Plasma-assisted processing and deposition of materials is an important component of modern industrial applications, with plasma reactors sharing 30% to 40% of manufacturing steps in microelectronics production [1]. Development of new flexible electronics increases demands for efficient high-throughput deposition methods and roll-to-roll processing of materials. The current work represents an attempt of practical design and numerical modeling of a plasma enhanced chemical vapor deposition system. The system utilizes plasma at standard pressure and temperature to activate a chemical precursor for protective coatings. A specially designed linear plasma head, that consists of two parallel plates with electrodes placed in the parallel arrangement, is used to resolve clogging issues of currently available commercial plasma heads, as well as to increase the flow-rate of the processed chemicals and to enhance the uniformity of the deposition. A test system is build and discussed in this work. In order to improve operating conditions of the setup and quality of the deposited material, we perform numerical modeling of the plasma system. The theoretical and numerical models presented in this work comprehensively describe plasma generation, recombination, and advection in a channel of arbitrary geometry. Number density of plasma species, their energy content, electric field, and rate parameters are accurately calculated and analyzed in this work. Some interesting engineering outcomes are discussed with a connection to the proposed setup. The numerical model is implemented with the help of high-performance parallel technique and evaluated at a cluster for parallel calculations. A typical performance increase, calculation speed-up, parallel fraction of the code and overall efficiency of the parallel implementation are discussed in details.