Modeling Coupled Heat and Mass Transfer in Pineapple Drying: A Comparative Study of Infrared, Hot-Air, and Hybrid Modes

Figures 1 and 2 define the physical and mathematical basis for the drying simulation. Figure 1 displays a fresh pineapple slice, which serves as the physical specimen for both the numerical and experimental portions of the study. Figure 2 provides the corresponding computational domain, representing the pineapple slice as a cylindrical geometry within a cylindrical coordinate system. In this domain, $\delta / 2$ represents the half-thickness of the slice along the z-axis, while $\phi / 2$ denotes the radius along the r-axis, establishing the spatial boundaries used to solve the coupled heat and mass transfer equations.

Figure 1. Fresh pineapple slice for drying in numerical and experimental works of this study

Figure 2. Computational domain

In the IR drying process, thermal energy is supplied to the pineapple slice via simultaneous surface convection and IR radiation. Given the product's opacity, these heat transfer mechanisms act primarily on the surface. The material is modeled as a homogeneous medium with constant thermophysical properties. Concurrently, moisture migrates from the internal core to the surface through molecular diffusion, where it is subsequently evaporated into the surrounding environment. Based on these phenomena, the coupled heat and mass transfer governing equations for this investigation are formulated as Eqs. (1) and (2).

Heat transfer equation

$\frac{1}{\alpha} \frac{\partial T}{\partial t}=\frac{\partial^2 T}{\partial r^2}+\frac{1}{r} \frac{\partial T}{\partial r}+\frac{\partial^2 T}{\partial z^2}$            (1)

where, T is temperature, a is thermal diffusivity, and t is time.

Mass transfer equation

$\frac{1}{D} \frac{\partial M}{\partial t}=\frac{\partial^2 M}{\partial r^2}+\frac{1}{r} \frac{\partial M}{\partial r}+\frac{\partial^2 M}{\partial z^2}$         (2)

where, M is moisture content (dry basis – db), and D is effective mass diffusivity.

To formulate a tractable coupled heat and mass transfer model, several standard engineering simplifications are adopted. The pineapple slice is assumed to be isotropic and homogeneous, with constant thermophysical properties ($k, ~\alpha, ~\rho$). These assumptions are reasonable and widely accepted for thin agricultural slices subjected to moderate drying temperatures (below 65 ℃), where global transport dynamics are governed primarily by bulk surface evaporation and internal moisture diffusion rather than local structural variations.

Nevertheless, these simplifications introduce potential physical limitations. In reality, pineapple tissue exhibits cellular heterogeneity, and moisture loss during drying induces volumetric shrinkage as well as localized changes in thermal conductivity and porosity. Neglecting structural deformation and property variation may lead to minor local inaccuracies, particularly near the outer boundaries where moisture gradients are steepest. Nonetheless, as confirmed by our experimental validation, these assumptions provide a computationally efficient framework that accurately predicts average drying kinetics and overall thermal behavior within an acceptable engineering error margin.

The effective mass diffusivity can be estimated by Arrhenius equation as [10]:

$D=1.823 \times 10^4 \exp \left(-\frac{9050.5}{T+275.15}\right)$            (3)

The boundary conditions for the coupled heat and mass transfer are defined as follows. At the axes of symmetry, there is no gradient for temperature or moisture, meaning no heat or mass flux crosses these lines (Eqs. (4) and (5)) [13].

At r = 0:

$\frac{\partial M}{\partial r}=\frac{\partial T}{\partial r}=0$           (4)

At z = $\delta / 2$:

$\frac{\partial M}{\partial z}=\frac{\partial T}{\partial z}=0$             (5)

At r = $\phi / 2$, the thermal energy entering the surface through convection and IR radiation is balanced by the energy conducted into the material (Eq. (6)). The moisture reaching the surface via internal diffusion is equal to the amount of water vapor removed by the surrounding air through convective mass transfer (Eq. (7)) [16, 17].

$-k \frac{\partial T}{\partial r}=h_t\left(T_d-T\right)+q_{I R}$                (6)

where, $k$ is the thermal conductivity of the material, $h_t$ is the heat transfer coefficient, $q_{I R}$ is the IR radiation absorbed by the pineapple slice surface, and $T_d$ is the drying air temperature. The effective absorbed heat flux $q_{I R}$ is challenging to determine purely theoretically due to radiative view factors, wall reflections, and radiation losses to the surroundings. To calibrate this parameter, an initial theoretical maximum value was estimated by dividing the total lamp capacity by the total surface area of the loaded pineapple slices. Because a portion of this energy is dissipated to the chamber walls and internal components, this initial estimate represents an upper theoretical limit. Starting from this value, $q_{I R}$ was systematically reduced in the numerical model using a trialand-error procedure until the simulated drying time matched the experimental results. Through this iterative process, an effective absorbed heat flux was identified for the present experimental setup.

$-D \frac{\partial M}{\partial r}=h_m\left(M-M_e\right)$                     (7)

where, h_m is the mass transfer coefficient, and M_e is the equilibrium moisture content.

Similarly, At z = 0:

$-k \frac{\partial T}{\partial z}=h_t\left(T_d-T\right)+q_{I R}$               (8)

$-D \frac{\partial M}{\partial z}=h_m\left(M-M_e\right)$                     (9)

The governing equations and boundary conditions are solved using an explicit finite difference method. The study utilizes a central difference approach and a forward difference approach to approximate spatial derivatives and unsteady terms, respectively [18, 19].

$\frac{1}{\alpha} \frac{T_{i, j}^{n+1}-T_{i, j}^n}{\Delta t}=\frac{T_{i+1, j}^n-2 T_{i, j}^n+T_{i-1, j}^n}{\Delta r^2}+\frac{1}{i \Delta r} \frac{T_{i+1, j}^n-T_{i-1, j}^n}{2 \Delta r}+\frac{T_{i, j+1}^n-2 T_{i, j}^n+T_{i, j-1}^n}{\Delta z^2}$               (10)

$\frac{1}{D} \frac{M_{i, j}^{n+1}-M_{i, j}^n}{\Delta t}=\frac{M_{i+1, j}^n-2 M_{i, j}^n+M_{i-1, j}^n}{\Delta r^2}+\frac{1}{i \Delta r} \frac{M_{i+1, j}^n-M_{i-1, j}^n}{2 \Delta r}+\frac{M_{i, j+1}^n-2 M_{i, j}^n+M_{i, j-1}^n}{\Delta z^2}$                (11)

where, n is the time level, i is the index in the radial direction, and j is the index in the axial direction.

The thermophysical and transport properties of the pineapple samples used in the numerical simulations are summarized in Table 1. The convective mass transfer coefficient is determined through the Chilton-Colburn analogy of the heat transfer coefficient, relating the transport phenomena at the product surface. The IR heat flux $\left(q_{I R}\right)$ absorbed by the pineapple surface is empirically determined based on the experimental data obtained from the drying tests in Section 3. The time step ($\Delta \mathrm{t}$) and spatial steps ($\Delta \mathrm{z}, \Delta \mathrm{r}$) listed in Table 1 were carefully selected to ensure the stability of the explicit finite difference method and to achieve grid independence for the numerical solution. The computational program described in the study was developed and implemented using the MATLAB environment.

Table 1. Input parameters

Figure 4 presents the numerical simulation results for the moisture distribution within the pineapple slice under two different drying conditions. Specifically, Figure 4(a) illustrates the drying process using only IR radiation, where the ambient air temperature (T_d) is maintained at room temperature (36 ℃). In contrast, Figure 4(b) shows the results for HA drying alone, using a resistance heater to maintain T_d  at 50 ℃ with no IR heat flux applied (q_IR = 0). The figure illustrates the spatial distribution of moisture within the pineapple slice over a 4-hour period for both IR and HA drying modes. The contour plots show that moisture content decreases more rapidly at the surface and corners of the slice, where the material is in direct contact with the drying medium. The moisture gradients are steeper in the IR mode compared to HA drying, as evidenced by the tighter contour lines near the boundaries. This distribution lies in the internal molecular diffusion process, where moisture migrates from the high-concentration core toward the surface to replace the water evaporated by convective mass transfer and radiative heat.

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Figure 4. Comparison of moisture distribution of IR and HA drying with time

Figure 5 displays the temperature profiles across the computational domain during the first 30 minutes of drying. The surface temperatures rise rapidly while the core temperature lags, illustrating the conduction of heat from the exterior to the interior. The IR drying mode achieves higher surface temperatures (51.7 ℃) more quickly than the HA mode (49.9 ℃), even though both utilize an air temperature of 50 ℃. The IR radiation provides a direct heat flux that is absorbed at the surface, accelerating the heating process beyond what convection alone can achieve. Figure 6 provides a quantitative comparison of the drying kinetics for the three operational modes over time. All curves follow a typical falling-rate drying period, where the drying rate slows as the material becomes drier. The combination of radiation and convection enhances moisture removal efficiency and significantly reduces overall processing time. In addition, despite the IR-only mode operating at a lower ambient temperature (room temperature, 36 ℃) compared to the 50 ℃ used in the HA mode, the moisture content in the IR process decreases at a faster rate. This is evident in the steeper gradient of the IR curve relative to the HA curve throughout the drying period.

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Figure 5. Comparison of temperature distribution of IR and HA drying with time

Figure 6. Average simulated moisture content profile of pineapple drying

Figure 7 tracks the average product temperature throughout the drying process. The hybrid (IR+HA) mode reaches a steady-state temperature of approximately 65 ℃, which is significantly higher than the IR-only (»52 ℃) or HA-only (»50 ℃) modes. The temperature rises sharply in the initial stages before leveling off once a thermal equilibrium is reached between the energy supplied and the energy used for water evaporation. The physical meaning of the higher hybrid temperature is that the additional energy from the 2100 W IR lamps combined with the resistors drives the material to a higher energy state, which in turn increases the effective mass diffusivity (D) according to the Arrhenius equation.

Figure 7. Average simulated temperature profile of pineapple drying

To understand the distinct kinetics among the three drying modes, it is essential to analyze the underlying coupled heat and mass transfer interactions. In HA drying, thermal energy is transferred solely through surface convection from the heated air stream (T_d = 50 ℃). Because heat conduction into the wet tissue is constrained by the thermal conductivity of the material (k = 0.549 W/m‧K), the internal product temperature rises slowly and stabilizes at approximately 50 ℃. Internal moisture migration relies purely on liquid diffusion toward the surface under concentration gradients. At this thermal level, the effective mass diffusivity (D) remains relatively low, causing the drying rate to be governed by slow internal diffusion. In IR drying, energy transfer does not rely on convective air heating. Instead, radiative heat flux (q_IR) is directly absorbed by the surface layer of the opaque pineapple slice. This direct energy absorption creates an immediate thermal input at the surface, establishing a sharp surface-to-core thermal gradient. This rapid surface heating accelerates moisture vaporization at the boundary, which in turn enhances the internal moisture concentration gradient and drives faster outward capillary diffusion compared to convective drying, even under ambient air conditions (36 ℃). In Hybrid IR-Convective drying, a strong synergistic coupling between radiative and convective energy transport is established. Convective HA reduces thermal losses from the product surface to the surrounding air, while simultaneous IR radiation continuously deposits high energy flux onto the surface. This dual-energy input drives the average product temperature to a significantly higher steady state of ~65 ℃. Exponentially governed by the Arrhenius relationship (Eq. (3)), this elevated core-to-surface temperature field exponentially boosts the effective moisture diffusivity (D). Consequently, internal moisture diffusion is dramatically accelerated to continuously supply water to the surface, matching the high convective-radiative evaporation capacity and preventing localized surface hardening.

Table 2 validates the numerical model against experimental data across all three drying modes. The predicted drying times show excellent agreement with experimental results (<2% discrepancy), confirming that the explicit finite difference formulation accurately captures the coupled transport physics. Notably, single-mode IR drying achieves a slightly shorter drying time (8.13–8.26 h) than hot-air drying at 50 ℃ (8.37–8.43 h), as direct surface radiation eliminates convective thermal resistance. Most prominently, the hybrid IR-convective mode demonstrates the fastest kinetics (3.95–4.12 h), achieving over 50% time reduction. This performance stems from the synergistic energy input that elevates product temperature to ~65 ℃, thereby boosting effective mass diffusivity (D) via the Arrhenius relationship.

From an engineering and industrial processing perspective, the reduction in drying time achieved by the hybrid IR-convective mode carries significant practical implications. First, equipment throughput and operational capacity are substantially enhanced. Reducing the processing cycle from over 8.2 hours (for single-mode IR or HA) to approximately 4 hours allows commercial processing facilities to double their daily production capacity using the same dryer volume, thereby lowering capital expenditure per unit mass of dried fruit. Second, in terms of energy performance, although the hybrid mode engages both IR lamps and electrical heaters simultaneously, the drastic reduction in total processing duration reduces cumulative parasitic energy losses. Shortening the cycle by half minimizes continuous fan power consumption and thermal heat dissipation through the chamber walls over time, leading to overall lower specific energy consumption per kilogram of evaporated water. Third, regarding product quality, long exposure to elevated temperatures during extended single-mode drying typically leads to thermal degradation of heat-sensitive nutrients (e.g., Vitamin C and bromelain) and adverse color changes due to non-enzymatic browning. The rapid dehydration kinetics in hybrid drying shorten thermal exposure while preventing surface case hardening, yielding dried pineapple slices with superior nutritional and visual quality.

To provide a realistic picture of model applicability, its scope and limitations should be noted. The 2D finite-difference framework accurately captures transient internal transport and drying kinetics for thin cylindrical slices with high computational efficiency (<2% error). However, key simplifications (including constant thermophysical properties, neglected volumetric shrinkage, and an experimentally calibrated q_IR) limit direct extension to complex 3D shapes, bulk bed drying, or industrial continuous systems without re-evaluating radiative view factors and property variations.