NOVELTY - Producing tubular ceramic structures of non-circular cross section involves: rotating mandrel-spindle assembly (40) having non-circular external cross section corresponding to non-circular internal cross section of tubular ceramic structure; applying ceramic-forming composition to external surface of mandrel component oldie rotating mandrel-spindle assembly to produce tubular ceramic structure; removing spindle from bore of mandrel to provide mandrel-tubular ceramic structure assembly; and heat shrinking the assembly to cause mandrel to undergo shrinkage to a reduced size.    USE - For producing tubular ceramic structures of non-circular cross section, which is used in patterned array of tubular solid oxide fuel cells of non-circular cross section; and in solid oxide fuel cell (SOFC) device (claimed).    ADVANTAGE - The process lies in its ability to provide ceramic or cermet bodies over a wide range of ratios of length to external diameter and ratios of external diameter to wall thickness while meeting very precise predetermined dimensional tolerances. The process for producing a tubular ceramic structure of non-circular cross section has its capability for readily and conveniently varying, or modifying, the ceramic-forming composition along the length of the structure. The process also utilizes quick-drying ceramic-forming compositions thus dispensing with the need for a carefully conducted and monitored drying operation. Also, since the heat-shrinkable tubular mandrel upon which the tubular ceramic structure is first formed when carrying out the process is eventually separated from the tubular product, there is no requirement that the latter be permanently united to a tubular substrate as is the case with dip coating. The external surface of the spindle possesses an anti-friction cladding or lubricious coating to facilitate removal of the spindle from the mandrel-spindle assembly.    DETAILED DESCRIPTION - Producing tubular ceramic structures of non-circular cross section involves: rotating a mandrel-spindle assembly (40) having a non-circular external cross section corresponding to the non-circular internal cross section of the tubular ceramic structure to be produced, where the mandrel-spindle assembly contains mandrel (41) component and spindle (43) component, the mandrel component is a heat shrinkable polymeric tube of non-circular cross section the external surface of which corresponds to the internal surface of the tubular ceramic structure of non-circular cross section to be produced and the internal surface of which defines a bore, the spindle component has non-circular cross section corresponding to that of the bore of the mandrel and being in close fitting but slidably removable contact with it; applying a ceramic-forming composition to the external surface of the mandrel component oldie rotating mandrel-spindle assembly to produce a tubular ceramic structure of non-circular cross section the internal surface of which is in contact with the external surface of the mandrel; removing the spindle from the bore of the mandrel to provide a mandrel-tubular ceramic structure assembly in which the interior surface of the tubular ceramic structure of non-circular cross section remains in contact with the external surface of the mandrel; and heat shrinking the mandrel component of the mandrel-tubular ceramic structure assembly to cause the mandrel to undergo shrinkage to a reduced size in which the external surface of the mandrel separates from the interior surface of the tubular ceramic structure of non-circular cross section facilitating removal of the mandrel from it. The tubular mandrel is fabricated from shape memory polymer. The ceramic-forming composition is an anode-forming composition for producing the tubular anode component of a tubular solid oxide fuel cell. INDEPENDENT CLAIMS are included for the following:    (1) a patterned array of tubular solid oxide fuel cells of non-circular cross section; and    (2) an solid oxide fuel cell (SOFC) device incorporating the patterned array of tubular solid oxide fuel cells.    DESCRIPTION OF DRAWING(S) - The figure shows a view of formation of a mandrel-spindle assembly of generally triangular cross section for use in the process.    Mandrel-spindle subassembly (40)    Mandrel (41)    Spindle (43)    Pair of end plates (46)    Array of apertures (48)