Convective and Microwave Assisted Drying of Wet Porous Materials with Prolate Spheroidal Shape: A Finite-Volume Approach
Abstract
:1. Introduction
2. Methodology
2.1. The Geometry and Physical Problem
2.2. Mathematical Modeling
- (a)
- The porous body is assumed to be isotropic;
- (b)
- The mass transport occurred only by diffusion inside the body and convection at the surface;
- (c)
- The heat transfer occurred only by conduction and volumetric heating inside the solid, and convection at the surface;
- (d)
- Thermo-physical properties are considered to be constant;
- (e)
- Dimension variations were neglected.
2.3. Numerical Solution
2.4. Validation
- (a)
- Mass transfer process in a prolate spheroidal body $\dot{\mathrm{Q}}=0$, without heat transfer and convective condition at the surface.
- (b)
- Heating process of a spherical body with a constant volumetric heat source, without mass transfer and equilibrium condition at the surface.
2.5. Simulated Cases
3. Results
4. Conclusions
- (a)
- For a fixed microwave power density, a drying process with a higher Biot number for heat and mass transfer will result in the solid drying and heating up faster. The effect is more evident in moisture ratio than in average temperature;
- (b)
- In hybrid processes, for a shorter drying time, moisture migration occurs from the center to the surface and heat flux occurs in the opposite direction, generating high thermal and hydric gradients inside the solid;
- (c)
- In hybrid processes, for a longer dying time, moisture migration and heat flux occurs in the same direction, from the center to the surface, generating low hydric gradients and high thermal gradients inside the solid;
- (d)
- The higher the microwave power density, the greater the amount of heat generated, and the higher the temperature inside the solid. For the drying of prolate spheroidal solids, a microwave power density less than 10^{6} W/m^{3} provoked temperatures less than 450 K inside the solid.
- (e)
- The lower the attenuation factor (higher penetration depth), the higher the temperature inside the solid. For the drying of prolate spheroidal solids, an attenuation factor less than 50 m^{−1} provoked an average temperature greater than 410 K inside the solid.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Case | ${L}_{2}/{L}_{1}$ (-) | h_{m} (m/s) | h_{c} (W/m^{2}K) | P_{0} (W/m^{3}) | Bi (-) | $\Psi $ (m^{−1}) |
---|---|---|---|---|---|---|
1 | 2.000 | 1.22 × 10^{−7} | 33.95 | 1.0 × 10^{3} | 1.0 | 0.0 |
2 | 2.000 | 3.66 × 10^{−7} | 101.85 | 1.0 × 10^{3} | 3.0 | 0.0 |
3 | 2.000 | 6.10 × 10^{−7} | 169.75 | 1.0 × 10^{3} | 5.0 | 0.0 |
4 | 2.000 | 12.20 × 10^{−7} | 339.50 | 1.0 × 10^{3} | 10.0 | 0.0 |
5 | 2.000 | 1.00 × 10^{30} | 1.00 × 10^{30} | 1.0 × 10^{3} | ∞ | 0.0 |
6 | 2.000 | 6.10 × 10^{−7} | 169.75 | 1.0 × 10^{7} | 5.0 | 0.0 |
7 | 2.000 | 6.10 × 10^{−7} | 169.75 | 1.0 × 10^{6} | 5.0 | 0.0 |
8 | 2.000 | 6.10 × 10^{−7} | 169.75 | 1.0 × 10^{5} | 5.0 | 0.0 |
9 | 2.000 | 6.10 × 10^{−7} | 169.75 | 1.0 × 10^{4} | 5.0 | 0.0 |
10 | 2.000 | 6.10 × 10^{−7} | 169.75 | 1.0 × 10^{6} | 5.0 | 0.0 |
11 | 2.000 | 6.10 × 10^{−7} | 169.75 | 1.0 × 10^{6} | 5.0 | 1.0 |
12 | 2.000 | 6.10 × 10^{−7} | 169.75 | 1.0 × 10^{6} | 5.0 | 10.0 |
13 | 2.000 | 6.10 × 10^{−7} | 169.75 | 1.0 × 10^{6} | 5.0 | 50.0 |
14 | 2.000 | 6.10 × 10^{−7} | 169.75 | 1.0 × 10^{6} | 5.0 | 100.0 |
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Silva, E.G.; Gomez, R.S.; Gomes, J.P.; Figueirêdo, R.M.F.; Queiroz, A.J.M.; Silva, W.P.; Santiago, Â.M.; Macedo, A.D.B.; Ferreira, J.P.L.; Gomes, Í.A.; Lima, A.G.B. Convective and Microwave Assisted Drying of Wet Porous Materials with Prolate Spheroidal Shape: A Finite-Volume Approach. Agriculture 2020, 10, 507. https://doi.org/10.3390/agriculture10110507
Silva EG, Gomez RS, Gomes JP, Figueirêdo RMF, Queiroz AJM, Silva WP, Santiago ÂM, Macedo ADB, Ferreira JPL, Gomes ÍA, Lima AGB. Convective and Microwave Assisted Drying of Wet Porous Materials with Prolate Spheroidal Shape: A Finite-Volume Approach. Agriculture. 2020; 10(11):507. https://doi.org/10.3390/agriculture10110507
Chicago/Turabian StyleSilva, Edna G., Ricardo S. Gomez, Josivanda P. Gomes, Rossana M. F. Figueirêdo, Alexandre J. M. Queiroz, Wilton P. Silva, Ângela M. Santiago, Antonio D. B. Macedo, João P. L. Ferreira, Ítalo A. Gomes, and Antonio G. B. Lima. 2020. "Convective and Microwave Assisted Drying of Wet Porous Materials with Prolate Spheroidal Shape: A Finite-Volume Approach" Agriculture 10, no. 11: 507. https://doi.org/10.3390/agriculture10110507