In the present work a coupled numerical analysis for the two flows in a double pipe heat exchanger is intended, considering counter or co-current hydrodynamically incompressible fully developed flow with constant properties, and thermally developing flow. A coupling between the two fluid currents is reached by means of the natural boundary conditions, a compatibility of temperatures and heat fluxes closed to the solid wall which separates the fluid currents. Wide ranges of Reynolds and Prandtl numbers are used, including laminar and turbulent flows and involving different kinds of fluids. Semi-analytical equations are derived for the time-averaged profiles of velocity and both momentum and thermal eddy diffusivities in the tube and concentric annulus. The most relevant features of the proposed profiles are their applicability through all flow field without discontinuities and the laminar flow considered as a particurlar case of the turbulent flow. The determination of the proposed profiles is done by using an inverse method, wich is based on some experimental data or correlations for the fiction factor and the Nusselt number. The results of the present study are classified into two different categories as follows (i) semi-analytical results for the turbulent thermal and momentum diffusivity profiles for both flows and (ii) numerical results for the double pipe heat exchanger, mainly the local values of the mean bulk temperatures, local and average values of the heat transfer coefficients and overall heat transfer coefficient. Finally, the number of transfer units and effectiveness of the double pipe heat exchanger are evaluated. Wide ranges of the characteristics parameters (Reynolds and Prantdl numbers of each stream, geometric parameters and thermal capacity rate ratio) are covered. The differential equations of the problem accompanied by suitable boundary conditions are solved nemerically, considering the thermal diffusivities as independent of the thermal boundary condition at the solid wall which separate the fluid currents. The finite difference scheme, based on the control volume approach is used, and iterative procedures are developed, in order to implement the calculations. The advantage of having a previously stablished analytical solution for some parts of the problem is to compensate the greater computational work due to the coupled calculation domains. Also, it eliminates the risk of discontinuities and the necessity of interpolation during the grid refining. Both the validation of the proposed method and the check of the accuracy of the results are possible, by comparison with the great amount of data, which is available in the bibliography.