Development of an enhanced electrical injera baking pan (Ethiopian Traditional mitad) using steel powder additives and gypsum insulation

Abstract

Electric Injera baking Pan are prevalent in Ethiopia but are highly inefficient, resulting in significant heat loss, high energy consumption, and increased energy bills. This research investigates improving these devices using steel powder as an additive and gypsum as an insulator. The study examines thermal conductivity, baking time, energy consumption, heat loss, and insulation effectiveness. The objectives of this research are to improve the thermal conductivity of the baking surface while ensuring even heat distribution, enhance the insulation properties of the pan to reduce heat loss, improve the safety of the user by reducing the risk of excessive heat exposure to the outer surfaces, and reduce the overall energy consumption of the Injera baking process. Temperatures were measured using an infrared thermometer, digital thermometer, and thermocouple. Four samples (A0, A1, A2, & A3) with different steel powder compositions (0 %, 15 %, 25 %, and 35 %) and a constant 75 % clay soil composition were tested. The analysis showed an average baking energy of 0.45 kWh per kg of injera (0.198 kWh per injera) and a thermal efficiency of 86.4 % when baking 4.395 kg of injera. The total heat energy loss was 1402.78 KJ (14.08 % of 10300 KJ input energy). The losses were distributed among the retained (92.17 %), the baking plate (3.95 %), the bottom enclosure (2.08 %), the side enclosure (1.04 %), and the cover lid (0.76 %).

1. Introduction

Injera, a fundamental food in Ethiopian cuisine, is crafted from a blend of cereals like teff, maize, wheat, rice, or a mix thereof. Its production entails fermentation and meticulous baking. This flatbread is a dietary mainstay in Ethiopia, traditionally enjoyed frequently throughout the day and often served two to four times per day [1]. Injera is usually cooked on a clay plate known as a pan positioned over a three-stone fire or a specialized electric stove, necessitating temperatures ranging from 180 °C to 220 °C [[1], [2], [3]]. In the standard electric Injera baking system, heat is produced using high-resistance heating elements through which electric current flows. This resistance within the elements generates heat in the coil, which is then transferred to the baking pan via conduction. Depending on the clay construction, single- and double-plate pans are available in the market. In a double plate system, the bottom plate is designed to house the heating element, while the top plate functions as the surface where the baking takes place, heated and ready for cooking [4]. Electric stoves are recognized for their significant energy use and comparatively low efficiency. This is largely due to factors such as the thickness of the heating elements, the thermal properties of the materials used in the cookware, and insufficient insulation systems. In traditional electric baking pans, there is a risk of uneven heat distribution due to inherent manufacturing inaccuracies. These issues include variations in the depth of the groove where the electrical resistor is embedded, inconsistencies in resistor density along its length, and slight differences in the thickness of the baking plate. Moreover, these pans typically require a considerable amount of time (approximately 24 min) to initially heat up and for the baking process [1,3,5]. Energy is vital for fundamental household tasks like cooking, baking, lighting, and heating water. Ethiopia has one of the lowest access levels to modern energy services, relying primarily on biomass for its energy supply. Although different studies show some variation in the data, researchers generally agree that around 90 % of the country's total energy consumption is from the household sector. Within this sector, approximately 95 % of energy comes from biomass, 1.5 % from petroleum, 3.3 % from electricity, and 0.2 % from other [1,[6], [7], [8], [9]]. Electric Injera baking is primarily seen in urban areas of Ethiopia and plays a significant impact on the country's electricity consumption. These pans consume between 50 % and 75 % of total household energy and account for 60 %–70 % of the hydroelectric power generated in Ethiopia [5,7,10]. However, each existing electric Injera baking pan consumes a substantial amount of electricity, approximately 3.5 kW–3.9 kW per baking session, resulting in significant energy waste during the process [11,12]. The current electrical pan is often criticized for its inefficiency, stemming from its outdated design and manufacturing flaws dating back to the 1960s, with no design improvements made since then [3,13]. The average thermal efficiency of an electric Injera baking pan is found to be 50 % for those with a clay plate and 60 % for those with a ceramic plate [8,10]. Most researchers have found that the efficiency of a better-controlled electric Injera baking pan ranges from 43 % to 55 % [6,14,15]. In almost all research done on electric Injera baking stoves, the amount of energy dissipated (loss) during the baking process is roughly predicted to vary from 50 to 60 percent [3,16,17]. In a solar-powered Injera baking system, heat is not supplied directly to the baking pan; Instead, the system uses energy storage methods, such as phase change materials and pressurized water vessels with auxiliary heating components. The solar system collects heat from solar radiation, transfers it to a working fluid or storage medium, and then delivers the heat to the pan for baking Injera [1,12,14]. The main issue is that the solar-powered Injera baking system is efficient only during sunlight hours. It takes over 100 min to heat initially the baking pan and has a higher idle time of over 3 min between baking sessions compared to the electrical Injera baking system [11,16]. In contrast, biomass Injera baking stoves use firewood as the primary energy source, but they have significant drawbacks, such as indoor air pollution, rampant deforestation, low efficiency, and high wood consumption. Researchers have estimated that traditional biomass Injera baking stoves have an efficiency ranging from 5 % to 35 % [3,9]. The importance of this study lies in developing a new, improved electric mitad by incorporating steel powder as an additive and gypsum as an insulator and evaluating its energy consumption and heat loss across various parts of the baking system. From the literature review above, the current electric mitad suffers from low efficiency due to inadequate thermal properties of the pan plate, significant heat loss, long initial heating times, extended baking durations, and high energy consumption for heating and baking. Steel powder can improve the thermal conductivity of the baking surface, promoting more even heat distribution, which helps achieve a consistent cooking temperature and reduces hot spots, thereby enhancing the quality of Injera. Gypsum, known for its thermal insulation properties, can help to prevent excessive heat from reaching the pan's outer surfaces, improving user safety, protecting the baking environment, reducing burn risks., lowering energy usage, and boosting baking efficiency. This research may also shed light on how various materials and additives impact cooking appliance performance, potentially leading to further innovations and improvements in traditional cooking tools and household appliances.

2. Materials and methods

2.1. Materials used for experimental test

The devices employed for measuring various parameters during the experimental tests are detailed in Table 1. This table includes essential information such as the names and images of each device, along with their specific characteristics and accuracy. Additionally, it highlights the particular applications of these devices, primarily focusing on how they are used to measure different temperature parameters of various components of the baking pan.

Table 1.

Devices utilized for measuring experimental parameters.

Name of thermometer	Picture of device	Device Features and Accuracy	Uses of device
Digital thermometer		⁃Temperature measurement: −50 °C–300 °C ⁃Temperature accuracy: $\pm$ 1 °C/$℉$ ⁃On/off keys switching	⁃Measure the temperature at the bottom of a baking pan.
Infrared Thermometer		⁃Temperature measurement: −50 °C–380 °C ⁃Temperature accuracy: $\pm$ 1.5 °C/$℉$ ⁃Response time 500 ms. ⁃Non-contact thermometer	⁃Measure the surface temperature of stove enclosures and baking pan surfaces.
Digital mass balance		⁃Mass measurement: 0.01g–610g ⁃Measurement accuracy: 0.1 mg	⁃Measure the weight of the dough and injera.
Multimeter		⁃Voltage measurement: 200 mV–1000V ⁃Measurement accuracy: $\pm$ 3 %	⁃Measure the current and voltage flowing to the stove.

2.2. Methods

Composite materials for baking pans are prepared using clay soil and steel powder. The clay soil is sourced from Kolay, near Deber Tabor in the Amhara region of Ethiopia. Clay soil is dried and powdered to increase its contact surface area for better mixing with the steel powder. The steel powder is made by grinding steel bars with a grinding machine. Fig. 1a, b below shows the steel powder and clay soil used for pan preparation.

Fig. 1.

a) Clay soil and b) Steel powder.

2.3. Sample preparation

The samples were created by mixing a consistent amount of clay soil with varying amounts of steel powder, as specified in Table 2. To the mixture, 45 g of water were added and stirred at 200 RPM for 15 min. The resulting mixtures were then poured into standard molds with a diameter of 40 mm, as shown Fig. 2a, b below.

Table 2.

Sample dimensions and weight composition.

Sample labeling	Diameter (mm)	Length (mm)	Clay (g)	Steel powder (g)	Water (g)
A0	40	52	75	0	45
A1	40	52	75	15	45
A2	40	52	75	25	45
A3	40	52	75	35	45

Fig. 2.

a) Instrument used for sample preparation; b) Samples created using the materials.

2.4. Thermal conductivity test

A thermal conductivity meter (WL 374) was employed to measure the thermal conductivity of the samples, as illustrated in Fig. 3. The thermal conductivity values obtained for each sample are presented in Table 3.

Fig. 3.

Thermal conductivity testing machine, and procedures.

Table 3.

Thermal conductivity reading for each sample.

Sample	Thermal conductivity $\left(\raisebox{1ex}{$\mathbf{W}$}\!\left/ \!\raisebox{-1ex}{$\text{mK}$}\right.\right)$
A0	0.85
A1	1.18
A2	1.46
A3	1.59

A composition of 25 % steel powder and 75 % clay soil was chosen for baking pan preparation. This blend increases the thermal conductivity of clay soil by 42 %. Consequently, sample A2 was selected to prepare the new electric pan. As the thermal conductivity of a composite material increases, its specific heat capacity typically decreases. Materials with high thermal conductivity indicate how heat moves through a material; heat capacity measures how much heat the material can store. Both properties impact the material's overall thermal performance in different ways. Achieving an optimal heat capacity is essential to effectively store thermal energy and minimize idle time between consecutive injera baking sessions. Further, increasing thermal conductivity value can complicate the baking process, similar to baking on metal, and reduce the significance of heat capacity in the process.

2.5. Fabrication of pan (Ethiopian Traditional mitad)

Traditionally, flat and circular clay pans with diameters ranging from 500 mm to 600 mm and a thickness of 20 mm are commonly used as baking pans. However, for this research, the pan plate was designed with a thickness of 12 mm and a diameter of 580 mm, which closely matches the dimensions of existing baking pans; with other physical dimensions of the various components of the pan shown in Table 4. This decision ensures social acceptance among users accustomed to the typical size of injera, as significant changes could affect their willingness to adopt the new system. The manufacturing process of the pan plate begins with creating the composite material by mixing clay soil (75 %) and low-carbon steel (25 %) in appropriate proportions. The composite material is then mixed with water until it attains a plaster-like consistency using a mixer operating at 200 RPM. Subsequently, the moit pan is allowed to dry slowly, during which it loses excess water while retaining moisture bound in crystal lattices. The surface finishing of the new pan involves smoothing the baking side and bottom surfaces using emery paper and shaping the effective baking diameter using a metal file. Finally, the pan plate is fired at high temperatures to reduce pores, increase density, and strengthen the structure. Fig. 4a–d below, illustrates the manufactured pan plate.

Table 4.

The physical dimensions of the various components of the pan.

Parameters	Dimensions	Unit
Baking pan plate thickness	12	Mm
Mass of the baking mitad	6	Kg
Mitad plat diameter	580	Mm
Effective pan diameter	560	Mm
Gypsum insulation thickness (bottom)	20	Mm
Side Gypsum insulation thickness	10	Mm
Groove depth	6.5	Mm
Distance b/n grooves or pitch	14.5	Mm
Resistance wire diameter	0.9	Mm
Resistor coil diameter	6	Mm
Resistance coil length before stretching	680	Mm
Resistance coil length after stretching	8500	Mm

Fig. 4.

Part manufacturing of the Pan: a) Modeling and manufacturing of the pan; b) Modeling and manufacturing of the cover lid; c) Pan plate casing; d) Manufactured leg of the electric pan plate.

3. Experimental tests and procedures

During the experimental setup, temperature readings were collected from various points across the pan surface, as illustrated in Fig. 5a. Specifically, temperatures were measured at the following locations.

• ⁃At the center of the baking plate, both on the top and bottom surfaces.
• ⁃At a distance of 13.75 cm from the center of the baking plate, at both above and below positions.
• ⁃At a distance of 27.5 cm from the center of the baking plate, on both the top and bottom surfaces.
• ⁃Immediately after removing the injera, the surface temperature of the baking plate was recorded.
• ⁃Intermittent baking surface temperature measurements were taken just before the baker placed the dough.
• ⁃Temperatures were recorded on the side enclosure at different points.
• ⁃Temperature measurements were taken at the center tip, middle, and bottom of the lid cover.
• ⁃Room temperature and dough temperature were also monitored.
• ⁃The temperature of the injera was measured immediately after removal from the pan.

Fig. 5.

Experiment setup of a pan stove: a) Digital and infrared thermometer positions; b) Thermometer positions strategically across the setup; c) Different viewpoints on experimental studies; d) The experimental setup and equipment arranged for the research project.

3.1. Input and useful energy

The heat generated by the heating element serves as the input energy for the baking process. This energy depends on the voltage (V) and current (I) passing through the heating element.

$${\mathrm{E}}_{\text{in}}=\mathrm{V}\ast \mathrm{I}\ast {\mathrm{t}}_{\mathrm{T}}$$ (1)

Where: ${\mathrm{E}}_{\text{in}}$ = input energy (W), V = voltage (volt), I = current flow (A), ${\mathrm{t}}_{\mathrm{T}}=$ Total time required for baking 10 injera.

The useful baking energy is estimated as the sum of sensible heat, which heats the dough from room temperature to the boiling point of water, and latent heat, which evaporates some of the water content in the dough.

$${\mathrm{E}}_{\mathrm{u}}={\mathrm{m}}_i{\mathrm{C}}_{\text{Pi}}\left({\mathrm{T}}_{\mathrm{b}}-{\mathrm{T}}_{\mathrm{a}}\right)+{\mathrm{h}}_{\text{fg}}\left({\mathrm{m}}_{\mathrm{d}}-{\mathrm{m}}_{\mathrm{i}}\right)+\left({\mathrm{m}}_{\mathrm{d}}-{\mathrm{m}}_{\mathrm{i}}\right){\mathrm{C}}_{\mathrm{w}}\left({\mathrm{T}}_{\mathrm{b}}-{\mathrm{T}}_{\mathrm{a}}\right)$$ (2)

Where: ${\mathrm{E}}_{\mathrm{u}}=$ useful energy, ${\mathrm{m}}_{\mathrm{d}}=$ mass of dough, ${\mathrm{m}}_{\mathrm{i}}=$ mass of injera, ${\mathrm{C}}_{\text{Pi}}=$ specific heat capacity of injera, ${\mathrm{C}}_{\mathrm{w}}=$ specific heat capacity of water, ${\mathrm{T}}_{\mathrm{b}}=$ boiling temperature of water, ${\mathrm{T}}_{\mathrm{a}}=$ room temperature, ${\mathrm{h}}_{\text{fg}}=$ latent heat of evaporation for water based on water boiling point temperatures at atmospheric pressure.

3.2. Heat energy loss analysis during baking process

During the electric injera baking process, heat energy was lost from the top, bottom, and sides of the pan plate During the electric injera baking process, heat energy was lost from the top, bottom, and sides of the pan plate, which can be quantified using Equations (7), (9), (13). This heat transfer occurs through conduction, convection, and radiation. Fig. 6 below depicts a thermal circuit that represents the different pathways through which heat is transferred from the electric injera baking stove to the surrounding environment. This thermal circuit effectively illustrates the intricate nature of heat loss in various directions and through multiple mechanisms.

• a.Heat loss on the cover lid to the surrounding

Fig. 6.

Thermal circuit diagram and heat loss for Injera baking stove.

Heat energy is lost from the cover lid to the surroundings by natural convection and radiation heat transfer modes. The cover lid, when heated by the electric mitad, emits infrared radiation. This radiation transfers heat directly from the lid to the surrounding environment. The intensity of radiation loss depends on the temperature of the lid and its surface characteristics. Warm air rises from the stove cover lid as it heats up. This creates convection currents around the stove. Heat is lost to the air, which then spreads this heat throughout the room.The natural convective heat transfer coefficient can be calculated by Heat energy lost from the cover lid to the surroundings through natural convection and radiation. The natural convective heat transfer coefficient can be calculated using empirical correlations that depend on the properties of the fluid (air in this case), the temperature difference between the cover lid and the surrounding air, and the physical dimensions of the lid. Typically, the natural convective heat transfer coefficient (${\mathrm{h}}_{\text{cov}}$) can be calculated using equation (3).

$${\mathrm{h}}_{\text{cov}}=\frac{{\mathrm{N}}_{\mathrm{u}}\ast \mathrm{K}}{\mathrm{L}}$$ (3)

Where: ${\mathrm{h}}_{\text{cov}}=$ natural convection ${\mathrm{N}}_{\mathrm{u}}=$ Nusselt number, $\mathrm{K}$ thermal conductivity ($\raisebox{1ex}{$\mathrm{w}$}\!\left/ \!\raisebox{-1ex}{$mk$}\right.$) and $\mathrm{L}=$ characteristic length of circular plate = 0.3 $D_m$.

The fundamental parameters for natural convection include the Grashof number (Gr), Rayleigh number (Ra) can be determined by equation (4), Nusselt number (Nu), and Prandtl number (Pr).

$${\mathrm{R}}_{\mathrm{a}}={\mathrm{G}}_{\mathrm{r}}\ast {\mathrm{P}}_{\mathrm{r}}=\frac{\mathrm{g}\beta \Delta \mathrm{T}{\mathrm{L}}^3}{{\mathrm{v}}^2}\ast {\mathrm{P}}_{\mathrm{r}}$$ (4)

Where: $\mathrm{g}=$ gravitational acceleration ($\mathrm{m}/{\mathrm{s}}^2)$, $\mathrm{\beta }=$ Coefficient of volume expansion (1/K), $\Delta \mathrm{T}=$ Temperature change of the surface (°C), L characteristic length of the geometry (m)& $\nu$ Kinematic viscosity of the air (${\mathrm{m}}^2/\mathrm{s})$.

$${\mathrm{Q}}_{\text{loss},\text{cl}-\mathrm{s}}={\dot{\mathrm{Q}}}_{\mathrm{c}-\mathrm{c}-\mathrm{a}}+{\dot{\mathrm{Q}}}_{\mathrm{r}-\mathrm{c}-\mathrm{a}}={\mathrm{U}}_{\text{cl}-\mathrm{s}}\mathrm{A}\left({\mathrm{T}}_{\text{cl}}-{\mathrm{T}}_{\mathrm{a}}\right)\ast {\mathrm{t}}_{\mathrm{T}}$$ (5)

Where: ${\dot{\mathrm{Q}}}_{\text{loss},\text{cl}-\mathrm{s}}=$ heat energy loss from cover lid to the surrounding (KJ), $\mathrm{A}$ = area of conic cover lid heat loss surface ($m^2$), ${\mathrm{t}}_{\mathrm{T}}=$ Total time required for baking 10 injera, ${\mathrm{T}}_{\text{cl}}=$ average temperature of the cover lid (°C), ${\mathrm{T}}_{\mathrm{a}}=$ ambient temperature of the experimental room (°C), ${\dot{Q}}_{c-c-a}$, ${\dot{Q}}_{r-c-a}=$ heat energy lost by convection & radiation heat transfer from cover lid to surrounding (KJ), $U_{cl-s}$ = overall heat transfer coefficient for convective and radiative heat transfer modes from cover lid to surrounding, $(\mathrm{W}/{\mathrm{m}}^2\mathrm{K}$) and it can be calculated by equation (6).

$${\mathrm{U}}_{\text{cl}-\mathrm{s}}={\left[\frac{1}{{\mathrm{h}}_{\mathrm{c},\text{cl}-\mathrm{s}}}+\frac{1}{{\mathrm{h}}_{\mathrm{r},\text{cl}-\mathrm{s}}}\right]}^{-1}$$ (6)

$h_{c,cl-s}=$ Convective heat transfer coefficient from cover lid to surrounding $=\frac{{\mathrm{N}}_{\mathrm{u}}\ast \mathrm{K}}{\mathrm{L}},(\mathrm{W}/{\mathrm{m}}^2.\mathrm{k}$) $h_{r,cl-s}=$ Radiative heat transfer coefficient from cover lid to surrounding = $ϵ\delta \left({{\mathrm{T}}_{\text{cl}}}^2+{{\mathrm{T}}_a}^2\right)\left({\mathrm{T}}_{\text{cl}}+{\mathrm{T}}_a\right),\left(\mathrm{W}/{\mathrm{m}}^2.\mathrm{k}\right)$.

• b.Heat Losses on Baking Mitad to Cover Lid

Heat loss from the baking pan plate to the cover lid can happen through natural convection and radiation heat transfer mechanisms. The baking plate radiates heat upwards towards the cover lid. The cover lid, once heated, absorbs this radiation and may then emit heat to the ambient environment. The amount of heat lost through radiation depends on the temperature difference between the plate and the lid, as well as the surface emissivity of the materials. Heat from the baking plate warms the air directly above it, which then transfers heat to the cover lid through convective currents. The warmed air between the plate and the lid circulates, carrying heat away from the plate. This heat is then conducted and convected through the lid to the ambient environment. Condensation was considered negligible in this heat transfer scenario.

$${\mathrm{Q}}_{\text{loss},\mathrm{b}-\text{cl}}={\dot{\mathrm{Q}}}_{\mathrm{c}-\mathrm{p}-\mathrm{c}}+{\dot{\mathrm{Q}}}_{\mathrm{r}-\mathrm{p}-\mathrm{c}}={\mathrm{U}}_{\mathrm{b}-\text{cl}}\mathrm{A}\left({\mathrm{T}}_{\mathrm{b}}-{\mathrm{T}}_{\text{cl}}\right)\ast {\mathrm{t}}_{\mathrm{T}}$$ (7)

Where: ${\mathrm{Q}}_{\text{loss},\mathrm{b}-\text{cl}}=$ heat energy loss from baking pan plat to the cover lid, (KJ), $\mathrm{A}=$ area of baking pan, $\left({\mathrm{m}}^2\right)$, ${\mathrm{t}}_{\mathrm{T}}=$ Total time required for baking 10 injera, ${\mathrm{T}}_{\mathrm{b}}=$ Average temperatures of baking pan surface, ${\mathrm{T}}_{\text{cl}}$ = Average Temperatures of cover lid, ${\mathrm{U}}_{\mathrm{b}-\text{cl}}=$ overall heat transfer coefficient for convective and radiative heat transfer modes from baking surface to cover lid, $\left(\mathrm{W}/{\mathrm{m}}^2\mathrm{K}\right)$ and calculated by equation (8).

$${\mathrm{U}}_{\mathrm{b}-\text{cl}}={\left[\frac{1}{{\mathrm{h}}_{\mathrm{c},\mathrm{b}-\text{cl}}}+\frac{1}{{\mathrm{h}}_{\mathrm{r},\mathrm{b}-\text{cl}}}\right]}^{-1}$$ (8)

• c.Heat Loss from the Bottom Enclosure To Surroundings

Gypsum, chosen for its low thermal conductivity, serves as thermal insulation to minimize heat loss from the bottom of the electric injera baking pan. A 20 mm thick layer of gypsum reduces the amount of heat lost through the bottom surface of the pan. The heat energy lost during the baking of injera can be expressed in terms of the surface temperatures at the top ($T_T$) and bottom ($T_B$) of the insulation.:

$$Q_{loss,bo-s}=U_{bo-s}\mathrm{A}\left({\mathrm{T}}_{\text{bo}}-{\mathrm{T}}_{\mathrm{a}}\right)\ast {\mathrm{t}}_{\mathrm{T}}$$ (9)

Where: $Q_{loss,bo-s}$ = heat lost from the bottom enclosure to surrounding with an insulator, (KJ) ${\mathrm{T}}_{\text{bo}}=$ Average temperatures of the bottom enclosure, ${\mathrm{t}}_{\mathrm{T}}=$ Total time required for baking 10 injera, ${\mathrm{T}}_{\mathrm{a}}$ = Temperatures of ambient, $U_{bo-s}=$ allover heat transfer coefficient from the bottom enclosure to surroundings evaluated as follow equation (10).

$$U_{bo-s}={\left[\frac{{\mathrm{t}}_{\text{insu}}}{{\mathrm{k}}_{\text{insu}}}+\frac{1}{{\mathrm{h}}_{\mathrm{c},\text{bo}-\mathrm{s}}}+\frac{1}{{\mathrm{h}}_{\mathrm{r},\text{bo}-\mathrm{s}}}\right]}^{-1}$$ (10)

If an electric pan lacks insulation, the bottom surface of the pan is directly exposed to the aluminum enclosure, which has a thin thickness. This setup results in increased wastage of energy.

$${\mathrm{Q}}_{\text{loss},\text{bm}-\mathrm{s}}={\mathrm{U}}_{\text{bm}-\mathrm{s}}\mathrm{A}\left({\mathrm{T}}_{\text{bm}}-{\mathrm{T}}_{\mathrm{a}}\right)\ast {\mathrm{t}}_{\mathrm{T}}$$ (11)

Where: ${\mathrm{Q}}_{\text{loss},\text{bm}-\mathrm{s}}=$ Heat energy lost from the bottom enclosure of the pan to surroundings, without insulator (KJ), ${\mathrm{t}}_{\mathrm{T}}=$ Total time required for baking 10 injera, ${\mathrm{T}}_{\text{bm}},{\mathrm{T}}_{\mathrm{a}}=$ Temperature of the bottom surface of the electric pan and ambient respectively, ${\mathrm{U}}_{\text{bm}-\mathrm{s}}=$ Allover heat transfer coefficient from the bottom surface of the baking pan to the surroundings evaluated by equation (12).

$${\mathrm{U}}_{\text{bm}-\mathrm{s}}={\left[\frac{1}{{\mathrm{h}}_{\mathrm{c},\text{bm}-\mathrm{s}}}+\frac{1}{{\mathrm{h}}_{\mathrm{r},\text{bm}-\mathrm{s}}}\right]}^{-1}$$ (12)

• d.Heat loss on the side enclosure to the surroundings

Heat loss by convection and radiation from the side enclosure to the surroundings and by conduction through the thickness of side insulation. The side enclosure, which is in contact with or close to the baking plate and cover lid, also radiates heat to the surrounding environment. The effectiveness of this radiation loss is influenced by the temperature of the enclosure and its radiative properties.The side enclosure transfers heat to the surrounding air via convection. The air in contact with the hot surface of the enclosure heats up, rises, and is replaced by cooler air, creating convection currents. This process transfers heat from the enclosure to the ambient air.

$${\mathrm{Q}}_{\text{loss},\mathrm{s}-\mathrm{s}}={\dot{\mathrm{Q}}}_{\mathrm{c}-\mathrm{s}-\mathrm{a}}+{\dot{\mathrm{Q}}}_{\mathrm{r}-\mathrm{s}-\mathrm{a}}{=\mathrm{U}}_{\mathrm{s}-\mathrm{s}}\mathrm{A}\left({\mathrm{T}}_{\mathrm{s}}-{\mathrm{T}}_{\mathrm{a}}\right)\ast {\mathrm{t}}_{\mathrm{T}}$$ (13)

Where: ${\mathrm{Q}}_{\text{loss},\mathrm{s}-\mathrm{s}}=$ heat energy lost from the side enclosure, (KJ), $U_{s-s}=$ overall heat transfer coefficient from the side surface of the baking pan to the surroundings and ${\mathrm{t}}_{\mathrm{T}}=$ Total time required for baking 10 injera. The overall heat transfer coefficient With and without side insulator could be simply calculated by using equations (14), (15)) respectively:

$${\mathrm{U}}_{\mathrm{s}-\mathrm{s}}={\left[\frac{{\mathrm{t}}_{\mathrm{S},\text{insu}}}{\mathrm{k}}+\frac{1}{{\mathrm{h}}_{\text{cs}-\mathrm{s}}}+\frac{1}{{\mathrm{h}}_{\text{rs}-\mathrm{s}}}\right]}^{-1};\left(\text{With}\text{side}\text{insulation}\right)$$ (14)

$${\mathrm{U}}_{\mathrm{s}-\mathrm{s}}={\left[\frac{1}{{\mathrm{h}}_{\mathrm{c},\mathrm{s}-\mathrm{s}}}+\frac{1}{{\mathrm{h}}_{\mathrm{r},\mathrm{s}-\mathrm{s}}}\right]}^{-1};\left(\text{Without}\text{side}\text{insulation}\right)$$ (15)

• e.Retained heat loss at baking pan at the end of the baking process

After the baking process ends, heat energy retained within the pan plate contributes significantly to overall heat loss. During experiments, injera can continue to bake even after the power is turned off, till a pan surface temperature of 140 °C and prolonged baking times and may result in poorer quality. The gradual cooling from this elevated temperature (${\mathrm{T}}_{\mathrm{e}}=140°C$) back to ambient temperature (${\mathrm{T}}_{\mathrm{a}}=17.4°C$) takes approximately 14 and a half minutes. This heat exchange between the surroundings and the pan due to temperature differences is referred to as retained energy loss:

$${\mathrm{Q}}_{\mathrm{r}}={\mathrm{U}}_{\mathrm{m}}\ast \mathrm{A}\left({\mathrm{T}}_{\mathrm{e}}-{\mathrm{T}}_{\mathrm{a}}\right)\ast {\mathrm{t}}_{\mathrm{e}}$$ (16)

Where: ${\mathrm{Q}}_{\mathrm{r}}=$ Retained heat energy at the end of the baking process, (KJ), ${\mathrm{T}}_{\mathrm{e}}=$ Temperature at the end of baking, ${\mathrm{t}}_{\mathrm{e}}=$ Time required to cold the pan plat to ambient temperature,

${\mathrm{t}}_{\mathrm{m}}=$ Thickness of pan, $K_m=$ Thermal conductivity of improved pan, $(\mathrm{W}/\mathrm{m}.\mathrm{k}$), $U_m=$ Overall heat transfer coefficient of the baking pan, $\left(\mathrm{W}/{\mathrm{m}}^2.\mathrm{k}\right)$ it can be Computed by equation (17).

$${\mathrm{U}}_{\mathrm{m}}={\left[\frac{{\mathrm{t}}_{\mathrm{m}}}{{\mathrm{K}}_{\mathrm{m}}}\right]}^{-1}$$ (17)

• f.Total Heat Energy Loss

$${\mathrm{Q}}_{\text{total},\text{loss}}={\mathrm{Q}}_{\mathrm{r}}+{\mathrm{Q}}_{\text{loss},\mathrm{b}-\text{cl}}+{\mathrm{Q}}_{\text{loss},\text{bo}-\mathrm{s}}+{\mathrm{Q}}_{\text{loss},\mathrm{s}-\mathrm{s}}+{\mathrm{Q}}_{\text{loss},\text{cl}-\mathrm{s}}$$ (18)

• g.Thermal Efficiency of the System

The thermal efficiency of the enhanced electric pan is determined by dividing the net useful energy by the gross energy supply.

$${\mathrm{\eta }}_{\text{thermal}}=\frac{{\mathrm{E}}_{\mathrm{u}}}{{\mathrm{E}}_{\text{in}}}\ast 100$$ (19)

Where values of ${\mathrm{E}}_{\text{in}}$ and ${\mathrm{E}}_{\mathrm{u}}$ a are determined by equations (1), (2)), respectively.

4. Results and discussion

The temperature profile during the baking process is crucial for understanding how energy is used in the electric pan. This profile is analyzed under two conditions: without any load and with a load placed inside the pan.

4.1. No load Temperature profile

As shown Fig. 5b in the experimental investigation, temperatures at various parts of the mitad; specifically the bottom of the mitad plate, the top of the mitad plate, the side enclosure, the cover lid, and the bottom enclosure, were recorded every 2 min during the injera baking process. The results showed that the temperature increased over time at all measured locations. The temperature increasing rate is largest through the mitad plate, second, from the bottom enclosure, the third largest temperature increase rate from the side enclosure surface and least is from cover lid as depicted in Fig. 7. For analytical purposes, average temperatures for each component were used. The average temperatures recorded were 211.58 °C for the mitad plate, 105.5 °C for the bottom enclosure, 65.2 °C for the side enclosure, 45.8 °C for the cover lid, and 17.4 °C for the surrounding environment.

Fig. 7.

Surface temperature of electrical pan parts.

Fig. 8 depicts temperature changes recorded at different points: the center, 13.75 cm away from the center, and 27.5 cm away from the center of the baking pan. The temperature profiles begin from the ambient temperature of 17.4 °C and reach a maximum of 269.8 °C. Under no load conditions, the surface of the baking pan heats up almost uniformly, with temperature variations of less than 6 °C across the three measured points. This uniform heating is attributed to precise groove profiles and the homogeneous blending of low-carbon steel powder with clay soil.

Fig. 8.

Temperature variations over the surface of the baking pan.

4.2. With load Temperature profile

Fig. 9 illustrates the temperature profile observed during the baking process with a load. Initially, the temperature rises from the ambient temperature of 17.4 °C to the minimum required baking temperature of 170.1 °C for 0–13 min. This phase represents the heating-up period. Beyond 13 min, the temperature variation on the baking surface fluctuates: it decreases when the dough is poured onto the surface and increases after Injera removal during idle periods, oscillating within these intervals with some variation. The baking time for the first two Injera was longer, approximately 240 s because the baking process started at a lower temperature (170.1 °C–190 °C). Baking at lower temperatures reduces the quality of Injera, characterized by fewer "eyes" that contribute to its desired texture. Beyond 190 °C, the average baking time required is consistently 120 s, with 60 s of idle time between successive Injera baking cycles. Experimental findings indicate that the cover lid was open for 33.3 % of the baking process time (60 s) to remove baked Injera and pour dough. While previous studies suggest a temperature range of 180–220 °C for baking Injera, this investigation challenges that assertion by demonstrating that temperatures below 190 °C result in longer baking times. Therefore, the recommended acceptable temperature range is 190 °C–220 °C. Temperatures exceeding 220 °C lead to burnt Injera and lower-quality products.

Fig. 9.

Temperature profile of baking pan with load.

Fig. 10 demonstrates that the temperature of the dough started at 17.4 °C and rose to an average temperature of 101.5 °C upon being poured onto the hot pan surface. The average surface temperature of the baking pan, initially at 211.58 °C, decreased to 101.5 °C immediately upon contact with the dough. During idle periods, the surface temperature of the pan remains at the baking temperature due to the continuous supply of electrical energy.

Fig. 10.

Temperatures of pan surface and dough during each baking cycle.

Fig. 11 illustrates the temperature profiles of various parts of the enhanced pan stove under load conditions. The temperature of the bottom enclosure steadily increased over time without significant oscillation. In contrast, the temperature of the cover lid fluctuated over time: it was lower when the dough was poured onto the baking surface and higher just before removing freshly baked Injera from the pan and just before pouring new dough. The temperature of the side enclosure increased gradually over time, positioned between the temperatures of the bottom enclosure and the cover lid.

Fig. 11.

Temperature profiles of pan stove parts.

4.3. Energy consumption analysis

Despite reaching the required baking temperature early in the heating-up process, the temperature of the heating element continues to rise, indicating that the system is consuming additional power unnecessarily. Consequently, this excess energy is dissipated as various losses, including retained heat loss, side enclosure heat loss, bottom enclosure heat loss, and cover lid heat losses. Based on analytical calculations, the total heat loss in the Injera baking pan (for baking 10 Injera) is estimated to be 1402.78 kJ, as determined by Equation (18). Specifically, the heat energy losses due to retained heat at the end of the baking process were evaluated to be 1300 kJ, according to Equation (16). Additionally, the losses from the baking plate, bottom enclosure, side enclosure, and cover lid were calculated using Equations (5), (7), (9), (11), (13), (16), and resulting values of 55.7 kJ, 29.08 kJ, 7.3 kJ, and 10.7 kJ, respectively, as illustrated in Fig. 12.

Fig. 12.

Energy flow (Sankey) diagram of electric injera baking pan heat energy loss.

Insulation plays a crucial role in improving the efficiency of the electric pan. For example, heat losses without insulation were measured at 69.2 kJ for the bottom enclosure and 14.541 kJ for the side enclosure evaluated by equations (11), (13)). With insulation, these losses reduced significantly to 29.08 kJ and 7.3 kJ respectively. Minimizing losses due to plate heat retention can be achieved by prolonging cooking sessions and using a single pan rather than multiple pans simultaneously, a practice less common in Ethiopia where families often share electric pans to reduce retained heat losses. This strategy is particularly beneficial for larger pans like clay pans, which have a higher heat capacity. The retained heat within the plate can also be repurposed, such as for baking bread on the pan plate after the Injera baking process, as bread requires a lower temperature than Injera dough. Experimental findings indicate that the total heat energy lost from the electric pan was 1402.78 kJ, accounting for 14.08 % of the 10300 kJ input energy used for baking 10 Injera over 43 min. The efficiency of the electric injera baking mitad is measured at 86.4 % computed by equation (19). This indicates a high level of energy utilization during the baking process.Retained heat loss constituted the majority at 92.17 % of the total heat loss in the baking system, with the baking plate contributing 3.95 %. The losses from the bottom enclosure, side enclosure, and cover lid accounted for 2.08 %, 1.04 %, and 0.76 % respectively, as depicted in Fig. 13.

Fig. 13.

Percentage contribution of heat loss from each part.

4.4. Performance Comparisons with previous researchers work

Table 5, Table 6 present some parameters of recent research on electrical injera baking stove efficiency. After baking, a stove needs time to cool down to a safe handling or cleaning temperature. During this cooling period, any residual heat not used in baking results in retained energy loss. Stoves with effective insulation and thermal management can reduce this loss by managing the excess heat release. Retained energy loss affects the overall efficiency of the stove, indicating that not all electrical energy used for heating was transferred effectively to the food. This inefficiency can lead to increased energy consumption if the stove continues to draw power for subsequent cooking or baking tasks. There is currently no research on the amount of retained energy loss. This study reveals that 92.87 % of the total heat energy loss during baking is due to retained heat energy, alongside an investigation using steel powder as an additive for injera baking pans. Efficiency can be slightly improved by adjusting cooking methods and dough water content. To enhance the efficiency of electric baking pans, consider the following recommendations.

• ➢Injera Thickness: To the greatest extent possible reducing the dough's water content can decrease energy consumption during baking, as more energy is required to evaporate higher moisture levels.
• ➢Baking Session Duration: Shorter baking sessions result in a higher fraction of heat being stored in the baking plate, increasing overall energy use. Baking more injera at once and reducing the number of baking sessions can lower retained and heat-up energy loss.
• ➢Shared Baking stove: Instead of using multiple baking stoves, neighboring families could share a single pan. In Ethiopia, it's common for different households within a compound to use separate stoves, which increases retained and heating-up energy.
• ➢Utilizing Retained Heat: The heat retained in the baking plate can be used for other purposes, such as baking bread, which requires a lower temperature than injera.
• ➢Power Management: If the power exceeds what is needed for baking injera, bakers could turn off the stove briefly. Additionally, turning off the power a few minutes before the end of the baking session can also reduce retained energy loss.

Table 5.

Summary of analysis on the energy consumption of improved & convectional (reviewed) electric stove [6] [8] [18] [19] [20] [21].

Parameters	Improved mitad	Convectional Mitad	Difference
Input voltage (V)	214	214	0
Input current (A)	18.5	17	1.5
Mitad power requirement (kW)	3.96	3.64	0.32
Mass of dough (kg)	5.234	7.07	1.836
Total injera baked (kg)	4.395	5.25	0.855
Total mass of water evaporated (kg)	0.839	1.82	0.981
The energy required for heat up (KJ)	3089	5364	2275
Energy consumption for baking only(KJ)	7126	10836	3710
Gross energy consumption (kJ)	10215	16200	5985
Time for heat up (min)	13	24	11
Time for only baking process (min)	30	56	26
The energy required for baking only (kJ/injera)	712.6	1083.6	371
The energy required for baking only (KWh/injera)	0.198	0.250	0.053
Energy required for baking only (KWh/kg, injera)	0.45	0.573	0.123
Latent heat of water (KJ)	4883	4111	771.4
Sensible heat present in injera (kJ)	3969	1568	2401
Total useful energy (kJ)	8852	5679	3173
Specific useful energy (KJ/injera)	885.2	603.92	281.28
Total heat lost(KJ)	1400.02	10520.2	9120.28
Thermal efficiency of mita	86.4	38	49.3

Table 6.

Compares various parameters, drawing on both present work with recent research findings.

Name of authors	Materials for pan	Power source	Heating up Time (min)	Baking Time (min)	Idle Time (min)	Thermal Efficiency (%)	Energy consumption Kwh/Kg, injera	Retained heat loss after baking (KJ)
Present work (2024)	Low carbon steel(additive)	Electrical	13	2	1	86.4	0.45	1300
R. Jones et.al 2017	Glass pan	Electrical	8 $\frac{1}{2}$	3	–	Increased by 30 %		Non-evaluative
Mesele H et. Al (2017)	Aluminum sheet	solar	30–45	5	–	65		Non-evaluative
Hiwot B et al (2022)	Copper (additive)	Electrical	11	1.67	0.83	88.55	0.272	Non-evaluative
Garedew A. 2015	Ceramic	Electrical	12	2	2	82	0.554	Non-evaluative

4.4.1. Economic Feasibility of improved mitad

The average specific baking energy consumption was found to be 0.198 kWh and 0.250 kWh per Injera for the improved and conventional electric Injera baking pans respectively, as detailed in Table 4. This indicates a difference of 0.052 kWh per Injera, equivalent to 187.2 kJ per Injera. If an individual consumes an average of 2 Injera per day, this translates to 730 Injera per year per person. Therefore, switching to the improved pan could save 37.96 kWh per year per person, amounting to 91.104 ETB per year per person in electricity cost savings (calculated at a rate of 2.4 ETB/kWh). This potential energy savings would increase with more households adopting the improved pan. Choosing the improved pan over the conventional one not only benefits individual households but also has significant implications for the national grid. However, there remains a widespread lack of awareness about energy-saving practices among both Mitad pan manufacturers and end-users alike.

5. Limitations of this research

The addition of steel powder and gypsum insulation might increase the manufacturing costs of the pan. Higher production costs could lead to higher retail prices, potentially limiting the affordability and market acceptance of the enhanced pan. The process of incorporating steel powder and gypsum insulation might complicate the manufacturing process. This includes issues related to uniform distribution of additives, maintaining structural integrity, and ensuring consistency across production batches. Increased manufacturing complexity could affect production efficiency and consistency. Comprehensive testing is required to validate the performance of the enhanced pan under various conditions and ensure it meets the desired specifications for heat distribution, insulation, and safety. Inadequate testing could lead to unanticipated issues in real-world use, affecting the reliability and user satisfaction.

6. Conclusions

The comprehensive experimental investigations lead to the following conclusions.

• ➢The thermal conductivity of the pan plate improved significantly from 0.85 W/(m·K) to 1.46 W/(m·K), marking a 42 % enhancement in thermal performance compared to conventional pan plates. This improvement was achieved by incorporating 25 % steel powder into 75 % normal clay soil.
• ➢As shown Fig. 5c, d the development of the Enhanced Electrical Injera Baking Pan (Mitad) has significantly improved the quality of injera production. By incorporating steel powder additives and gypsum insulation, this innovative design enhances heat retention and distribution, ensuring uniform cooking. As a result, the injera produced exhibits improved texture, flavor, and consistency, meeting the high standards of traditional Ethiopian cuisine.
• ➢The enhanced thermal performance of the pan plate results in improved heating-up time, baking time, and idle time during the cooking process.
• ➢Specific baking energy consumption was measured at 0.198 kWh per Injera for the improved pan and 0.250 kWh per Injera for the conventional pan.
• ➢The total heat energy lost from the electric pan amounted to 1402.78 kJ out of 10300 kJ input energy. Specifically, retained heat at the end of the baking process accounted for 1300 kJ, while losses from the baking plate, bottom enclosure, side enclosure, and cover lid were 55.7 kJ, 29.08 kJ, 7.3 kJ, and 10.7 kJ respectively.
• ➢Insulation significantly enhances pan efficiency. For instance, heat losses without and with insulation on the bottom enclosure of the electric pan were reduced from 69.2 kJ to 29.08 kJ, and on the side enclosure from 14.541 kJ to 7.3 kJ. This represents a savings of 58 % and 49.89 % respectively in heat energy by using bottom and side insulation.

These findings underscore the potential for improving energy efficiency in cooking appliances, highlighting the benefits of material enhancements and insulation strategies in reducing energy consumption and heat losses.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Data availability statement

All data generated or analyzed during this study are included in this published article.

Nomenclature

${\mathrm{T}}_{\mathrm{m}}$	Main film temperature, $°C$
${\mathrm{T}}_{\text{cl}}$	Average cover lid surface temperature, $°C$
${\mathrm{T}}_{\mathrm{a}}$	Ambient cover lid surface temperature, $°C$
${\mathrm{T}}_{\mathrm{b}}$	Average baking mitad surface temperature, $°C$
${\mathrm{T}}_{\mathrm{T}}$	Average top surface temperature of insulator, $°C$
${\mathrm{T}}_{\mathrm{B}}$	Average bottom surface temperature of insulator, $°C$
${\mathrm{T}}_{\text{bo}}$	Average bottom enclosure surface temperature of, $°C$
${\mathrm{T}}_{\text{bm}}$	Average surface temperature of bottom baking mitad, $°C$
${\mathrm{T}}_{\mathrm{s}}$	Average side surface temperature, $°C$
$\Delta T$	Change in temperature, $°C$
A	Surface area, $m^2$
$R_L$	Rayleigh number
$G_r$	Grashof number
$P_r$	Prandtl number
g	Gravitational constant, $m/s^2$
$\beta$	Volumetric expansion coefficient, $k^{-1}$
$D_m$	Diameter of mitad, m
L	Characteristic length, m
$v$	Kinematic viscosity, $m/s^2$
$N_u$	Nusselt number
${\mathrm{h}}_{\mathrm{c}-\mathrm{p}-\mathrm{c}}$	Convective heat transfer coefficient from baking plat to cover lid, $W/m^2.k$
${\mathrm{h}}_{\mathrm{r}-\mathrm{p}-\mathrm{c}}$	Radiative heat transfer coefficient from baking plat to cover lid, $W/m^2.k$
${\mathrm{h}}_{\mathrm{c}-\mathrm{c}-\mathrm{a}}$	Convective heat transfer coefficient from the cover lid to surrounding, $W/m^2.k$
${\mathrm{h}}_{\mathrm{r}-\mathrm{c}-\mathrm{a}}$	Radiative heat transfer coefficient from the cover lid to surrounding, $W/m^2.k$
${\mathrm{h}}_{\mathrm{c}-\mathrm{s}-\mathrm{a}}$	Convective heat transfer coefficient from side of mitad to surrounding, $W/m^2.k$
${\mathrm{h}}_{\mathrm{r}-\mathrm{s}-\mathrm{a}}$	Radiative heat transfer coefficient from the side enclosure to surrounding, $W/m^2.k$
$U_{b-cl}$	Over heat transfer coefficient from baking mitad to cover lid, $W/m^2.k$
$U_{cl-s}$	Over heat transfer coefficient from cover lid to surrounding, $W/m^2.k$
$U_{s-s}$	All over heat transfer coefficient from the side enclosure to surrounding, $W/m^2.k$
$Q_{loss,b-cl}$	Heat loss from baking surface to cover lid, KJ
$Q_{loss,cl-s}$	heat energy loss from cover lid to the surrounding, KJ
$Q_{loss,s-s}$	Heat loss from side enclosure to surrounding, kJ
$t_{insu}$	Thickness of bottom insulators, m
$t_{S,insu}$	Thickness of side insulators, m
$t_T$	Total time required for baking session, min
$ϵ$	Emissivity of the material
$\mathrm{\delta }$	Stefan Boltzmann constant, $\raisebox{1ex}{$W$}\!\left/ \!\raisebox{-1ex}{$m^2{.K}^4$}\right.$

CRediT authorship contribution statement

Altaseb Kegne Sisay: Writing – original draft, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Melese Shiferaw Kebede: Visualization, Supervision, Conceptualization. Abayenew Muluye Chanie: Writing – review & editing, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.