Mathematical Models for Predicting Solar Radiation and Capacity of Solar Driven Refrigeration System for Milk Cooling

Abstract

The solar energy needed to drive solar-driven milk refrigeration systems is only abundant in the mid hours. It is completely unavailable in the early and late hours of the day. The mismatch between solar energy availability and the milk cooling load energy demands and intermittent availability of solar energy negates the application of solar-driven milk cooling refrigeration systems. It is prudent to harness and store solar energy during peak periods of high solar energy for milk cooling during low or insufficient solar energy availability. This study has analyzed solar energy predicting models from literature reviews and annual solar energy trends from different sites and selected a solar radiation prediction model for predicting mean daily solar radiation levels. The input parameters considered are readily available in most meteorological stations in remote regions. The performance of four mean daily solar radiation prediction models namely; Gadiwala (MI), Seme (M2), Sendanayake (M3) and Samani (M4) when compared with measured data in Nakuru indicated a strong correlation of coefficient R2 of 0.826, 0.735, 0.810 and 0.760 respectively. Three refrigeration systems with AC reciprocating compressor capacities of; 200 W, 250 W and 350 W were investigated for maximum cooling loads under varying mean daily solar radiations. Equal amounts of water stored in milk cans were surrounded by an ice layer, followed by an outer brine solution, which was then insulated by a polystyrene jacket. In each system, water in the milk can was cooled by an evaporator submerged in the brine solution, forming a layer of ice surrounding the milk cans. Four PV panels, each of 200 Wp, connected via an inverter provided the power required to operate the compressors in each refrigeration system. Temperature variation of the water in the milk cans and the amount of ice formed were used to determine the solar driven refrigeration system with maximum cooling load, based on solar radiation available. The cooling curve obtained in each refrigeration system provided nonlinear regression mathematical models for predicting maximum cooling loads for the solar-driven refrigeration systems. The coefficient of correlation R2 between the actual and predicted maximum cooling loads for the 200W, 250W and the 350W solar refrigeration systems were 0.8647, 0.9413 and 0.956 respectively. An accurate model for predicting the solar-driven refrigeration capacity of a milk cooling system with the provision of sensible thermal energy storage for matching solar energy availability and milk cooling load energy demands at any site could be a useful tool for optimization in the design and application of solar-driven milk cooling refrigeration systems. Designer and manufacturer of solar-powered milk cooling systems for large, medium and small businesses would find the solar driven refrigeration maximum cooling models load a suitable tool.