Convective heat transfer finds applications in several domains of industry like heat exchangers, gas turbine blades, IC engine surfaces etc. The surfaces of these heat transfer applications are either naturally rough owing to manufacturing techniques or become rough over a period of time during operation. These rough surfaces usually contain multiple length scales and exhibit random and heterogenous properties. Fractal roughness, in principal, is characterized by self-similar detail on smaller and smaller length scales and hence fractal dimension which is independent of any length scale can become a very viable option to characterize these multi-scale random surfaces. Therefore in the current thesis, rough surfaces characterized by fractal dimensions were designed and their role in the heat transfer enhancement relative to the pressure drop was studied using DNS.

The fractal surfaces were designed by randomly placing five generations of self-similar cuboids with decreasing sizes from higher to lower generations. The quantity of cuboids sprinkled randomly for each generation followed a fractal dimension. Two principal fractal dimensions were selected, i.e 퐷 = 1 and 퐷 = 2 and eight random realizations of each were generated in order to study the averaged effect of the heat transfer performance. Since the cuboids were randomly placed, different realizations within
the same fractal dimension experienced varied sheltering effects by larger generation cuboids. This ultimately produced a fluctuation in the ”sheltered” solidity of the fractal surface for different realizations whose effect was also studied. The cuboids were resolved in the simulation using an immersed boundary method.

To quantify the heat transfer performance of the rough surfaces, two performance factors namely the aero-thermal efficiency and Reynolds analogy factor were defined. It was found that the two types of fractal surfaces performed approximately similarly with a slight higher mean for 퐷 = 2 based on the above heat performance parameters even though the two surfaces looked very different. However, the above performance factors showed a very strong correlation with the ”sheltered” solidity of the fluctuating realizations displaying an increasing trend.