The effect of diffusive heat conduction and Brownian motion on the enhancement of thermal conductivity in nanofluids is presented here. Al$_{2}$O$_{3}$ and TiO$_{2}$ nanofluids were prepared at four different wt. fractions of 1%, 0.5%, 0.1% and 0.05% and their thermal conductivity values were measured over temperatures ranging from 25 to 55°C for every 10°C interval. The thermal conductivity of nanofluids increased with the increase in concentration and temperature. Diffusive thermal conduction and Brownian motion contribute to thermal conductivity enhancement. However, diffusive heat conduction has major contribution to thermal conductivity enhancement in nanofluids. The thermal boundary resistance was found to be increasing with wt. fraction and decreasing with temperature elevation. Finally, a correlation is presented using group method of data handling (GMDH) neural network to predict the thermal conductivity of nanofluids.