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Development of numerical code for evaluating the solidification of water has been scrutinized in this work. The container has two circular and sinusoidal cold walls at bottom and top surfaces. Galerkin-based code has been employed to model this phenomenon. To elevate the conductivity of phase change material (PCM), alumina particles with nanosized were utilized with incorporating different shapes. The conductivity of nanoencapsulated phase change material (NEPCM) is a function of concentration and shapes of nanoparticles. The freezing process is mainly dominated by conduction and selecting curved shaped and adding nanoparticles can affect this mechanism. Verification test reveals the good accommodation and applying adaptive grids leads to higher accuracy. As shape coefficient increases, the period of process declines around 10.65% owing to stronger conduction. Also, mixing water with alumina nanopowders with blade shape causes decrement in needed time around 32.51%. Besides, outputs reveal that utilizing blade shape of powders has more effect on required time than that of cylindrical shape.

This work contains simulation of solidification within a container with new structure. The assumption of neglecting velocity term for solidification formulation leads to the reduction of number equation for such 2D modeling to two equations and FEM was selected for this purpose. This model involves adaptive grid that incorporates the implicit approach for transient terms. The water that incorporates various sizes of nanopowders leads to creating new material and for predicting the properties, the formulation based on homogeneous mixing has been utilized. Adding nanoparticles leads to a reduction of the required time around 26.52% and 12.25% when [Formula: see text] and 50 nm while its effect for [Formula: see text] nm is 41.19%. As the size of the particles augments upto 40 nanometer, the required time declines around 19.96% while augmenting upto 50 nanometer leads to augment of time of around 49.2%.

Single helical tube has been widely investigated in both smooth wall and corrugated wall structures. However, for the first time, this paper proposes and works on a helical tube-in-tube heat exchanger in which both inner tube and outer tube are corrugated (see graphical abstract for possible interesting configurations). The idea of the fabrication process of such heat exchanger will be the first challenge; and that is why the first part of this research explains what steps are required to fabricate the mentioned heat exchanger with affordable and available industrial techniques. When both inner tube and outer tube are corrugated, the relative position of the corrugations on both tubes provides different configurations (see case “c” and “d” in the graphical abstract) with completely different behaviors. In the second step, the numerical simulation of the mentioned heat exchanger is validated with the experimental results. At the third part of the paper, a comprehensive simulation is performed to analyze the mentioned heat exchanger from thermal, frictional and exergetic viewpoints. The results show that the corrugating of the outer tube in addition to the inner tube significantly boosts the thermal capacity of the heat exchanger without any further weight, area or size of the heat exchanger (case “d” provides 125% higher Nu number compared to the case “a”). Besides, the mentioned relative position of the corrugations plays a significant role so that the obtained Nu number of case “d” is 35% higher than that of case “c” (the difference of these cases is only the relative position of the corrugations). The reason of all these phenomenon and other remarkable findings are reported in this paper.