Bee Bread Drying Process Intensification in Combs Using Solar Energy

Abstract

This study presents the development and evaluation of a stand-alone solar dryer designed to improve the efficiency of bee bread dehydration. Unlike the electric prototype powered by conventional energy sources, the proposed system operates autonomously, utilizing solar energy as the primary drying agent. The drying chamber is equipped with solar collectors located in its lower section, which ensure convective heating of the product. Active convection is generated by a set of fans powered by photovoltaic panels, maintaining the drying agent’s temperature near 42 °C. The research methodology integrates both numerical simulation and experimental investigation. Simulations focus on the variations in temperature (288–315 K) and relative humidity (1–1.5%) within the honeycomb structure under convective airflow. Experimental trials examine the relationship between moisture content and variables such as bee bread mass, airflow rate, number of frames (5–11 units), and drying time (2–11 h). A statistically grounded analysis based on an experimental design method was conducted, revealing a reduction in moisture content from 16.2–18.26% to 14.1–15.1% under optimized conditions. Linear regression models were derived to describe these dependencies. A comparative assessment using enthalpy–humidity (I–d) diagrams demonstrated the enhanced drying performance of the solar dryer, which is attributed to its cyclic operation mode. The results confirm the potential of the developed system for sustainable and energy-efficient drying of bee bread in decentralized conditions.

1. Introduction

The economic significance of beekeeping is attributed to its production of various high-value products with nutritional and therapeutic properties, as well as the indispensable role of bees in pollinating agricultural crops, thereby enhancing both yield and quality [1,2].

If production levels were restored to those existing before the dissolution of the USSR (pre-1980), export revenues from bee bread sales could potentially increase tenfold. The intensification of this sector is feasible through the development of advanced technologies and equipment for beekeeping enterprises [3,4,5].

Among these, bee bread is one of the most expensive and labor-intensive to obtain, with a market value 8–10 times higher than that of honey. Due to its unique chemical composition, bee bread is widely used in the treatment of various human ailments, including gastrointestinal disorders, atherosclerosis, and cardiovascular diseases [6,7].

A single honeycomb cell contains approximately 140 mg of bee bread (ranging from 102 to 175 mg). A honeycomb where ¾ of the cells (about 6000 on both sides) are filled with bee bread contains approximately 840 g of the product. In 7000 cells, 1 kg of bee bread is stored. The biological requirement of a single bee colony for bee bread is approximately 20 kg per year. Experimental studies indicate that during the active season, bees require 1 kg of bee bread for every 4 kg of honey consumed. Inside the hive, honeycombs are naturally ventilated to maintain optimal temperature and humidity. However, for human consumption, bee bread must be extracted from honeycombs, presenting certain technical challenges [8,9].

Despite its high value and beneficial properties, there is currently no standardized industrial technology for large-scale bee bread processing. This challenge is further compounded by the lack of regulatory frameworks governing the commercial sale of bee bread. The Russian Federation remains the only European country with established regulations for bee bread production and trade [10,11,12]. The most promising and industrially viable method for bee bread extraction has been developed by researchers at Ryazan Agrotechnical University, named after P.A. Kostychev, in collaboration with the Beekeeping Institute of the Russian Federation [8]. This technology has undergone continuous refinement and has been tested on industrial equipment. The process involves collecting bee bread combs, scarification, drying, cooling, grinding, separation into bee bread granules and wax raw material, and final drying at a heat carrier temperature of 40–42 °C to achieve the required moisture content [9]. In this processing method, bee bread undergoes two stages of heat treatment:

• The first drying stage occurs after the scarification of the bee bread combs.
• The second drying stage takes place after separating the wax and bee bread mass, during which moisture is further reduced to ensure long-term storage, with the final moisture content of granules kept below 12%.

According to research findings [4,5], a substantial portion of the energy consumed in this process (over 50%) is allocated to drying. Therefore, optimizing the drying process and developing more energy-efficient drying devices represent critical challenges in bee bread production.

Studies conducted by various researchers worldwide [13,14,15,16] indicate that both traditional and innovative methods are employed for drying bee bread. However, most research focuses on drying bee bread granules, while studies on drying bee bread in honeycomb cells (wax cells) are primarily limited to the Russian Federation [17,18]. Several factors contribute to this research gap:

• Bee bread extraction remains a relatively new area of study with limited available literature.
• Production volumes remain low.
• Specialized equipment is required, leading to high costs.

Due to these challenges, many beekeepers attempt to produce bee bread without adequate technical support, resulting in increased expenses, particularly for drying processes that rely on energy-intensive methods.

The drying of bee bread and other dry bee products is a crucial step in ensuring product quality, preventing spoilage, and extending shelf life [13,14,15]. Traditional drying methods include freeze-drying (sublimation), solar drying, and hot air drying. Compared to solar drying, hot air drying is faster, provides better sanitary conditions, reduces the risk of microbial contamination, and allows for better process control. However, exposure to high temperatures during hot air drying can negatively impact the quality, organoleptic properties, physicochemical composition, and morphological structure of bee products [19].

Cyclic convective drying has been found to be less energy-intensive than continuous convective drying while preserving biologically active substances by preventing overheating [20]. Freeze-drying in a gentle mode demonstrated high rehydration capacity and maximum retention of amino acids, meeting European market standards [21,22]. However, some researchers argue that deep vacuum sublimation can degrade vitamins and other bioactive compounds [23].

Infrared (IR) drying of pollen collected by bees yielded positive results, reducing water content without causing thermal degradation of key bioactive compounds [24,25,26]. However, for compacted materials such as bee bread, excessive heating can lead to sugar caramelization, resulting in nutrient losses [9].

Microwave vacuum drying (MW-VD) has been shown to produce bee bread with higher antioxidant activity compared to hot air drying (HAD), regardless of pressure or power level [26]. However, these methods have not yet been widely implemented in industrial production due to a lack of comprehensive energy efficiency and cost-effectiveness assessments.

A review of the existing methods and equipment for drying beekeeping products allows for the following conclusions: All the examined drying technologies and designs provide a certain degree of moisture removal; however, their efficiency varies depending on the structural characteristics of the dried material. Most of the reviewed equipment is designed for drying bulk materials. With the exception of traditional solar dryers, all the considered technologies are energy intensive. Moreover, many of these systems, including innovative ones, present challenges in terms of adaptation for use in beekeeping.

In the European Union, the drying equipment produced by Lyson for beekeeping products is not specifically adapted for drying bee bread but is primarily designed for flower pollen. This limitation is due to the construction of these drying chambers, where products are placed on racks similar to mine dryers. As a result, uniform drying cannot be ensured without manually rotating the shelves during the drying process. According to most researchers, the most suitable equipment for drying bee bread in combs is the SP-40 model developed by the Ryazan State Agrotechnological University, named after Pavel A. Kostychev (Russia). This model is utilized in industrial bee bread processing as part of an integrated system for its production [23,27].

However, given the current advancements in solar energy utilization, this drying system can be further improved by incorporating new technical innovations in science and engineering. Such advancements would enhance the efficiency of bee bread comb drying and contribute to energy-efficient processing solutions [28,29,30,31,32].

In the Republic of Kazakhstan, the production of beekeeping products, particularly bee bread obtained through the processing of bee bread combs, is primarily conducted under field conditions. This is due to the fact that apiaries are typically located in areas with sufficient forage resources for bees. Following the dissolution of the Soviet Union and the transition to private ownership, beekeeping operations predominantly consisted of small-scale apiaries, each maintaining approximately 200–300 bee colonies. Given their limited financial resources, such enterprises often lack the capability to invest in expensive drying equipment.

As a cost-effective alternative, readily available transparent polymer materials, which are widely used in agriculture for various seasonal operations, can be employed for solar drying applications. These materials, being inexpensive and accessible on the market, can facilitate the development of low-cost, energy-efficient solar drying devices suitable for processing beekeeping products. The integration of solar energy into the drying process not only reduces operational costs, but also enhances the sustainability and environmental compatibility of bee bread production.

• Research Objective and Tasks
  Objective

To enhance the efficiency of bee bread drying in honeycomb cells using solar energy.

• Research Tasks

• Numerical modeling of temperature and humidity variations in bee bread combs during convective drying.
• Experimental investigation of humidity variations in bee bread combs under different drying conditions (airflow rate, number of combs, and chamber retention time).
• Comparative evaluation of drying efficiency using an electric dryer and a proposed solar dryer.

• Hypothesis

The increased use of solar dryers can reduce the cost of bee products by eliminating electricity consumption, thereby improving the profitability of beekeeping enterprises.

2. Materials and Methods

2.1. Construction and Operation of a Developed Solar-Powered Solar Dryer for Bee Bread in Combs

The prototype solar dryer was based on the more efficient SP-40 drying device (Figure 1a and Figure 2a), which operates on a 220 V electrical power supply and is manufactured by the Russian beekeeping industry. Given the high solar energy potential in Central Asia, particularly in the southeastern region of Kazakhstan, a solar-powered solar dryer was developed for the moisture removal of bee bread combs following scarification (Figure 1b and Figure 2b).

The drying chambers of both devices are designed as shaft-furnace-type convective dryers, where bee bread combs are arranged within hives in either a single- or double-layer configuration. In the SP-40 dryer (FGSHE HPE RGATU, Ryazan, Russia), a fine metal grate (3) is placed beneath the beehive to prevent wax crumbs and other particles from reaching the electric heater unit (8), thereby ensuring fire safety during the drying process.

To regulate the drying temperature of the bee bread combs, a microprocessor-based single-channel temperature controller (7) is installed on the heat-insulating casing (4) and operates in conjunction with a temperature sensor (5). A fan (9) draws in ambient air and directs it toward the electric heater unit (8). The heated air then moves upward between the bee bread combs, facilitating moisture removal from their surfaces and subsequently venting it into the atmosphere.

The developed solar dryer operates exclusively on solar energy. Air heating is achieved through solar collector (7) trays positioned along three sides of the lower perimeter, while an additional solar panel (8) is placed above them to convert solar energy into electricity. This electricity powers both a battery pack (14) and a fan unit (9), which is positioned atop the upper hive to extract the spent drying agent from the chamber. The fan unit comprises nine fans that operate according to a predefined program, dynamically adjusting their speed based on the air temperature at the chamber inlet, as regulated by the temperature controller (5). When the air temperature exceeds 40 °C, the number of active fans increases, thereby enhancing airflow. Conversely, as the temperature decreases, the number of operational fans is reduced to maintain the required drying conditions. If continuous air extraction is needed—such as during experimental studies or when drying high-moisture materials—the operating mode can be adjusted by reconfiguring the control program.

The accumulation of fine wax particles and other residues does not affect the dryer’s operation, as these materials can be removed upon completion of the drying process. The air heaters positioned at the bottom of the dryer are covered with transparent polyethylene to allow the passage of solar radiation while protecting the collector surfaces from dust accumulation.

The first beehive (2) is mounted on a drying frame (6) above the metal grate (3), with three additional hive units stacked above it. Each upper hive case is rotated 90 degrees relative to the one below to optimize airflow through the vertically arranged bee bread combs. The heated air passes over the comb surfaces, enabling efficient heat and moisture exchange. The thermal energy absorbed by the bee bread combs facilitates moisture evaporation from their surface and heats both the bee bread within the cells and the wax base of the combs. The resulting moisture-laden air is subsequently expelled from the dryer, maintaining an optimal drying environment.

2.2. Numerical Simulation of the Bee Bread in Combs Drying Process

For numerical simulation of air flow distribution, geometry was chosen that copies the current (real) hive. For correctness, a box of 500 by 500 mm and 90 mm in height was used, inside which there is a frame where the bees build up the honeycombs. In this case, the cell and honeycombs were drawn in arbitrary size and order, the dimension is shown in Figure 3. The inner frames of the honeycombs were given the empirical parameters of bee bread to obtain a reliable result of the calculations.

The mathematical model underlying this study is based on the equations of Navier–Stokes, which include the equation of continuity, the equation of motion, and the equation of energy [33,34,35,36,37]. To simulate the dynamics of humidity, a concentration transfer equation was included to describe the expansion of humidity, and more precisely the concentration of water vapor in air [38].

Continuity equation:

$$\nabla u=0.$$

(1)

Motion equation:

$$\rho \left({\displaystyle \frac{𝜕u}{𝜕t}}+u\nabla u\right)=-\nabla P+\mu {\nabla }^{2}u+f.$$

(2)

Energy equation:

$$\left({\displaystyle \frac{𝜕T}{𝜕t}}+u\nabla T\right)=\alpha {\nabla }^{2}T$$

(3)

Concentration transfer equation:

$$\left({\displaystyle \frac{𝜕C}{𝜕t}}+u\nabla C\right)=\gamma {\nabla }^{2}C$$

(4)

Energy equation (temperature):

$${\displaystyle \frac{𝜕T}{𝜕t}}+u{\displaystyle \frac{𝜕T}{𝜕x}}+v{\displaystyle \frac{𝜕T}{𝜕y}}+w{\displaystyle \frac{𝜕T}{𝜕z}}=\alpha \left({\displaystyle \frac{{𝜕}^{2}T}{𝜕x^2}}+{\displaystyle \frac{{𝜕}^{2}T}{𝜕y^2}}+{\displaystyle \frac{{𝜕}^{2}T}{𝜕z^2}}\right)$$

(5)

where $\alpha$—coefficient of temperature conductivity defined as $\alpha ={\displaystyle \frac{k}{c_p\rho }};$

$k$—thermal conductivity; $\mathsf{\rho }$—density;

$c_p$—isobar specific heat capacity.

Next, we consider the Boussinesq approximation, which introduces buoyancy effects to change temperature. The equation of motion in the Boussinesq approximation for an uncompressible liquid is as follows:

$$\rho \left({\displaystyle \frac{𝜕u}{𝜕t}}+u{\displaystyle \frac{𝜕u}{𝜕x}}+v {\displaystyle \frac{𝜕u}{𝜕y}}+w{\displaystyle \frac{𝜕u}{𝜕z}}\right)=-{\displaystyle \frac{𝜕P}{𝜕x}}+\mu \left({\displaystyle \frac{{𝜕}^{2}u}{𝜕x^2}}+{\displaystyle \frac{{𝜕}^{2}u}{𝜕y^2}}+{\displaystyle \frac{{𝜕}^{2}u}{𝜕z^2}}\right)$$

(6a)

$$\rho \left({\displaystyle \frac{𝜕v}{𝜕t}}+u{\displaystyle \frac{𝜕v}{𝜕x}}+v {\displaystyle \frac{𝜕v}{𝜕y}}+w{\displaystyle \frac{𝜕v}{𝜕z}}\right)=-{\displaystyle \frac{𝜕P}{𝜕y}}+\mu \left({\displaystyle \frac{{𝜕}^{2}v}{𝜕x^2}}+{\displaystyle \frac{{𝜕}^{2}v}{𝜕y^2}}+{\displaystyle \frac{{𝜕}^{2}v}{𝜕z^2}}\right)+{\rho }_{0}g\left(1-\beta \left(T-T_0\right)\right),$$

(6b)

$$\rho \left({\displaystyle \frac{𝜕w}{𝜕t}}+u{\displaystyle \frac{𝜕w}{𝜕x}}+v {\displaystyle \frac{𝜕w}{𝜕y}}+w{\displaystyle \frac{𝜕w}{𝜕z}}\right)=-{\displaystyle \frac{𝜕P}{𝜕z}}+\mu \left({\displaystyle \frac{{𝜕}^{2}w}{𝜕x^2}}+{\displaystyle \frac{{𝜕}^{2}w}{𝜕y^2}}+{\displaystyle \frac{{𝜕}^{2}w}{𝜕z^2}}\right).$$

(6c)

In this system, the expression ${\rho }_{0}g\left(1-\beta \left(T-T_0\right)\right)$ is the buoyancy force arising from temperature changes that causes natural convection in the liquid. The deciphering of variables entering previous equations is presented in

Table 1. Interpretation of variables.

Designation	Deciphering	Designation	Deciphering
$\rho$	density	$\mu$	Dynamic viscosity
$u,v,w$	Velocity’s components	$g$	gravitational acceleration
$P$	pressure	${\rho }_0$	Reference density
$\beta$	thermal expansion coefficient	$T-T_0$	Temperature—(minus sign) reference temperature

.

The transfer of humidity is performed by means of the transport equation of the concentration of water vapor in the air, where the form of the transport equation of diffusion is used. This equation shows changes in water vapor concentration due to air flow and diffusion (concentration gradient).

Concentration transfer equation:

$${\displaystyle \frac{𝜕C}{𝜕t}}+u{\displaystyle \frac{𝜕C}{𝜕x}}+v{\displaystyle \frac{𝜕C}{𝜕y}}+w{\displaystyle \frac{𝜕C}{𝜕z}}=\gamma \left({\displaystyle \frac{{𝜕}^{2}C}{𝜕x^2}}+{\displaystyle \frac{{𝜕}^{2}C}{𝜕y^2}}+{\displaystyle \frac{{𝜕}^{2}C}{𝜕z^2}}\right),$$

(7)

where $\mathsf{\gamma }$—diffusion coefficient of water vapor in the air.

The enclosed geometric form in Figure 4 explains the boundary conditions used in this numerical simulation to investigate the reduction in humidity in hive blocks.

Numerical values of boundary conditions indicators are presented in

Table 2. Boundary conditions.

Inlet (inflow)	$\mathrm{Velocity}: u=0 \mathrm{m}/\mathrm{s}, v=0.1 \mathrm{m}/\mathrm{s}$$\mathrm{and} 0.5 \mathrm{m}/\mathrm{s}$ $\mathrm{Temperature}: T_1=315 \mathrm{K}$ $\mathrm{Concentration}: C_{air}=1, C_{water-vapor}=0$
Outlet (outflow)	$\mathrm{Velocity}: {\displaystyle \frac{𝜕u}{𝜕x}}={\displaystyle \frac{𝜕v}{𝜕y}}=0$ $\mathrm{Temperature}: {\displaystyle \frac{𝜕T}{𝜕n}}=0$ $\mathrm{Concentration}: {\displaystyle \frac{𝜕C}{𝜕n}}=0$
Walls	$\mathrm{Velocity}: u=v=w=0$ $\mathrm{Temperature} \mathrm{and} \mathrm{concentration}: {\displaystyle \frac{𝜕C}{𝜕n}}={\displaystyle \frac{𝜕T}{𝜕n}}=0$

.

Input velocity is 0.1 m/s and 0.5 m/s. This input condition is key because it determines the field of velocities entering the computational domain, and therefore affects the moisture transfer. Initial conditions for water vapor and air concentration are set at 0.01 and 0.99, respectively. The temperature in the computed area is set at level ${\mathrm{T}}_0=288 \mathrm{K}$, which provides a thermal base against which the influence of the thermal effects of the input opening ${\mathrm{T}}_1=315 \mathrm{K}$ can be estimated.

2.3. Computational Geometry

The calculation area is a rectangular block with an internal structure (Figure 5), imitating a frame with cells in the in comb. For the implementation of numerical modeling on the calculated area, a calculation grid was built, which covers the entire block volume, also pointing to the three-dimensional problem.

For the construction of the calculation grid, an unstructured grid was chosen, which consists mainly of pyramids (tetrahedrons). As the implemented modeling is aimed at high resolution to accurately reflect the physical processes of heat and air flow propagation, the mesh density is set high with a minimum step x = 0.001 m, and the maximum reaches x = 0.01 m. As a result, this grid for this calculation area has 1,631,380 calculation elements.

To ensure accurate application of boundary conditions and adequate heat distribution over the design area, boundary condition crowding was used (Figure 6).

The inner row consists of a series of repeating hexagonal patterns that imitate the complex internal structure of the comb frame with cells. The hexagonal cells point to a highly organized and periodic inner frame. The unstructured nature of the grid allows for better placement of complex geometry in internal rows. The density of the grid in the inner series is very high, which implies a focus on a detailed description of physical phenomena and interactions in this area (Figure 7).

2.4. Justification of the Temperature Regime of the Air Solar Collector (Absorbent) of the Solar Dryer

The fundamental parameters for justifying the operational efficiency of the solar absorber include the absorber heating temperature and the air temperature at the device outlet. The structural design of the solar absorber is depicted in Figure 8.

According to the operational conditions of the solar dryer, the solar absorber is positioned horizontally on the ground surface, with air entering through an inlet located at the terminal section of the absorber. The base value is considered to be the slope that exactly corresponds to the geographical latitude of the area [39]. The adjustment is made according to the season, with a decrease in the angle to the vertical in winter and an increase in summer. For Almaty City, located at 43° N, the angle of inclination by December smoothly changes to 43° N—12° N = 31° N, and by July it increases to 43° N + 12° N = 55° N.

The efficiency of the air collector (solar heat input) was calculated together with the justification of the absorption capacity and the selection of transparent polyethylene film using the known method [28,40].

The calculation of the absorber and air temperature is based on the well-known Stefan–Boltzmann law.

To simplify the calculations, the following assumptions were made: During the short period under consideration, the absorber temperature remains constant, and heat losses through the bottom insulation of the collector are negligible. The incident solar radiation passes through a transparent, colorless polyethylene film with a reflection coefficient of 20%. Considering the heat flux losses due to reflection, the heat flux balance equation is formulated as follows:

$$q·k=\epsilon ·\sigma \left[{\left({\displaystyle \frac{T_1}{100}}\right)}^4-{\left({\displaystyle \frac{T_2}{100}}\right)}^4\right],$$

(8)

where σ = 5.67$\times {10}^{-8}$ W/(m²K⁴)—Stefan–Boltzmann constant;

ε = 0.8—emissivity coefficient;

k = 20%—film reflectance.

The research was conducted in the Zhambyl region, located at a latitude of 42.89568° N and a longitude of 71.37812° E. Table 1 presents the total (direct and diffuse) solar radiation incident on the horizontal collector surface during August under cloudless conditions. For the case of forced convection, the heat exchange model in the air collector is described by:

$$q·k=\epsilon ·\sigma \left[{\left({\displaystyle \frac{T_1}{100}}\right)}^4-{\left({\displaystyle \frac{T_2}{100}}\right)}^4\right]+\alpha {\displaystyle \frac{\left(∆T^{\prime }-∆T\right)}{ln\frac{∆T}{∆T}}},$$

(9)

where α—heat transfer coefficient, W/(m² K).

Experimental investigations on heat transfer were conducted in August 2024 at the manufacturing site of the individual entrepreneur “Ulan” in the Zhambyl region. The experimental setup consisted of a solar air heater with the following dimensions: length 1.6 m, width 0.5 m, and height 0.5 m. The experiments were carried out under conditions of natural daytime solar radiation. Upon reaching a quasi-stationary state under a given solar radiation flux, the air temperature at the heater inlet (T’) and outlet (T″) was recorded, along with the temperature of the absorber walls and the air flow rate. The heat transfer coefficient of the absorber was determined after the establishment of a steady-state absorber wall temperature under constant solar radiation intensity. In each experimental series, the heat flux was determined using the following equation:

$$Q=G·C_p(T^{″}-T^{\prime })$$

(10)

where $C_p$—the specific heat capacity of air.

The air mass flow rate was determined as follows:

$$G=U·\rho ·S,$$

(11)

where $\rho$ = 1293 kg/m³–air density;

S—channel cross-sectional area, m².

The air velocity was measured using a smart measuring device (Testo-Smart 405i. Testo SE & Co. KGaA, Titisee-Neustadt, Germany) in accordance with standardized procedures (Figure 9).

The heat transfer coefficient (α) was calculated using the formula:

$$\propto ={\displaystyle \frac{Q}{F (T_w-T_l)}},$$

(12)

where $F$—absorber surface area, m²;

$T_w$—absorber surface temperature, °C;

$T_l$—air temperature at the absorber surface, °C.

The obtained value of the heat transfer coefficient (α) was subsequently used to determine the air temperature above the absorber.

2.5. Experimental Studies of the Bee Bread Drying Process in Combs Under Laboratory Conditions

Experimental studies on bee bread drying in combs were carried out to determine the change in the humidity and temperature field in the comb with bee bread from the following: air flow velocity; retention time; and number of combs with bee bread in the drying chamber. Experimental data measurements were carried out according to the methodology of the state standard “Drying machines and agricultural installations” [41]. The air flow velocity was measured at the outlet of the dryer chamber and the moisture content of the drying agent at the inlet and outlet of the chamber as shown in Figure 2. To measure these parameters, the digital instrument Testo—Smart Probes 605i and 405i (Testo SE & Co. KGaA, Titisee-Neustadt, Germany) were used, respectively, for humidity and air temperature [42]. The data obtained from the protocol were transmitted wirelessly to the mobile device, then they were subjected to statistical processing to find averages and other values. For measuring air parameters, the instrument placement (Figure 10a) above the surface of the bee bread comb (at the exit of the drying chamber) is presented according to the diagram (in the right part) in Figure 10b.

Similarly, measurements of the drying agent were carried out at the entrance of the drying chamber in the space under the bee bread comb. As the drying chamber used a beehive, it can be used in two levels, if necessary, under operating conditions. For the experiment, a hive was used in one level.

The laboratory study was carried out to obtain a regression equation, reflecting as a function of heat temperature and humidity of the bee bread combs depending on the above-mentioned independent factors. All of the bee bread combs were scarified before experiments and subjected to moisture evaluation by separating pieces from different areas and then drying in an exicator. Similarly, after drying, all bee bread combs were evaluated for residual moisture. Determination of the moisture was carried out by the standard method according to GOST 31776-2012 [11].

To obtain this function, a multi-factor design experiment was carried out for two types of air-heating dryers: electrically and with the aid of a solar collector [43]. Since the geometrical parameters of the dryer chamber for both devices are selected by the same, the controlled factors in exposure time and the number of cells exposed to drying are selected by the same. However, the drying agent speed factor for two types of dryers is different due to the design feature of the air supply and suction mechanism. The levels and intervals of variation in independent factors are shown in

Table 3. Independent factor levels and intervals.

Status of Factors	Coded Values	Factors
		Air Flow Velocity, m/s		Exposure Time in the Camera, Hour	Number of Bee Bread Combs in the Dryer Chamber, pcs
		Electric Heating	Solar Heating
Basic level	0	0.89	0.55	6.5	8
Range	$\epsilon$	0.33	0.37	2.5	2
The upper level	+1	1.22	0.77	9	10
The lower level	−1	0.56	0.33	4	6
High point	+1.68	1.45	0.92	11	11
Low point	−1.68	0.33	0.18	2	5
Code mark	$x_i$	$x_1$		$x_2$	$x_3$

.

The design of the experiment is shown in

Table 4. Planned matrix for multi-factor experiment.

Numbering Experiment	Air Flow Velocity			Time of Exposure		Number of Combs
	${\mathit{x}}_1$	m/s	m/s	${\mathit{x}}_2$	hour	${\mathit{x}}_3$	pcs
1	−1	0.56	0.33	−1	4	−1	6
2	+1	1.22	0.77	−1	4	−1	6
3	−1	0.56	0.33	+1	9	−1	6
4	+1	1.22	0.77	+1	9	−1	6
5	−1	0.56	0.33	−1	4	+1	10
6	+1	1.22	0.77	−1	4	+1	10
7	−1	0.56	0.33	+1	9	+1	10
8	+1	1.22	0.77	+1	9	0	8
9	−1.68	0.33	0.18	0	6.5	0	8
10	+1.68	1.45	0.92	0	6.5	0	8
11	0	0.89	0.55	−1.68	2	0	8
12	0	0.89	0.55	+1.68	11	−1.68	5
13	0	0.89	0.55	0	6.5	+1.68	11
14	0	0.89	0.55	0	6.5	0	8
15	0	0.89	0.55	0	6.5	0	8
16	0	0.89	0.55	0	6.5	0	8
17	0	0.89	0.55	0	6.5	0	8
18	0	0.89	0.55	0	6.5	0	8
19	0	0.89	0.55	0	6.5	0	8
20	0	0.89	0.55	0	6.5	0	8

, considering the variation interval (Table 3) at five points with three repetitions at each point.

The airflow rate in the dryer chambers was controlled by changing the rotation frequency of the electric motors driving the fans in both dryers. The revolutions of the electric motors were controlled by a frequency converter according to the pre-calibrated values of the frequency of the revolution of the electric motors.

All nine motors were connected in parallel in the solar dryer unit during the experiment to ensure a uniform flow of air along the exhaust section. However, the air flow rate is 37% lower than in a dryer with electric heating. This limitation is not related to the heating of the air above the solar collectors, because in the operating modes as described above, the air flow temperature regimes were controlled by changing the number of fans. To maintain the temperature value of the air in the solar collector at low flow rates (during the experiment), there is a change in the active area of the solar collector.

3. Study Results

3.1. Results of the Study on Solar Collector (Absorber) Parameters for Air Heating

As a result of the experimental study, a graphical dependence of air temperature along the length of the solar collector (absorber) was obtained for different air flow velocities (Figure 11).

Based on the obtained data, the optimal parameters of the solar collector (absorber) for air heating were determined and are presented in

Table 5. Solar heat collector (absorber) Parameters.

Times of Day	6–7	7–8	8–9	9–10	10–11	11–12	12–13	13–14	14–15	15–16	17–18	17–18
Total solar radiation, W/m2	305	500	615	693	738	763	761	729	683	615	525	405
Collector temperature, °C	67	89	97	103	106	110	109	105	101	97	91	80

.

Figure 12 shows the results of a computational experiment on the ANSYS FLUENT 2020 R2 application package. It illustrates the changes in the moisture state of bee bread combs when cooled by warm air flowing parallel to the material plane from bottom to top. The figure includes an axonometric view (top) and a frontal view (bottom), showing the moisture distribution at different time intervals—100, 200, and 500 s after the start of the process. The left column in the figure shows the moisture condition when drying with an electric dryer (for continuous convective drying), and the right column shows the moisture interpretation of drying in a solar dryer (for cyclic convective drying).

Similarly, the results of a computational experiment (in ANSYS FLUENT 2020 R2) are presented in Figure 13 as a change in temperature on the plane of the bee bread combs (upper—view in axonometry; lower—view in front plane) when blowing with warm air parallel to the material plane from the bottom up for different values of time after the process starts at 100, 200, and 500 s. The left column shows the temperature changing when drying with an electric dryer, and the right column shows the interpretation of the temperature changing when drying in a solar dryer.

3.2. Results of the Experimental Part Study

According to the presented experimental study method, change in humidity in the bee bread combs during electric and solar drying depending on the controlled parameters (speed of air flow, exposure time of drying, and number of bee bread combs) obtained the mathematical models for two kinds of experiments.

The equation obtained on the conventional SP-40 electric dryer is presented as a linear correlation model of three factors:

Y = 17.463 + 0.13 X₁ − 0.16 X₂ − 0.268X₃.

(13)

Based on the results of experimental studies with a developed solar dryer, the following regression equation was obtained in a similar way:

Y = 12.767 + 2.513 X₁ − 0.108 X₂ + 0.157 X_3.

(14)

A graphical interpretation of the value of the function (humidity) in regression Equations (13) and (14) is shown in Figure 14 in three-dimensional space with different fixed values of the number of bee bread combs to be dried. The left column in the figure shows the humidity change of bee bread combs from the three variable parameters, and the right column similarly shows the humidity change function of bee bread combs exposed to drying in a solar dryer.

The result of the study is shown in a graphical interpretation of the drying process on an I-D diagram for two types of dryers and a comparison of the humidity content in the used agent. To do this, the air parameters (temperature and relative humidity) at the entrance of the chamber and at the exit of it were used (Figure 15). The changes in air water content when passing through the dryer chamber were determined by the difference in air humidity content at the inlet and outlet.

Additionally, a comparative analysis of drying efficiency was conducted between an electrically heated dryer (SP-40) and the solar dryer (

Table 6. Comparative analysis of drying efficiency.

Quality Metric	Electrical Dryer (SP-40)	Solar Dryer
Voltage consumption, V	220	12
Fan motor power consumption, W	1600	32.4
Power consumption for air heating, W	2000	Equivalent to 1500
Power supply	Electricity network (220 V)	Solar panel SVC PC-100 (12 V) (OEM, China)
Own power source	-	Battery (26 Ah)
Electrical system controller	TRM-1 (LLC “PA OWEN”, Moscow, Russia)	TRDM—W 3001 (Kabasi Connector Co., Ltd., Xiamen, China)

).

4. Discussion of the Results

An advanced solar dryer for drying bee bread combs can operate independently of a conventional electrical grid, making it suitable for remote areas where beekeeping farms are typically located. Compared to an industrial electric dryer, the use of a solar dryer reduced electrical energy consumption by 60%. In the electric drying system, air heating and supply were powered by a 220 V electrical source with a total power consumption of 1.5 kW [4]. In contrast, the solar dryer, with comparable performance, consumed electricity solely for operating the fan unit responsible for air circulation. The required electricity was generated by a photovoltaic panel installed above the dryer chamber, while air heating was achieved through solar collectors positioned on three sides at the bottom of the drying chamber.

A numerical simulation of the continuous and cyclic convective drying processes of bee bread combs was conducted to compare their efficiency and their impact on the quality of the drying product. The analysis of moisture variation demonstrated that relative humidity (RH) is a key parameter influencing the drying process, as it determines the air’s capacity to absorb moisture. At the initial stage, the air passing through the bee bread layer becomes saturated with moisture, leading to an increase in RH. However, when the process is properly managed, the moist air is efficiently removed and replaced with drier air, facilitating effective moisture removal. The numerical simulation conducted in ANSYS FLUENT confirmed a gradual decrease in RH over time (Figure 12), indicating that the drying process was well-optimized. At the final stages, RH reached minimal values, confirming the complete removal of moisture while preventing both over drying and insufficient drying—critical factors for maintaining the quality of bee bread in the honeycomb.

In contrast, continuous drying with a higher airflow rate (0.5 m/s) resulted in an uneven temperature distribution, leading to localized overheating and partial degradation of the bee bread structure within the combs. The numerical simulation results, illustrated in Figure 13, allow for a visual comparison of the efficiency of the two drying modes. The right side of the figure represents cyclic convective drying (0.1 m/s), while the left side depicts continuous convective drying (0.5 m/s). The presented data highlight key differences in humidity distribution, temperature conditions, and the retention of bee bread in the combs depending on airflow velocity.

The temperature variations of bee bread within the honeycomb during drying at airflow rates of 0.1 m/s and 0.5 m/s, ranging between 288 K and 315 K, provide the following insights: In the cyclic drying mode (right), heating occurred gradually and uniformly at an airflow velocity of 0.1 m/s, preventing overheating and preserving the integrity of the bee bread within the combs. The product temperature remained within safe limits, ensuring that its structure remained intact. Conversely, continuous drying (left) with an airflow velocity of 0.5 m/s caused localized overheating, accelerated moisture evaporation, and thermal damage to the bee bread structure. Excessive temperatures led to partial degradation of both the quality and shape of the bee bread.

From an energy efficiency perspective, cyclic drying was less energy-intensive due to the lower airflow velocity, which minimized overall energy consumption. In contrast, continuous drying required a significantly higher energy input to sustain elevated airflow rates and temperatures. Based on geo-information data and by the results of the experimental investigation, the air temperature dependence on the length of the solar collector of dryer for different airflow velocities was obtained. These data have made it possible to justify the geometrical parameters of the solar collector.

Experimental studies based on the principles of experimental design confirmed the theoretical modeling results of the heat and mass exchange process in both drying systems (Figure 10). The graphical regression model of heat and mass exchange demonstrated that the drying process in the solar dryer followed a smoother trajectory, which is attributed to the lower airflow velocity necessary for maintaining air temperature. All experimental models exhibited linear behavior, which can be explained by the constrained variation in the controlled parameters required for the drying process.

An experimental assessment of air moisture content changes in both drying systems, based on the I-D diagram (Figure 15), revealed that the air moisture content in the solar dryer exceeded that of the electric dryer. This indicates improved moisture removal efficiency within the solar drying chamber. The saturation of the drying agent was achieved at lower airflow speeds due to the cyclical operation of the fan.

5. Conclusions

The use of a solar dryer for drying bee bread combs is a viable technology in terms of energy efficiency and the implementation of cyclic drying modes.

The numerical simulation results confirm the superior efficiency of a solar dryer operating in the cyclic drying mode compared to a convective electric dryer operating in the continuous mode. Experimental studies further validated that the drying process in the solar dryer proceeded in a more controlled and uniform manner.

A comparative evaluation of moisture removal, based on the I-D diagram, demonstrated that the solar dryer improved moisture extraction efficiency by 30% in the cyclic mode compared to the electric dryer.

The reduction in energy consumption and the simplicity of solar dryer equipment contribute to lowering the production cost of bee bread, a valuable apicultural product. As a result, this technology enhances the overall profitability of beekeeping enterprises.

To further reduce the cost of bee products, solar dryers could also be utilized for the final drying stage of bee bread in granulated form. However, improving the design of existing dryers is necessary to optimize this processing step. Therefore, future research will focus on the intensification of the drying process for bee bread granules to ensure the efficiency of the selected technology.