Abstract : This dissertation presents a theoretical study of heat transport in nanoporous composites andin nanowire and also theoretical study of thermoelectric properties of the Si0:8Ge0:2 alloywith some experimental new and old measurements.The first study on the porous alloys show that its can display thermal conductivity reductionsat considerably larger pore sizes than nonalloyed porous materials of the same nominalporosity. The thermal conductivity of Si0:5Ge0:5 alloy with 0.1 porosity becomes half thenonporous value at 1000 nm pore sizes, whereas pores smaller than 100 nm are required toachieve the same relative reduction in pure Si or Ge. Using Monte Carlo simulations, we alsoshow that previous models had overestimated the thermal conductivity in the small pore limit.Our results imply that nanoporous alloys should be advantageous with respect to nanoporousnonalloys, for applications requiring a low thermal conductivity, such as novel thermoelectrics.The second theoretical study on the nanowire thermal conductance reveals the structureeffect on the phonon transport. With a theoretical model that considers the frequency dependenceof phonon transport, we are able to quantitatively account for the experimental resultsof straight and bent nanowires in the whole temperature range which shows that due to andouble bend on the straight thermal conductance reduced by 40% at temperature 5K.Finally, we theoretically investigate the thermoelectric properties of sintered SiGe alloys,compare them with new and previous experimental measurements, and determine their potentialfor further improvement. The theoretical approach is validated by extensive comparisonof predicted bulk mobility, thermopower, and thermal conductivity, for varying Ge and dopingconcentrations, in the 300 �� 1000K temperature range. The effect of grain boundariesis then included for Si0:8Ge0:2 sintered nanopowders , and used to predict optimized valuesof the thermoelectric figure of merit at different grain sizes. Our calculations suggest thatfurther optimization of current state of the art n-type (p-type) material would be possible,possibly leading to 6% (5%) ZT enhancement at 1000K and 25% (4%) at room temperature.Even larger enhancements should be possible if the phonon scattering probability of the grainboundaries could be increased beyond its present value of 10%.