## 1 Introduction
The moisture transfer in agricultural products occurs through different mechanisms, such as molecular penetration, capillary movement, Knudsen flow, liquid penetration through solid, and other methods, and it is very difficult to separate the moisture transfer mechanisms in drying. However, in research, it is assumed that the mass transfer inside the product takes place only through diffusion. Hence, the parameter of effective moisture diffusion coefficient (\(\alpha_{\text{f}}\)), obtained from the solution of Fick's second law by [PERSON] 1975 and [PERSON] 2002, regardless of the moisture removal mechanism, describes well the moisture transfer of the product [28]. It can be held that diffusivity is the transfer rate of water molecules in porous bodies to a different direction in a unit time by random molecular motion. Diffusion mass transfer rate depends on factors such as humidity, porosity, and drying temperature. Therefore, the moisture movement from inside the drying product to its surface can be considered through diffusion and from the product's surface to the surrounding air through convection [29; 30]. In recent years, researchers have investigated the product's internal and external mass transfer during the drying process. The effective moisture diffusion coefficient and energy efficiency for apple slices in a convective dryer were found in the range of 12 \(\times\) 10\({}^{-9}\)-6.75 \(\times\) 10\({}^{-7}\) m\({}^{2}\)/s and 2.89-9.11%, respectively [31]. In another research study, the effective moisture diffusion coefficient and convective mass transfer coefficient for Cyrana cardunculus using two mass transfer models (the thin layer model and the Crank model) were calculated [24]. According to the results, the effective moisture diffusion coefficients for the thin layer model and the Crank model were obtained in the range of 2.78-1.40 \(\times\) 10\({}^{-8}\) and 1.92 \(\times\) 10\({}^{-10}\)-1.20 \(\times\) 10\({}^{-9}\) m\({}^{2}\)/s, respectively. In that research, the convective mass transfer coefficients for the thin layer model and Crank model were obtained in the range of 8.43 \(\times\) 10\({}^{-8}\)-8.46 \(\times\) 10\({}^{-7}\) and 5.82 \(\times\) 10\({}^{-9}\)-7.23 \(\times\) 10\({}^{-8}\) m/s, respectively. In research, the effect of the heat pump and airflow return on the internal and external mass transfer of kiwi slices in a convective dryer was investigated using the Crank and Dancer models [32]. In this research, the effective moisture diffusion coefficient was 1.94 \(\times\) 10\({}^{-9}\)-7.12 \(\times\) 10\({}^{-9}\) m\({}^{2}\)/s, the convective mass transfer coefficient was 4.12 \(\times\) 10\({}^{-7}\)-8.55 \(\times\) 10\({}^{-7}\) m/s, and, also, the activation energy was obtained in the range of 14.04-20.39 kJ/mol. In another study [33], values of effective moisture diffusion coefficient, convective mass transfer coefficient, and Biot number by using the Dincer model were found in the range of 0.16-1.45 \(\times\) 10\({}^{-8}\) m\({}^{2}\)/s, 1.93-4.95 \(\times\) 10\({}^{-7}\) m/s, and 0.103-0.225, respectively. The review of past research for combined hot air-infrared dryers shows that the conducted research for this model of combined dryers was focused mainly on drying kinetics and the effect of the simultaneous use of infrared waves with hot air. Investigations show that not much research has been devoted to studying the effect of two-stage apple slice drying and using different drying strategies for combining these two drying methods. Moreover, not much research has been conducted regarding mass transfer and energy consumption in these dryers, and the effects of the simultaneous or two-stage application of these two drying methods on mass transfer, energy consumption, and product quality have not been investigated. Thus, in this research, internal and external mass transfer have been studied by relying on Crank and Dincer models.