Votators (SSHEs) are a type of heat exchangers widely used in pharmaceutical, food, and chemical industries, to name a few from those. These heat exchangers are designed for cooling or heating of fluids, especially highly viscous ones. Since increasing the size of heat exchangers brings with itself the negative consequence of increasing the pumping power, it is recommended to use smaller heat exchangers instead. Therefore, reducing the heat transfer because of the shrinking heat exchanger has to be compensated. Using a rotor and mounting blades on it is a common approach that helps the fluid to be more agitated. As the fluid mixes, the heat transfer from the walls also increases, consequently, CHTC is improved, which is always desired for heat exchangers .
Because of their high heat transfer rate, SSHEs have attracted the attention of many researchers for many years, especially in the production of ice cream . Blasiak and Pietriwicz numerically studied the SSHE while considering the turbulence flow. Their findings demonstrated that the heat flux was between 500 and 1500 W/m2 and CHTC varies between 20 and 45 W/m2K and affected by the rotor speed. They presented a relationship for the Nusselt number, in terms of flow Reynolds and Prandtl numbers. In another study, Ali and Baccar numerically examined the presence of helical ribs on the performance of a SSHE within which a Bingham fluid was flowing in steady-state, laminar condition. The positive effects of rotational speed, axial and rotational Reynolds number on the thermal performance by increasing CHTC were reported. Saraceno et al. focused on how to improve the ice-cream production by SSHEs and presented two relationships for the heat transfer rate. Blasiak and Pietriwicz performed a 2D simulation on a SSHE while considering the Reynolds number, Prandtl number, and the dimensionless gap in the ranges of 100 to 1000, 0.71 to 56, and 0.0005 to 0.15, respectively. Their results revealed that the increase of either Prandtl number or Reynolds number increases the heat transfer, while the increase in the dimensionless gap slightly decreases the heat transfer. Boccardi et al. improved the relationships proposed for SSHEs by including the viscous dissipation effect. Comparing two different blade geometries for the rotor, Bayareh et al. numerically examined the effect of blade geometry on the heat transfer of an SSHE within which pure glycerin was flowing as the working fluid. In another study, Crespí-Llorens et al. studied the pressure drop and heat transfer. They examined laminar, transient, and turbulent flows and presented relationships for the Nusselt number and friction factor. Using Particle Image Velocimetry (PIV) method, Yateghene et al. experimentally studied the flow pattern inside a SSHE. Their results showed that the turbulence is weak near the rotor wall, and the mixing occurred mostly alongside the rotor blades. Focusing on the flow pattern and the temperature field, Shiryan Dehkordi et al. investigated the effects of blade numbers, stator length, inlet velocity, fluid viscosity, the geometry of rotor blades, stator material, and rotor speed on heat transfer and OT. For the purpose of cooling down of viscous fluids, the rotor speed was found to have a positive effect on the heat transfer. Furthermore, a decrease in the stator length reduced OT so that its minimum value happens for the case of a three-blade rotor, while its maximum value happens when a single blade is mounted on the rotor. Lakhdar et al. experimentally examined the heat transfer of ethylene glycol and water in a SSHE. They studied the effects of flow rate, rotor speed, and the clearance between blades and casing. Heat transfer under different conditions was investigated by many researchers. Particle shape, particle concentration, and fluid viscosity were studied by Alhamdan and Sastry . The geometry of scrapers in different axial and rotational Reynolds numbers was examined by Baccar and Abid . Lee and Singh studied the effects of rotor speed and flow rate of potato cubes on residence time. Harrod focused on the principal design of different SSHEs. Couette flow regime and Taylor vortices regime were compared in the study of Trommelen and Beek.
Many studies were conducted focusing on heat transfer problems from the statistical point of view among which using Response Surface Methodology (RSM) to optimize a SSHE has many advantages over other machine-learning methods such as Artificial Neural Network (ANN) . RSM is a mixed mathematical-statistical method, which provides correlations between the responses and the independent variables. Using RSM, Vahedi et al. investigated the heat transfer through and over a cylinder. Two correlations were proposed for the friction factor and Nusselt number with respect to effective parameters affecting the problem. Pordanjani et al. Vahedi et al. proposed correlations for the Nusselt number of enclosures. Proposing correlations provides an in-depth understanding of how much the output is affected by a factor. In first sight, it is very difficult to conclude that using a super-conductive fin inversely affects the heat transfer rate. RSM not only provides the initial estimates for pre-design calculations for designers also offers a broad information through regression equations and sensitivity analysis and optimization. Designers can learn from sensitivity analysis obtained from regression modeling in order to understand how much a slight change in a variable affects the response. Pordanjani et al. reported that the designer should not pay more attention to the angle between the pin fin and the hot sidewall. In fact, their sensitivity analysis showed that changing the inclination angle over a board range leads to a negligible change in the Nusselt number. Vahedi et al. revealed that the thermal performance of the typical differentially-heated enclosure is not delicate to the sidewalls thickness.