Cooling of electronic components is one of the most important issues concerned in the electronic industry for design of equipment. Maintaining the temperature of an electronic device within its safe operating temperature limits is essential to operate the equipment safely with proper functionality. According to the Arrhenious law of failure rate, for a device with activation energy 0.65eV, every 10°C increase in temperature doubles the failure rate. Recent miniaturisation of components and high device heat dissipation rates lead to high heat fluxes, which cause temperature rise. Hence, there is an increasing need for research to achieve high heat removal rates and optimal design. Several cooling techniques are used for cooling of electronics based on the application and cooling rate requirements. Air-cooling of electronics has a wide range of applications due to its greater reliability, simplicity, easy maintenance, low cost, easy availability of coolant (air), and light weight. Air-cooling is also free from boiling and dripping problems. Air-cooling is used in applications such as avionics, cooling of personal computers, cooling of data centers, and in automobile electronics. In a typical electronic cooling application, cooling fluid is driven by the combination of external pressure forces and buoyancy forces. Based on the relative contribution of these forces towards the total driving force, the cooling techniques can be categorized as forced, natural or mixed convection cooling. However, in many of the electronic cooling situations, such as in the applications with very high heat fluxes, tall Printed Circuits Boards (PCBs) with low forced convection velocity, and in large scale applications such as data centers, the contributions of the buoyancy forces and external pressure forces for the total driving force are comparable, which results in a mixed convection situation. In the present study, mixed convection in vertical channels heated with five heating configurations, which represent typical electronic cooling applications, is studied numerically. The five different heating configurations are channels with flush-mounted continuous heater, flush-mounted strip heaters, flush-mounted square block heaters, protruding rib heaters and protruding square heaters. The first three configurations are categorised as flush-mounted heating configurations and the latter two configurations are categorised as protruded heating configurations. One of the channel walls represents the substrate on which the heaters are mounted and the heat sources represent the heat generating electronic components. Heat transfer under steady state conditions is considered in the study. The study includes laminar as well as turbulent heat transfer. For a systematic study of mixed convection, an analytical or semi-analytical formulation is desirable for a simplified model, as it can highlight the effect of relevant non-dimensional parameters on the heat transfer characteristics of a system. The results of a simplified model can be used for benchmarking the results of practical situations. Hence, before numerically solving the governing equations for mixed convection in channels, mixed convection boundary layer flows over a heated vertical plate is considered for study. Perturbation technique is used to solve the boundary layer equations with non-isothermal boundary conditions. The perturbation analysis is carried out for an arbitrarily variation of wall temperature or heat flux. Subsequently, the results are extended to find heat transfer rates in the cases of power-law variation of temperature and heat flux, as special cases. It is always required to design a cooling system to remove maximum possible amount of heat, keeping the device temperature within its safe operating limits. Hence, optimization of heat transfer in boundary layers is attempted, whose results can be used as guidelines to achieve optimal heat transfer in practical situations of channels with continuous as well as discrete heating. Similarity analysis is used for the optimization of heat distribution in boundary layer flows. In the similarity analysis, in the search of optimal heat transfer from the plate, the boundary layer equations are solved for various power-law heat flux variations and the appropriate power-law variation of optimal heat transfer is found. Similarly, the heat flux variation for optimal heat transfer is found for the cases of natural and forced convection, as they are the limiting cases of mixed convection. In the numerical part of the study, the generalised three-dimensional governing equations for the five heating configurations considered for the study are solved numerically with appropriate boundary conditions. Separation of natural, forced and mixed convection regimes is carried out in all the heating configurations using a criterion based on individual contributions of pressure force and buoyancy force towards the total driving force for the fluid movement. Heat transfer characteristics are studied in laminar as well as turbulent regimes in terms of parameters such as Grashof number, Reynolds number, Nusselt number, maximum temperature of heaters, pressure drop across the channel, and so on. The influence of conjugate effects on the heat transfer characteristics is studied by varying the substrate thermal conductivity. A systematic comparison of various effects such as the effect of discrete heating in plain channels, effect of discrete heating in channels with heated ribs, and the effect of three-dimensional protrusions on heat transfer, is achieved. The parameters in the individual configurations, which affect heat transfer, are explored for better cooling solutions. Optimal heat distribution among the heaters to minimise the temperature of the hottest heater for a given total amount of heat generation in the channel is found for all the channel configurations, which are heated either continuously or discretely. In the process of finding the optimal heat distribution among heaters, guidelines are taken from the optimal heat distribution in boundary layer flows. Compared to usual optimization approaches such as genetic algorithm, the present physics based optimisation procedure requires fewer runs to arrive at the optimal distribution. The fluid flow characteristics in all the three configurations with flush-mounted heaters are found to be similar. However, heat transfer characteristics in channels with flush-mounted square heaters differ from those in the other two flush-mounted channel configurations. Hot spots with higher temperatures are found at heater locations in channels with flush-mounted square heaters. The effect of substrate follows the same trend in all the flush-mounted configurations. At lower thermal conductivities, the maximum temperature decreases sharply with increasing thermal conductivity. However, at higher conductivities, the influence reduces. In all the flush-mounted configurations, heat transfer will not be influenced by substrate thermal conductivity increment at conductivities more than 150 times the fluid thermal conductivity. The fluid flow and heat transfer characteristics in channels with protruded heaters differ significantly from those in channels with flush-mounted heaters. The protrusions in the channels interact with the fluid flow and make it different from that of smooth channels. In turn, the protrusions affect heat transfer characteristics in the channels. The influence of the protrusions on the heat transfer and locations of hot spots in the domain is examined. Effect of thermal conductivity in channels with protruded square heaters is similar to that in channels with flush-mounted heaters. However, conductivity in channels with protruded rib heaters affects the heat transfer in a wider range of conductivities than in the other heating configurations. Unlike in the other configurations, at low thermal conductivities, maximum temperature does not drop sharply with increase of conductivity. In channels with protruded square heaters, staggering arrangement of heaters results in higher heat transfer rates than those with in-line heater arrangement. In all the configurations, pressure drop is found to be independent of Grashof number in the range of heat dissipation rates considered in the study. Heat transfer rates in turbulent region are much higher than the heat transfer rates in laminar regime. However, the pressure drops encountered are also high in the turbulent regime. Turbulent heat transfer results in a more uniform temperature distribution in channels. The cooling performances of the individual configurations are compared. For a given pressure drop the cooling performances decreases in the order of flush-mounted strip heating, protruded square heating, flush-mounted square heating, protruded rib heating. For a given inlet fluid flow rate, the cooling performances decreases in the order of protruded rib heating, protruded square heating, flush-mounted square heating, flush-mounted strip heating. However, for a given inlet fluid flow rate, the pressure drop increases in the order of increasing cooling performance.