Numerical solutions have been carried out for representative conditions in a tubular reactor in fully developed laminar and turbulent flow. The computations are unique in two respects. First, they take into account the radial transport of both species and energy by molecular and turbulent fluctuations for the combination of energetic reactions and heat exchange with the surroundings. Second, those for turbulent flow are based on an essentially exact model for transport by the fluctuating velocities, concentrations, and temperature. The mixed-mean conversion for finite radial rates of transport is found to differ significantly from those for the common idealizations of negligible or perfect radial mixing. Although the numerical solutions are essentially exact, some idealizations such as invariant physical properties and a rate mechanism in terms of concentration have been made in the interests of generality. The numerical results are limited to a single first-order irreversible equimolar reaction, but the methodology can readily be extended to other reaction mechanisms, including multiple ones. Correlative equations based on asymptotic behavior are devised for the primary effects of the thermal parameters.