Air-to-refrigerant heat exchangers are a key component for heating, ventilation, air conditioning, and refrigeration (HVAC&R) systems. The performance of these heat exchangers is limited by their air-side thermal resistance. Finless non-round bare tube designs have the potential to improve the air-side thermal-hydraulic performance over their finned counterparts and consequently improve the coefficient of performance (COP) of air-conditioning systems. Previous researchers have used heuristic methods such as multi-objective genetic algorithms (MOGA) with approximation-assisted optimization (AAO) methods utilizing computational fluid dynamics (CFD) based metamodels to shape and topology optimize non-round bare tube heat exchangers. A rather unexplored optimization technique used for heat exchanger optimizations is the gradient based adjoint method. CFD solvers utilizing discrete adjoint methods can be used to shape optimize bare tube heat exchangers and can reveal unintuitive, organic, and potentially superior designs. Additionally, additive manufacturing technology has the capability of building these previously unrealizable heat exchanger designs.The objectives of this dissertation are to experimentally evaluate the performance of shape and topology optimized compact bare tube heat exchangers with non-round bare tubes on a 1) component level, and 2) system level integrated into an air conditioner. Plus, 3) develop new shape optimized variable geometry compact bare tube heat exchangers using discrete adjoint methods for HVAC&R applications. First, a comprehensive experimental investigation of multiple shape and topology optimized compact non-round bare tube heat exchangers was conducted under dry and wet evaporator, condenser, and radiator conditions. For all heat exchangers, air-side pressure drop and heat transfer capacity were predicted within 37% and 15%, respectively. Next, an experimental test facility capable of evaluating the system level performance of a 7.03-8.79 kW commercial packaged air conditioning unit was designed and constructed. The performance of the air conditioning unit was evaluated before and after its conventional tube-fin evaporator was replaced with a shape and topology optimized bare tube evaporator. Results are presented and discussed. Lastly, an ε-constraint and penalty method optimization scheme was implemented which utilizes a commercial CFD software with a built-in discrete adjoint solver to perform multi-objective shape optimizations of 2D bare tube heat exchangers. Critical solver/mesh set-up to best optimize heat exchangers with 0.5-10.0 mm diameter bare tubes were identified and established. The optimized designs can achieve a 40-50% reduction in air-side pressure drop with at least the same heat transfer capacity compared to the initial circular bare tube geometry. An adjoint shape optimized 500 W bare tube radiator was additively manufactured in polymer and experimentally tested. Air-side pressure drop and heat transfer capacity were predicted within 15% and 10%, respectively. The experimental performance confirms the adjoint method shape optimized designs improve the thermal-hydraulic performance over the initial circular bare tube geometry.