The effect of the heating of neutrinos by scattering with electrons and positrons and by e ^ { - } e ^ { + } annihilation on nucleosynthesis is calculated for a spherically symmetric baryon inhomogeneous model of the universe .
The model has a high baryon density core and a low density outer region .
The heating effect is calculated by solving the Boltzmann Transport Equation for the distribution functions of electron and muon/tau neutrinos .
For a range of baryon-to-photon ratio \ln ( \eta _ { 10 } ) = [ 0 , 1.5 ] and r _ { i } = [ 10 ^ { 2 } , 10 ^ { 8 } ] cm the heating effect increases the mass fraction X _ { { } ^ { 4 } { \mathrm { H } } { \mathrm { e } } } by a range of \Delta X _ { { } ^ { 4 } { \mathrm { H } } { \mathrm { e } } } = [ 1 , 2 ] \times 10 ^ { -4 } .
The change of the value of X _ { { } ^ { 4 } { \mathrm { H } } { \mathrm { e } } } appears similiar to the change caused by an upward shift in the value of \eta _ { 10 } .
But the change to deuterium is a decrease in abundance ratio Y ( { \mathrm { d } } ) / Y ( { \mathrm { p } } ) on the order of 10 ^ { -3 } , one order less than the decrease due to a shift in \eta _ { 10 } .