This research thoroughly investigates and models the energy and exergy efficiencies of a novel solar water heating system that includes integrated storage. The unique water heater design incorporates a spherical glass outer casing to enhance solar radiation absorption. This study evaluated three types of storage tanks: truncated conical, cylindrical, and spherical, all equipped with a top outlet and bottom intake for water circulation. A Computational Fluid Dynamic simulation in charging mode was utilized to evaluate thermal storage quality based on dimensionless numbers Richardson (Ri) and stratification (Str), energy efficiency (η), exergy efficiency (ε), and temperature profiles of eight fluid layers. At a solar radiation of 950 W m−2, the truncated cone tank has the highest thermal efficiency, reaching 0.84, while the spherical and cylindrical tanks have a thermal efficiency of 0.75 and 0.74, respectively. The findings indicate that the conical tank outperforms the other tanks in terms of both quantity and quality. Although the spherical tank is more energy-efficient than the cylindrical tank, it exhibits the lowest storage quality when the dimensionless time exceeds 0.2. Additionally, the research demonstrates how tank shape influences thermal layering and storage dynamics using a diffusion–advection equation.
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