Optimisation techniques for solar drying systems: a review on modelling, simulation, and financial assessment approaches

Figures & data

Figure 1. Numerical methods, Simulation tools, and Economic assessments and simulation criteria for optimisation of solar drying systems.

Figure 2. Stepwise methodology for Taguchi Method Modelling.

Figure 3. Classification of Taguchi optimisation problems S/N ratio can be calculated by: (Hussein et al. 2021).

Figure 4. Various steps in GA optimisation.

Figure 5. Various models used in ANOVA Modelling.

Table 1. Optimisation techniques using numerical/mathematical modelling.

Optimisation method	Products investigated	Type of dryer	Variables Analysed	Efficiency Calculated	Significant results	References
Taguchi Method	Phase Change Materials (Paraffin Wax, Grease, Coconut Oil)	Hybrid Dryer with PCM	Drying Time, Solar Radiation, Temperature	Energy efficiency = (22.69–22.80)%	S/N ratio played a vital role in heat transfer and energy storage. A 90-minute study at 30 ° C Celsius with 1525 W/m^2 radiation on coconut oil resulted in an 82.35% contribution out of 100% in the analysis of variance in energy.	(Kolioak, Radhakrishna, and Prasad 2020)
Taguchi Method	A slab of moist apple fruit	Convective dryer	Temperature, Velocity, Thickness ratio	S/N ratio was found to be 1.83%, 7.92%, and 3.62% for the three cases investigated.	The optimal conditions revealed from the Taguchi approach showed the temperature of 60° C, air velocity of 0.1 m/s, and a thickness ratio of 0.1, which predicts that combined optimisation is the same as the condition of minimum energy consumption.	(Majdi and Esfahani 2019)
Artificial Neural network (ANN)	Potato cylinders	Natural convection mixed-mode solar dryer	Product Temperature, Moisture Ratio	R^2 values are almost similar for FE model (R^2 = 0.988–0.995) and ANN model (R^2 = 0.973–0.997)	The FE model was created with the COMSOL Metaphysics software to investigate the solar-dried potato cylinder’s temperature and moisture ratio. ANN was used for validation of experimental results and reflected R^2 values between the range of (0.98–0.99)	(Dhalsamant 2021)
Artificial Neural Network (ANN)	Spent grains from microbreweries	Natural convection solar dryer	Drying Time, Temperature, CO2 emissions, Solar Irradiance	Economic efficiency = 0.45% cheaper than the electric convective dryer	ANN-CFD model developed helps generate irradiance values at any location. In contrast, the ANN model helped predict how the irradiance values directly govern the drying rates and average batch time.	(Capossio et al. 2022)
Genetic Algorithm (GA) – (ANN)	Watermelon rind pomace	Forced convective	Drying time, Temperature, Pressure drop, Heat transfer coefficient, Moisture ratio, Airflow	Type I and Type II solar transfer efficiencies were found to be 30–50% and 55–75%, respectively.	An ANN model was developed to analyse watermelon’s convective drying to produce non-traditional flour. Optimisation of ANN with GA resulted in 9 optimal neurons for the first layer and 10 for the second. Also, ANN performed better than the best-fitted empirical model.	(Fabani et al. 2021)
Particle Swarm Optimisation (PSO)	Performance of a smooth flat plate air heater	Forced convective	Irradiance, Tilt Angle, Air velocity, Temperature, Number of Glass covers, Surface Emissivity	Maximum thermal efficiency = 72.42%	Particle Swarm Optimisation model developed found suitable for finding the optimal set of design and operating parameters at which the thermal performance of air heater could be maximum.	(Siddhartha and Varun 2012)
Analysis of variance (ANOVA)	Paddy	PV integrated hybrid solar dryer	Optimal Temperature, Drying Time, Moisture content, Hardness, Yellowness index, Diffusion coefficients	Milling Yield =71.48%	Analysis of variance (ANOVA) was performed at a significance level (P < 0.05) for the linear and interaction effects of the variables on various quality parameters. The simulation studies were performed using the COMSOL Multiphysics platform.	(Jha and Tripathy 2021)
Analysis of variance (ANOVA)	Date fruits (fully ripe) stage of Khalas and Ruzeiz varieties	Forced convective	physicochemical properties such as linear dimensions of length and width, mass, colour L, a, and b values and pH	NA	In experiments with fixed solar drying conditions, some physicochemical properties of mass and pH of date fruits were affected, while properties of linear dimensions (length and width) and colour L, a, and b values were not.	(Al-Amri et al. 2021)
Analysis of variance (ANOVA)	Grapes	Open sun drying and Tunnel drying	Air temperature, Surface temperature, Relative humidity, moisture content, Water diffusivity	Water diffusivity was higher in the tunnel than in the open-air–drying by 54%	(ANOVA) was applied to estimate the mean values of CFU/mL, OTA (μg/kg) detected in infected grapes (red and white grapes), as well as the measured temperatures (air and grape berries’ surface)	(Templalexis et al. 2021)

Figure 6. (a) Inference in modelling stage (b) Inference in simulation stage (Sanchez 2007).

Figure 7. Frequently used simulation platforms classified on the design of the solar dryer (own creation) based on literature from Chauhan et al. (2015).

Figure 8. 3D streamline flow behaviour of airflow in inflatable solar dryer with (a) top view and (b) side view for drying of paddy rice (Salvatierra-Rojas et al. 2021).

Figure 9. Difference between (a) simulated and (b) experimental temperature profiles over time along the length of an inflatable solar dryer for paddy rice drying (Salvatierra-Rojas et al. 2021).

Table 2. Software tools and numerical model combinations using simulations.

Simulation method	Products investigated	Type of dryer	Variables Analysed	Model used	Software Package used	Significant results	References
CFD	Myrtus Communis L (Medicinal Herb)	Indirect solar dryer	Heat transfer, Mass transfer, Diffusive flowrate		COMSOL software	The CFD analysis and experiments provided better insights into the airflow distribution inside the dryer.	(Amouiri and Belhamri 2022)
CFD	Sweet Potato	Pyramid-shaped Cabinet dryer	Temperature, Airflow velocity	k – ϵ Turbulent model	ANSYS FLUENT	Comparison between lumped capacity model and lumped model on the temperature evolution predicts lumped capacity model could also provide insights as of CFD	(Tegenaw, Gebrehiwot, and Vanierschot 2019)
CFD	Apple slices	Solar Cabinet dryer with thermal energy storage	Temperature, Airflow velocity, Drying time, Drying efficiency, Mass flow rate	k – ϵ Turbulent model	ANSYS FLUENT	Drying time was reduced by approx 100 min with a drying efficiency of 39.9%	(Iranmanesh, Samimi Akhijahani, and Barghi Jahromi 2020)
CFD	Banana	Solar dryer with a double pass solar air collector	Temperature, Airflow velocity	k – ϵ Turbulent model	ANSYS FLUENT 18.2	At optimal peak temperature of 71.85°C the operational efficiency was 72.5%	(Mutabilwa and Nwaigwe 2020)
CFD	Grains	Forced convective solar dryer	Temperature, Airflow rate, and Pressure variation	k – ϵ Turbulent model	ANSYS FLUENT 17.0	An orifice was introduced at the inlet for recycling, and the simulations helped in optimising the size of the orifice and fan placement for recycling air inside the dryer	(Chavan et al. 2021b)
MATLAB	Crops	Mixed mode natural convection solar dryer	Temperature, Airflow Rate, and Heating coefficient	Mathematical modelling	MATLAB 2013a	The temperature predictions were observed to be accurate within 0.03% to 9.3% for solar heating mode, 0.20% to 7.49% for Backup heating mode, and 0.03% to 12.8% for hybrid heating modes, respectively.	(Sekyere et al. 2020)
MATLAB	LAVA Rock (Porous Media)	Double-pass solar air heater	Irradiance, Temperature, Thermal efficiency, Mass flow rate, porosity	Mathematical modelling with Energy balancing	MATLAB 2013a	Optimal thermal efficiency achieved at around 62% with a mass flow rate of 0.035 kg/s and 89% porosity was found to be optimal thermal efficiency and pressure drop trade-off.	(Ismail et al. 2022)
MATLAB	Crop	Hybrid photovoltaic–thermal (PVT) greenhouse solar dryer	Temperature, Thermal energy, and Thermal exergy	Thermal Modelling	MATLAB 2013a	Theoretical and experimental values of overall thermal energy be 1.92 and 2.03 kW h, respectively with r = 0.98, e = 10.76	(Tiwari, Tiwari, and Al-Helal 2016)
MATLAB	White Maize	Tractor mountable solar-biomass hybrid dryer	Temperature, Moisture content, Drying Time,	Thin layer Mathematical Model	MATLAB (version R2015a)	480 Kg of White maize was dried from 19% to 13% MC with a drying time of 5 h from 15 h	(Akowuah, Bart-plange, and Dzisi 2021)
MATLAB	Green Peas	Indirect type solar dryer	Temperature, Drying time, Moisture content	Thermal and Numerical Modelling	MATLAB 2013a	The centre of the product lost 93.33% of its initial moisture content at time t = 7 h while the temperature increased up to 74.85°C	(Arunsandeep et al. 2018)
FORTRAN	Onions	Solar batch dryer	Temperature, Drying time, Moisture content, Velocity	Mathematical model	FORTRAN 77	The gauss-Seidel iterative method was used to re-solve the two sets of equations written in matrix form with and without heater scenarios.	(Bennamoun and Belhamri 2003)
FORTRAN	Camomile	Directly irradiated solar dryer with integrated collector	Temperature, Drying time, Moisture content		FORTRAN 77	The moisture content of 43 Kg of Camomile reduced from 75% to 7% with a drying time of 57 h	(Mahapatra et al. 1994)
TRNSYS	Wood	hybrid solar-electrical dryer	Temperature, Drying time, Moisture content, Meteriologiocal data, Dry air velocity	Two numerical models	TRNSYS software	Performance analysis of the dryer system shows that throughout the year, the drying time in the proposed dryer system with latent heat storage does not exceed Five days	(Lamrani and Draoui 2020)
TRNSYS	Wood	Indirect hybrid solar dryer	Temperature, Drying time, Moisture content, Irradiance, Timber thickness	Mathematical model	TRNSYS software	Compared to other simulations, codes of thermal behaviour such as CODYRUN and EnergyPlus, TRNSYS software was identified as the most suitable energy simulation program and can be used on any thermal system	(Lamrani, Khouya, and Draoui 2019)
TRNSYS	Grapes	Greenhouse solar dryer	Temperature, Drying time, Moisture content, Solar radiation, Timber thickness	Numerical model	TRNSYS software	The moisture content of the grape was reduced to 0.22 (g water/g dry matter) from its the initial moisture content of 5.5 (g water/g dry matter) in 128 h.	(Hamdi et al. 2018)

Figure. 10. TRNSYS module Flowchart for wood drying reproduced from Reuss et al. (1997).

Table 3. Sustainability related criteria and its evaluation for solar dryers.

SN	Sustainability Criteria	Formula	Reference
1.	Energy Payback Period	$EBPT={\displaystyle \frac{EmbodiedEnergy}{AnnualEnergyOutput}}$	(Prakash and Kumar 2014)
2.	Carbon Emissions	$C{O}_{2}Emissions/Year={\displaystyle \frac{EmbodiedEnergy\times 0.98}{Lifetime}}$	(Prakash and Kumar 2014)
3.	Carbon Credit earned	$NetC{O}_{2}mitigation\times Pricepertonofmitigation$	(Prakash and Kumar 2014)
5.	Sustainability Index	$SI={\displaystyle \frac{1}{1-{\eta }_{ex}}}$	(Ndukwu et al. 2022)
5.	Environmental Destruction Coefficient	$EDC={\displaystyle \frac{1}{{\eta }_{ex}}}$	(Ndukwu et al. 2022)
6.	Waste Exergy ratio	$WER={\displaystyle \frac{E{x}_{loss}}{E{x}_{in}}}$	(Ndukwu et al. 2022)
7.	Environmental Impact factor	$EIF=WER\times {\displaystyle \frac{1}{{\eta }_{ex}}}$	(Ndukwu et al. 2022)
8.	Improvement Potential	$IP=(1-{\eta }_{ex})\times E{x}_{loss}$	(Ndukwu et al. 2022)

Table 4. Parameters used for economic optimisation in solar dryers.

SN	Parameters	Equation
1.	Annualised Cost of Dryer	$P_a=P_{ac}+P_m-V_a+C_{ea}$
2.	Annualised Capital cost	$P_{ac}=P_{cc}{F}_{cr}$
3.	Running cost of electricity	$C_{ea}=N\times W_r\times P_e$
4.	Annualised Salvage value	$V_a=V{F}_v$
5.	Capital recovery factor	$F_{cr}={\displaystyle \frac{d{(1+d)}^n}{{(1+d)}^n-1}}$
6.	Salvage fund factor	$F_v={\displaystyle \frac{d}{{(1+d)}^n-1}}$
7.	Drying cost per Kg	$P_d={\displaystyle \frac{P_a}{m_a}}$
8.	Annual product outcome	$m_a={\displaystyle \frac{m_{d}D}{D_b}}$
9.	Cost of fresh product per Kg	$P_{dp}={\displaystyle \frac{P_{fp}{m}_f}{m_d}}$
10.	Cost saving for drying unit weight of the product	$S_y=P_b-P_{ds}$
11.	Savings per batch	$S_b=S_y{m}_d$
12.	Savings per day	$S_d={\displaystyle \frac{S_b}{D_b}}$
13.	Payback period	$PaybackPeriod={\displaystyle \frac{\ln \left[1-{\displaystyle \frac{P_{cc}}{V}(d-i)}\right]}{\ln \left[{\displaystyle \frac{1+i}{1+d}}\right]}}$

Figure 11. Graphical representation of some recent economic analyses on various types of products and dryers.

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