This study attempts to evaluate the flow and heat transfer characteristics of water-Al2O3 nanofluid in a narrow annulus. The effects of volume fraction, the size of particles and the ratio of inner wall heat flux to outer wall heat flux were investigated on the convective heat transfer coefficients and friction coefficients at inner and outer walls of the annulus. Using smaller particles caused a greater heat transfer coefficient. Meanwhile, at higher volume fractions, changing the size of particles led to more considerable changes in the convective heat transfer coefficient and friction coefficient. As per the observation made, the value of heat transfer coefficient at the inner wall was larger than that of the outer wall. In contrast with the results of applying constant properties, changing the volume fraction will change the friction coefficient in the case of using variable properties. Moreover, genetic algorithm was used in combination with compromise programming in order to find the optimum values of the input parameters using neural network correlation.