Abstract
In order to reveal the relationship between temperature, moisture content and stress during microwave drying, the paper establishes a mathematical model of heat and mass transfer as well as stress during microwave drying using corn kernels as the medium, and couples the two models to solve the electromagnetic equation, energy and momentum conservation and stress equation, and conducts experimental verification. The results show that the maximum errors between the simulated and experimental values of temperature and moisture content are 8.04 % and 9.21 %, respectively, and the theoretical model can be used to simulate the changes of temperature, moisture content and stress of corn kernels. Under the set drying conditions, the thermal stress increased with increasing temperature, and the stress maximum was obtained on the upper and lower surfaces of the seeds. The wet stress increased with increasing moisture gradient, and the stress and crack index were maximum at a moisture content (dry basis) of 16.13 %.
Abbreviations
- A :
-
Surface area, m2
- c 0 :
-
Concentration of initial water, mol/m3
- c g :
-
Concentration of steam, (mol/m3)
- C P :
-
Specific heat capacity, J/(kg·K)
- c w :
-
Concentration of water, (mol/m3)
- D d :
-
Stiffness matrix, Pa
- D w :
-
Capillary diffusivity, m2/s
- E :
-
Electric field strength, V/m
- E(t):
-
Elastic modulus, Pa
- E 0 :
-
Elastic modulus of corn kernel, Pa
- G :
-
Shear modulus, Pa
- h t :
-
Heat transfer coefficient, W/(m2·K)
- I :
-
Evaporation rate of liquid water, mol/(m3·s)
- j :
-
Imaginary part
- K:
-
Evaporation rate constant
- K b :
-
Bulk modulus of elasticity, Pa
- K eff :
-
Thermal conductivity, W/(m·K)
- k in,i :
-
Internal permeability, m2/s
- k r.i :
-
Relative permeability, m2/s
- M :
-
Moisture content of dry basis, kg/kg
- M w :
-
Molar mass of water, kg/mol
- n g :
-
Fluxes of steam, mol/(m2·s)
- n w :
-
Fluxes of water, mol/(m2·s)
- p :
-
Saturated vapor pressure of water, kg/m3
- p eq :
-
Equilibrium vapor pressure of water, Pa
- p g :
-
Vapor pressure calculated for the ideal gas law, Pa
- Q :
-
The volumetric heat generation, W/m3
- R:
-
Ideal gas constant
- S q :
-
Viscoelastic stress, Pa
- t :
-
Time, s
- T :
-
Temperature, K
- T 0 :
-
Initial ambient temperature, K
- u :
-
Relative magnetic permeability, N/m2
- u g :
-
Flow rates of steam, m/s
- u w :
-
Flow rates of liquid water, m/s
- v :
-
Poisson’s ratio
- V :
-
Volume, m3
- w :
-
Angular frequency, rad/s
- ε :
-
Total strain
- ε :
-
Complex dielectric constant
- ε′ :
-
Dielectric constant
- ε″ :
-
Effective loss factor
- ε 0 :
-
Dielectric constant of free space
- ε d :
-
Shrinkage strain
- ξ :
-
Total conversion time, s
- ρ :
-
Density, kg/m3
- ρ g :
-
Density of steam, kg/m3
- ρ w :
-
Density of water, kg/m3
- σ :
-
Total stress, Pa
- τ :
-
Relaxation time, s
- a M :
-
Variation factor caused by water
- a T :
-
Variation factor caused by temperature
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Acknowledgments
This work is supported by Anhui Provincial Natural Science Foundation (2208085ME140).
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Tongsheng Sun is a Professor of the School of Mechanical Engineering, Anhui Polytechnic University. He received his Ph.D in mechanical and electronic engineering from Southeast University of China. His research interests include drying technology and intelligent control equipment, microwave heating theory and electromagnetic system structure optimization.
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Sun, T., Cao, R. Analysis of thermal and wet stress of corn kernel based on microwave drying. J Mech Sci Technol 37, 1501–1508 (2023). https://doi.org/10.1007/s12206-023-0235-x
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DOI: https://doi.org/10.1007/s12206-023-0235-x