While there have been significant improvements in the non-thermal processing of food products to increase the quality without compromising the safety, thermal processing still continues to drive the food processing industry for extending the shelf-life and attain the safety (Van Droogenbroeck, Altin, Coskun, De Paepe, & Erdogdu, 2021). Among aseptic processing and canning as thermal approaches, canning has kept its dominant effect in manufacturing for over 200 years with the continuing trend for increasing product quality and process efficiency (Simpson et al., 2020). Following the introduction of retorts for canning, axial rotation followed by end-over-end (EoE) rotation processes were introduced to increase the heat transfer rate in liquid and solid-liquid particle products (Clifcorn, Petersson, Boyd, & O'Neil, 1950; Walden & Emanuel, 2010). Besides these two agitation approaches of axial and EoE modes, a recent improvement was presented two decades ago where a longitudinal high frequency agitation was involved (Ates, Skipnes, Rode, & Lekang, 2014).

Among these agitation approaches to increase the temperature uniformity within the product and the quality with energy efficiency (by reducing process time), EoE process, where the cans are forced to rotate on a circular trajectory in a circular plane, is still common in batch retort systems (Sarghini & Erdogdu, 2016). Rattan and Ramaswamy (2014) compared the effects of axial and EoE rotation rates (10 and 20 rpm) with static processing on process lethality and quality changes. The agitation mechanism, through convection heat transfer inside the cans (for liquid and solid-liquid mixtures), force to move the headspace to improve the agitation with a significant effect of liquid viscosity. This evolves complex interactions of gravitational and centrifugal forces with buoyancy forces (through the natural convection heat transfer) to increase the heat transfer rate. Analysis of these interactions require a computational approach to determine the evolved forces during the process.

A pioneer computational study for heat transfer and evolving temperature distribution with natural convection triggered velocity profile in canned products was presented by Datta and Teixeira (1988). Tutar and Erdogdu (2012) carried out a detailed mathematical analysis of the interaction of these forces and explained how these interactions affected the heat transfer rates and temperature evolution in an axial rotation process. Sarghini and Erdogdu (2016) presented a computational study on heat transfer characteristics of solid-liquid mixture canned foods during an EoE rotation, and effect of rotation rate (from 6.25 to 25 rpm) was demonstrated for low viscosity Newtonian and high viscosity non-Newtonian cases. Erdogdu, Tutar, Oines, Barreno, and Skipnes (2016) determined the optimal shaking rate for liquid foods in a reciprocally agitated system with a computational approach indicating the significance of the viscosity, and the viscosity effects for such a process were presented by Erdogdu, Tutar, Sarghini, and Skipnes (2017).

Compared to these advances on the process line with agitation effects, can geometry with its original conventional cylindrical shape was rarely explored for the objective of increasing the heat transfer rates with resulting process efficiency. In this aspect, geometry modification has been subjected to only a few studies. Brody (2002) indicated that the can geometry is not required to be cylindrical anymore. Depending on the type of food product to be canned and the sterilization process, different materials and geometries might be explored. Varna and Kannan, 2005, Varna and Kannan, 2006 investigated the heat transfer in cone-shaped cans while Tucker (2004) stated that the container geometry, in addition to the product viscosity and agitation rates, has a significant effect on improving the heat transfer rates. A break-through approach for modifying the can geometry was presented by Karaduman, Uyar, and Erdogdu (2012) when a toroidal can geometry was developed with improved heat transfer rates in solid and liquid food products in a static process. Erdogdu et al. (2021) determined the effect of axial rotation rates on low viscosity liquid products processed in toroidal cans for improving the heat transfer rates and attain a uniform temperature distribution. It was noted that there was a significant improvement of temperature uniformity over 20 rpm axial rotation rate due to the increase of the Coriolis force effects over gravitational and centrifugal forces. Van Droogenbroeck et al. (2021) used the toroidal cans to demonstrate their improving effects on thermal processing of liquid and solid-liquid mixtures under static and 10 rpm EoE rotation processes. The combined effect of EoE rotation with the toroidal geometry resulted in significant reduction in process time. For the EoE processes, there have been various experimental studies to demonstrate the increased heat transfer rates while the first computational study was presented by Sarghini and Erdogdu (2016). Presence of such a computational approach was rather important to observe the evolved temperature inside the cans and to better understand the heat transfer mechanism. Therefore, the objectives of this study were:

to develop a mathematical model to determine the temperature distribution during EoE rotation of toroidal cans,

to validate this model with experimental data, and

to determine the effects of EoE rotation rate and the amount of headspace on the temperature evolution.