the invention is more easily understood with reference to the accompanying drawings , fig1 and 2a - 2e , none of which are to scale and all of which are illustrative schematics . fig1 is a schematic view of a hydrocarbon pyrolysis reactor located within the radiant heat section of a pyrolysis furnace . the reactor includes tubes 10 for receiving a hydrocarbon charge f . as the charge f flows through tubes 10 , it is heated , pyrolyzed , and expelled into exit tube 12 . reactor affluent e flows from exit tube 12 and is then further processed and separated into olefins and unreacted feedstock . in one embodiment according to the invention , illustrated schematically in fig2 a , the inlet of reactor 10 , when viewed in cross - section , shows fins of height f with crests c on the interior surface of the reactor 10 . the outside radius of the reactor 10 is r 3 , the radial distance from the center of the tube to the fin valley is r 2 , and the radial distance from the center of the tube to the fin crest is r 1 . for simplicity , the effective radius of the tube is defined as r 4 0 . 5 ( r 2 + r 1 ). fig2 b is a cross - section taken at b -- b of fig2 a . this longitudinal cross - section of a reactor tube 10 according to the invention , shows inlet i with outlet o and an inner reactor volume rv . the reactor tube 10 has three segments : a feedstock heating section 13 , a pyrolysis section 14 , and an outlet section 15 . as used in the specification and claims , the feedstock heating section is that section of the reactor tube wherein efforts are concentrated on heating the feedstock to a temperature at which pyrolysis takes place at a commercially viable rate . the pyrolysis section is that section wherein the feedstock has reached and is maintained at a temperature at which pyrolysis takes place at a commercially viable rate . the outlet section is that section from which reaction product and any unreacted feedstock is expelled from the reactor . in the embodiment shown in fig2 b , the preheat section 13 has length l 1 . in the embodiment shown , l 1 has the cross - sectional configuration shown in fig2 a with fins of height f to allow maximum heat transfer to reactor charge f . when the reactor charge f travels through reactor 10 and reaches a temperature at which pyrolysis proceeds at a rapid rate , then the embodiment of fig2 b shows a decrease in fin crest height c ( or fin thickness f ) thereby allowing an increase in reactor volume rv for any given segment of reactor length δl throughout the pyrolysis section 14 . thus , the volume per unit length of reactor 10 increases from inlet to outlet . preferably , this increase is continuous . at the outlet o of the embodiment shown in fig2 b , the fin heights f have been reduced to substantially zero so that the radius of the outlet is r 2 . this is also illustrated in fig2 c . clearly , other embodiments are also possible . in another embodiment , the inner volume rv is increased per unit length δl of the reactor 10 by also increasing the outside diameter from r 3 to r 6 and increasing the distance from the center of tube 10 to the tube crest from r 1 to r 5 . thus , fins of significant height are retained throughout the length l 0 of the reactor 10 to enhance heat transfer while the volume per unit length of the reactor increases due to increasing the effective inside radius of the reactor . a cross - section of a reactor tube of this type according to the invention is shown in fig2 e . in general , the invention provides a reactor for thermally cracking hydrocarbons to produce olefins . the reactor contains at least one tube , the tube having an inlet for receiving reactor feedstock at one end and an outlet for debouching pyrolysis product and unreacted feedstock from the other end . the reactor , according to the invention , preferably has a feedstock heating section in the vicinity of the inlet , wherein the reactor is configured to enhance heat transfer from the outside of the tube to the charge within . as the feedstock travels further along the reactor , and is heated to a temperature at which pyrolysis proceeds at a significant rate , the feedstock enters a pyrolysis section of the reactor in which the volume per unit length of the reactor increases to compensate for the molar expansion of feedstock being converted to olefins . the rate of molar increase can be calculated by finite volume element analysis . this entails dividing the length of the reactor l 0 into discrete lengthwise elements and performing energy and mass balances over each successive element from inlet i to outlet o . in one embodiment of the invention , the tubes have an inner surface that defines a volume within the tube for containing a reaction mixture , the inner surface being shaped to provide a high heat transfer efficiency in the vicinity of the inlet of the tube , relative to the heat transfer coefficient in the vicinity of the outlet . further , the inner surface is shaped to provide reduced pressure drop between inlet and outlet of the tube , relative to a tube that has a uniform inner surface over its length that is identical to the inner surface in the vicinity of the tube inlet . the following example is illustrative of the invention and does not in any way limit the scope of the invention as described above and claimed below . a finite volume element analysis was carried out on three types of reactor tubes : smooth tubes , rifled straight fin tubes , and tubes of variable volume per unit length according to the invention . the simulation utilized straight run naphtha as the hydrocarbon charge stock ( specific gravity 0 . 71 , end point 400 ° f ., and the ratio of normal / isoparafin : olefin : naphthalene : aromatic was 38 / 33 : 0 : 23 : 6 ). as can be seen from the information summarized in table i , in the reactor according to the invention , there is a substantial decrease in maximum tube metal temperature relative to the smooth tube . table i further illustrates that reactors according to the invention have significantly lower pressure drop ( 7 . 8 psi versus 9 . 5 - 12 . 5 psi for finned prior art tubes ). for about a 4 % reduction in radiant heat energy consumption , the invention provides an 0 . 9 - 1 . 36 wt . % increase in yield of ethylene and propylene , even at a run length of 45 days , as compared to shorter run lengths of 12 and 35 days with prior art tubes . table i__________________________________________________________________________ smooth rifled straight coil according totube type coil fin coil invention__________________________________________________________________________hydrocarbon straight straight straight run run run naphtha naphtha naphthacracking high high highseveritycoil dimensionscoil length ( ft ) 40 40 40tube equivalent 1 . 2 1 . 2 inlet . sup . 1 outletinside diameter ( in ) 2 × 0 . 9 → 1 . 0 1 × 1 . 3 → 1 . 4 ( 2 × effectiveradius ) no . of fins 0 8 8 0fin heights ( in ) 0 0 . 2 0 . 22 → 0 . 10 . sup . 2 0fin spiral pitch 0 0 0 0mass velocity 17 . 0 17 . 0 12 . 5 ( lb / sec . sq - ft ) steam / hydrocarbon 0 . 45 0 . 45 0 . 45ratio ( lb / lb ) coil outlet pressure 14 . 5 14 . 5 14 . 5 ( psig ) radiant absorbed 0 . 49 0 . 49 0 . 47heat ( mm btu / h ) maximum tube metal 1895 1820 1790temperature ( f .) tube pressure drop 9 . 5 12 . 5 7 . 8 ( psi ) run length ( days ) 12 35 45average yields forentire cycle wt . % wt . % wt . % componentshydrogen 1 . 1 1 . 1 1 . 1methane 16 . 1 16 . 0 15 . 7acetylene 0 . 9 1 . 1 1 . 0ethylene 31 . 2 31 . 5 31 . 6ethane 3 . 1 3 . 2 3 . 2methyl 1 . 1 1 . 2 1 . 2acetylene andpropadienepropylene 13 . 3 13 . 2 13 . 5propane 0 . 4 0 . 3 0 . 41 - 3 butadiene 5 . 0 5 . 1 5 . 2butene 3 . 0 3 . 0 3 . 1butane 0 . 3 0 . 3 0 . 3c . sub . 6 - c . sub . 8 aromatics 3 . 2 3 . 1 3 . 2aromatics b 14 . 4 14 . 2 13 . 9c . sub . 6 - c . sub . 8 non - 2 . 1 1 . 9 2 . 6aromaticsfuel oil 4 . 8 4 . 8 4 . 0yield 44 . 5 44 . 7 45 . 1__________________________________________________________________________ . sup . 1 the coil is of the type shown in fig1 with two inlet tubes , each of 0 . 9 inch inlet inside diameter and 1 . 0 inch inside diameter at the tub outlets . the outlet tube has an inlet inside diameter 1 . 3 inches and outlet of 1 . 4 inches . . sup . 2 fin heights decrease from 0 . 22 inch at inlet to 0 . 10 at outlet of tube . the outlet tube has no fins . although the invention has been described with reference to its preferred embodiments , those of ordinary skill in the art may , upon reading this disclosure , appreciate changes and modifications which may be made and which do not depart from the scope and spirit of the invention as described above and claimed below .