an embodiment of the present invention will be hereinafter described in detail with reference to the accompanying drawings . fig2 is for description of the configuration of a cell of a direct - flame fuel cell according to a first embodiment of the invention as well as its manufacturing method . fig3 a and 3b show shapes of a green sheet of a solid electrolyte before firing which is used to manufacture a cell . as shown in fig2 , the configuration of the cell of the direct - flame fuel cell according to the invention is the same as the conventional cell in that an anode layer 12 is formed on one surface of a solid electrolyte layer 10 and a cathode layer 14 is formed on the other surface and electrodes 13 and 15 are connected to the anode layer 12 and the cathode layer 14 , respectively . however , in the invention , the cell is curved so that the anode layer 12 side assumes a concave shape and the cathode layer 14 side assumes a convex shape . oxygen or an oxygen - containing gas is supplied to the cathode layer 14 side and a flame 16 formed by a fuel gas such as methane is applied directly to the anode layer 12 side . as described above , in the invention , the cell is curved and a flame 16 is applied to the anode layer 12 side having a concave surface . since the flame 16 is curved along the concave surface 12 a at an acute angle ( smaller than 90 °) as indicated by arrows b , the flame 16 is prevented from going around to the cathode layer 14 side having a convex shape or the amount of flame that goes around to the cathode layer 14 side is reduced . as a result , the oxygen partial pressure on the cathode layer 14 side is prevented from decreasing and the reaction portion of the cell that is produced by the flame 16 can be enlarged substantially . the power generation efficiency can thus be increased . the cell , having the above shape , of the fuel cell is manufactured in the following manner . first , as in the conventional manufacturing method of a cell , as shown in fig3 a , a green sheet 10 a of a solid electrolyte layer is formed so as to have a circular thin - plate or thin - film shape . in the invention , no particular limitations are imposed on the material of the solid electrolyte layer . however , the solid electrolyte layer may be made of zirconia - based ceramics such as ysz ( yttria - stabilized zirconia ), scsz ( scandia - stabilized zirconia ), or ysz or scsz doped with ce , al , or the like , ceria - based ceramics such as sdc ( samaria - doped ceria ) or gdc ( gadolia - doped ceria ), lsgm ( lanthangallate ), or bismuth - oxide - based ceramics . next , as shown in fig3 b , the green sheet 10 a of the solid electrolyte layer is worked into a conical shape . the circular , flat - plate - like green sheet 10 a of the solid electrolyte layer is worked into a conical green sheet 10 b by simple methods . for example , the circular green sheet 10 a is cut straightly from the center in a radial direction , applying ethanol or the like to portions on both sides of the cutting line by such an amount that those portions become soft , laying those portions on each other , and shaping the green sheet 10 a into a conical shape using a proper die or the like ( not shown ). such simple working methods can be applied to not only sdc - type solid electrolyte layers but also ysz - type and gdc - type ones . in the manufacturing method of a cell shown in fig3 a and 3b , first a green sheet of a solid electrolyte is worked into a circular shape and then it is shaped into a conical shape and fired . therefore , the cell of the direct - flame fuel cell according to the invention can be manufactured easily at a low cost by merely adding the step of working a circular , flat - plate - like green sheet of a solid electrolyte into a conical shape to the process for manufacturing a conventional circular , flat - plate - like cell of a fuel cell . facilities for manufacturing a green sheet of a circular , flat - plate - like green sheet of a solid electrolyte , facilities for firing a green sheet , and other facilities can be used as they are . an anode layer , a cathode layer and an electrode are arranged as the conventional manner on the solid electrolyte layer obtained in this manner to complete a fuel cell . fig4 a to 4d show various possible shapes of the cell of the fuel cell according to the invention . the cell of the direct - flame fuel cell according to the invention may have various shapes as long as they are shaped in such a manner that one surface of the solid electrolyte layer has a concave surface and the other surface has a convex surface and so that a flame is prevented from going around to the cathode layer side when the flame is applied to the anode layer side . a pyramid shape ( fig4 a ), a bowl shape ( fig4 b ), a conical shape ( fig4 c ), a roof shape ( fig4 d ), and other shapes are possible . an optimum shape should be selected as appropriate taking into consideration various points such as the degree in which a flame is prevented from going around from the anode side to the cathode side , the degree in which the power generation efficiency is increased , and the possibility and easiness of working . for example , in the case of a conical cell , as shown in fig5 , the possible angular range θ between the slant surface and the horizontal surface is 5 ° to 30 °, most preferably 15 °. fig6 shows results of experiments that are conducted to compare a cell of a conventional specification produced by forming a circular green sheet 10 a of a solid electrolyte layer ( see fig3 a ) and firing it as it is and a cell according to the invention ( new specification ) produced by forming a conical green sheet 10 b in which the angle θ is equal to about 15 ° ( see fig3 b ). the specifications of the fuel cells used in the experiments are as follows : ( 1 ) compositions of fuel cells ( numerical values in brackets are percentages ) top layer of anode : nio 0 . 9 co 0 . 1 [ 70 ]/ sdc [ 30 ]+ rh 2 o 3 ( 5 wt %) conventional specification : circular , 15 mm in diameter ; the electrodes are 13 mm in diameter . new specification : conical , 14 mm in diameter ( of the bottom surface ); the electrodes are 13 mm in diameter . notes : in the conventional specification , a cut - out circular electrolyte green sheet is fired as it is and used to form a fuel cell . in the new specification ( invention ), a cut - out circular electrolyte green sheet of the same size is worked into a conical shape , fired , and used to form a fuel cell . ( 3 ) fuel : c 4 h 10 ( n - butane ) having a concentration of 6 . 5 % ( 4 ) total flow rate : 400 sccm as seen from fig6 , the power generation efficiency of the conical shape ( invention ) is higher than that of the flat , circular shape ( conventional ). this is considered due to the fact that , as described above , in the conical shape the degree in which a flame goes around to the cathode side is lowered and the oxygen partial pressure is prevented from decreasing on the cathode layer side . although the embodiment of the invention has been described above with reference to the accompanying drawings , the invention is not limited to the above embodiment and various modifications , changes , etc . are possible without departing from the spirit and scope of the invention . as described above , the invention can provide a cell of a fuel cell in which a flame is prevented from going around to the cathode side or goes around to the cathode side only in a small degree and which is therefore high in power generation efficiency . as such , the invention is applicable under every set of conditions of use of direct - flame fuel cells .