Vortex tube (VT) is a mechanical device with no moving parts. The fundamental principle of Vortex Tube is that it can split an incoming fluid flow of a constant pressure and constant temperature gas stream into two separate low pressure streams, one having higher enthalpy and the other having lower enthalpy than the inlet flow. So this device essentially works as a temperature separator. On separation from the device, a warmer flow exits through a terminal which is called the “hot end” and a low temperature stream comes out from another terminal known as the “cold end”. Just with a few bar pressure of compressed air at room temperature can produce a hot stream temperature of about 150°C and a cold stream temperature of about - 40°C. This temperature separation scheme allows us to get cooling and heating effect simultaneously using the same device which makes the Vortex tube one of the popular mechanical equipment and is used in many fields of engineering. The cooling or heating effect produced by this device is largely dependent on geometric parameters of the device itself. Since no exact theoretical correlation is there between the geometric parameters and the cooling (or heating) effect produced, VT design is solely based on empirical relations. There are quite a few geometric parameters which affect the cooling effect of this device and all the empirical correlation are needed to design the optimum VT for maximum cooling/heating effect. These relations can be derived in two ways, either by numerical methods or by experimental investigations. The first part of the thesis important geometric parameter of the VT namely the ratio of the “cold end” diameter (to the “tube diameter” , which has been numerically optimized in this work to achieve maximum temperature separation. In our efforts to design a VT based refrigeration system, optimization of the VT itself is not enough. A suitable heat exchanger (HX) which can extract the cold enthalpy from the VT also needs to be designed and cascaded with the VT to get the complete refrigeration system. The second part of the thesis is solely dedicated to the design of a suitable HX that can be used alongside a VT to produce refrigeration. The HXs design can be approached from two directions, dimensional aspect and material aspect. Rather than focusing on the dimensional aspect in this work we have concentrated of the material aspect of HX design. It is fairly obvious that the thermal conductivity (TC) of the HX material will play a crucial role on the cooling effect of the refrigeration system. Conventional metals with high TC can be used to design HXs but the downsides of using pure metals such as Copper, Iron are that they are heavy, quite expensive and highly reactive to corrosive fluids. Because of this, high TC ceramic material such as Aluminium Nitride (AlN) is quite often used to fabricate HXs and they are used for spot cooling in electronic systems. AlN has TC of 160 W/m-K which is high but not as high as of Copper or Iron. TC of AlN can be increased by mixing the right volume fraction of metal powder (such as pure Aluminium) with it to a great extent. So in a nutshell, instead of using pure AlN, if we use the particle reinforced binary composite [AlN + Al (powder)] to design a HX, we would achieve the benefits of having high TC as well as properties such as anti-corrosiveness, cost effectiveness and weight reduction. In the above context, prediction of TC of particle reinforced composite materials containing a base material of low TC and a filler material of high TC is of utmost importance. Till now a very few analytical heat transfer models are available in the literature that can accurately predict the TC value of such composites especially when high volume fraction of filler particles is added to the base material or if more than one type of filler particles are added. So in this thesis, three analytical heat transfer models have been developed that can predict the TC of binary as well as tertiary particle reinforced composites. The third and the final segment of the thesis deals with the performance study of a refrigeration system comprised of the optimized VT cascaded with a suitable HX made out of a particle reinforced composite material. The numerical results show how the HX effectiveness improves as the volume fraction of the filler particles in the composite increases. The key results of the works described in the thesis are as follows: • Through extensive numerical simulations it is shown that for = 0.5, the temperature separation in a VT is maximum. • The heat transfer models developed to predict the thermal conductivity of binary composites, shows the trend of how thermal conductivity varies with increasing volume fraction of filler. It has been shown that initially the thermal conductivity increases linearly with a small slope, then after a critical volume fraction an abrupt increment of slope is observed due to the formation of continuous heat conduction paths within the composite. Further increase in volume fraction shows linear increment of thermal conductivity with lesser slope as before. • The heat transfer model developed to predict the thermal conductivity of tertiary composites is suitable for low volume fraction (< 20 %). The model shows the addition of one component into the base matrix affects the distribution of the other component which is observed through the covariance. • The last part of the thesis shows that compared to a pure AlN heat exchanger, a heat exchanger made of AlN + 30 % volume fraction of pure Aluminium powder, has increased heat exchanger effectiveness by more than 50 %. Thesis outline is as follows: • Chapter 1 is a brief introduction to Vortex Tube. • Chapter 2 deals with the necessary literature review related to Vortex Tube as well as presently available heat transfer models that are equipped to handle composite materials to predict their TC. • Chapter 3 elaborates numerical modeling and optimization of a critical parameter ( to achieve maximum temperature separation in a VT. • Chapter 4 presents a stochastic heat transfer model to estimate the TC of Binary particle reinforced composites containing low volume fraction of filler particles. • Chapter 5 describes the development of a computational heat transfer model to predict the TC of Particle Reinforced Binary Composite materials containing high volume fraction of filler element. • Chapter 6 deals with a stochastic heat transfer model to calculate TC of Particle Reinforced Tertiary Composite materials containing low volume fractions of filler elements. • Chapter 7 consolidates all the necessary concepts and data from previous chapters to design the final cascaded VT based refrigeration system and presents a performance study. • The last chapter summarizes the entire work along with scope for future work.