Optimization of Air Velocity and Fan Speed for Improved Outlet Temperature in Water–Air Heat Exchanger Drying Systems

Abstract

The increasing demand for sustainable thermal energy solutions in food processing. House heating and other domestic applications has intensified interest in solar-assisted drying systems, particularly those integrating heat exchangers to deliver controlled drying air conditions. Efficient dehydration of agricultural products requires precise regulation of air temperature, humidity, and flow rate to preserve quality while minimizing energy consumption. However, determining the optimal combinations of these parameters remains a major challenge, especially for systems relying on variable renewable energy sources such as solar thermal input. This study develops a comprehensive mathematical model for a solar-powered food dryer incorporating a counter-flow water-to-air heat exchanger and a forced-convection drying chamber. The model describes heat and mass transfer dynamics using thermodynamic laws, fluid flow relationships, and heat exchanger effectiveness–NTU formulations. A detailed derivation of heat exchanger performance is presented, linking outlet air temperature to key variables including water inlet temperature, heat transfer area, overall heat transfer coefficient, air velocity, fan sweep area, and volumetric flow rate. By reformulating the number of transfer units (NTU) as a direct function of air velocity, an explicit expression for air-side control of outlet temperature is obtained. Simulations using experimentally realistic parameters show that air velocity, fan speed, and fan diameter exhibit inverse relationships with outlet air temperature; reducing air mass flow increases residence time within the exchanger, thereby improving thermal pickup and raising outlet temperatures. The drying chamber temperature evolution, and air–product interaction is regulated using a feedback-based control strategy to obtain robust drying conditions throughout the dehydration process, ensuring that food products are exposed to temperatures below their thermal degradation thresholds. Pontryagin’s Maximum Principle was used to determine the optimal drying air temperature, with respect to airflow velocity, and fan speed. Results demonstrate that a heat exchanger of area 2.827m² with inlet water temperature at 00⁰C flowing at V_l=1.128l/s, can transfer heat up to 75.6⁰C of air temperature up from 25⁰C working at efficiency of ε(v)=06826 and fitted with a fan of are A_f=0.05m² spinning at v=20 RPS. These parameters can be adjusted for a different desired output air temperature. The optimization model framework offers a tool for enhancing dryer performance, guiding design decisions, and reducing energy costs in solar-assisted food processing systems.