4 and 5 illustrate an embodiment b in which first and second cmc sheets 22 b 24 b each have semi cylindrical tubes 26 b 30 b providing fluid cooling channels 28 b 32 b in each sheet these tubes 26 b 30 b are connected in a parallel sequence by spans 29 b that are generally aligned along a common side of the tubes 26 b 30 b this forms a smooth first surface 36 b and a corrugated second surface 38 b on each sheet 22 b 24 b the sheets 22 b 24 b are stacked in a nested configuration with meshing corrugated surfaces as shown in fig5 to construct an interlocking cmc sandwich with non corrugated surfaces an insulating layer 40 b may be applied to a front surface 36 b of this sandwich resulting in a cmc wall 20 b with smooth non corrugated either planar or smoothly curved front and back surfaces 42 b 44 b embodiment b provides.