Skip to main content
SpringerLink
Log in

Significance of Bed Shrinkage on Heat and Mass Transfer During the Transport Phenomenon of Humid Air

  • Research Article-Physics
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Simultaneous heat and mass transfer inside a packed bed dryer between a fluid phase and corn kernels was studied. A developed two-phase model for evaluating the effect of bed shrinkage and non-constant physical properties on the drying efficiency was conducted. Experimental data were utilized to develop the governing equations of the bed shrinkage and structural parameters with moisture content inside the packed bed dryer. The developed model was verified by assessing predictions against experimentally obtained moisture content and temperature along the drying bed, as the standard errors of the experimental values compared to the model were found to be close to the accepted engineering accuracy of 5%. It has been concluded that the incorporation of bed shrinkage and alteration in properties within the operating model is capable of providing a more comprehensive and precise analysis of heat and mass transfer phenomenon in porous media drying, such as corn kernels.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

C pg :

Air-specific heat (J kg−1 K−1)

C ps :

Solid-specific heat (J kg−1 K−1)

d :

Particle diameter (m)

F m :

Mass flux (kg m−2 s−1)

H :

Height of the packed bed (m)

h sg :

Convective heat transfer coefficient at the solid–air interface (W m−2 K−1)

h 0 :

Heat transfer coefficient at the inlet of the bed (W m−2 K−1)

h 1 :

Heat transfer coefficient at the outlet of the bed (W m−2 K−1)

\(K_{\exp }\) :

Experimental value (–)

\(K_{\bmod }\) :

Model value (–)

\(\mathop m\limits^{ \bullet }\) :

Evaporation rate (kg m−3 s−1)

\(n\) :

Number of observations (–)

r :

Particle radius (m)

RH:

Relative humidity (%)

A :

Specific surface area (m−1)

S b :

Shrinkage coefficient ratio (–)

t :

Time (s)

T :

Temperature (K)

V g :

Air velocity (m s−1)

X :

Moisture content (kg/kg)

z :

Axial coordinate (m)

\(\nabla\) :

Standard error (%)

\(\Delta H\) :

Latent heat of vaporization (J kg−1)

ρ :

Density (kg m−3)

λ :

Thermal conductivity (W m−1 K−1)

λ g eff :

Effective thermal conductivity of the gas phase (W m−1 K−1)

λ s eff :

Effective thermal conductivity of the solid phase (W m−1 K−1)

Φ :

Humidity (–)

ε :

Porosity (–)

g:

Gas phase

eff:

Effective

eq:

Equilibrium

s:

Solid phase

sg:

Solid–gas interface

References

  1. Babu, A.K.; Kumaresan, G.; Antony Aroul Raj, V.; Velraj, R.: CFD studies on different configurations of drying chamber for thin-layer drying of leaves. Energy Sources Part A Recover. Util. Environ. Eff. 42, 2227–2239 (2020). https://doi.org/10.1080/15567036.2019.1607935

    Article  Google Scholar 

  2. Srzednicki, G.; Driscoll, R.H.; Niu, X.; Guo, D.: Strategies for in-store drying based on the analysis of weather data-case study: key grain storing regions of China. Dry. Technol. 30, 1863–1869 (2012). https://doi.org/10.1080/07373937.2012.690802

    Article  Google Scholar 

  3. Lemus-Mondaca, R.A.; Zambra, C.E.; Vega-Gálvez, A.; Moraga, N.O.: Coupled 3D heat and mass transfer model for numerical analysis of drying process in papaya slices. J. Food Eng. 116, 109–117 (2013). https://doi.org/10.1016/j.jfoodeng.2012.10.050

    Article  Google Scholar 

  4. Jhider, N.; Bagané, M.: Investigation of the effect of temperature on Tunisian clay product during drying process. Heat Mass Transf. und Stoffuebertragung. 56, 2015–2024 (2020). https://doi.org/10.1007/s00231-020-02816-x

    Article  Google Scholar 

  5. Akiyama, T.; Hayakawa, K.: Heat and moisture transfer and hygrophysical changes in elastoplastic hollow cylinder-food during drying. J. Food Sci. 65, 315–323 (2000). https://doi.org/10.1111/j.1365-2621.2000.tb16000.x

    Article  Google Scholar 

  6. Akiyama, T.; Hayakawa, K.: Heat and moisture transfer and hygrophysical changes in elastoplastic hollow cylinder-food during drying. Food Eng. Phys. Prop. Heat. 65, 315–323 (2000)

    Google Scholar 

  7. Kowalski, S.J.: Toward a thermodynamics and mechanics of drying processes. Chem. Eng. Sci. 55, 1289–1304 (2000)

    Article  Google Scholar 

  8. Kowalski, S.J.; Rajewska, K.; Rybicki, A.: Destruction of wet materials by drying. Chem. Eng. Sci. 55, 5755–5762 (2000)

    Article  Google Scholar 

  9. Kowalski, S.J.: Modelling of fracture phenomena in dried materials. Chem. Eng. J. 86, 145–151 (2002)

    Article  Google Scholar 

  10. Silva, M.A.: A general model for moving boundary problems—application to drying of porous media. Dry. Technol. 18, 37–41 (2007). https://doi.org/10.1080/07373930008917728

    Article  Google Scholar 

  11. Mihoubi, D.; Zagrouba, F.; Vaxelaire, J.; Bellagi, A.; Roques, M.: Transfer phenomena during the drying of a shrinkable product: modeling and simulation. Dry. Technol. 22, 91–109 (2004). https://doi.org/10.1081/DRT-120028216

    Article  Google Scholar 

  12. Hernandez, J.A.; Pavon, G.; Garcıa, M.A.G.: Analytical solution of mass transfer equation considering shrinkage for modeling food-drying kinetics. J. Food Eng. 45, 1–10 (2000)

    Article  Google Scholar 

  13. Perré, P.; May, B.K.: A numerical drying model that accounts for the coupling between transfers and solid mechanics. Case of highly deformable products. Dry. Technol. Int. J. 19, 37–41 (2001)

    Article  Google Scholar 

  14. Viollaz, P.E.; Rovedo, C.O.: A drying model for three-dimensional shrinking bodies. J. Food Eng. 52, 149–153 (2002)

    Article  Google Scholar 

  15. Mercier, F.; Kolenda, F.; Rodolphe, J.: Influence of the mechanical behavior law on the drying of an alumina gel. Chem. Eng. J. 86, 95–101 (2002)

    Article  Google Scholar 

  16. Nascimento, J.J.S.; Belo, F.A.; Barbosa De Lima, A.G.: Experimental drying of ceramics bricks including shrinkage. Defect Diffus. Forum. 365, 106–111 (2002)

    Article  Google Scholar 

  17. Lima, A.G.B.D.; Queiroz, M.R.; Nebra, S.A.: Simultaneous moisture transport and shrinkage during drying of solids with ellipsoidal configuration. Chem. Eng. J. 86, 85–93 (2002)

    Article  Google Scholar 

  18. Mujumdar, A.S.: Simulation of convection-microwave drying for a shrinking material. Chem. Eng. Process. Process Intensif. 41, 487–499 (2002)

    Article  Google Scholar 

  19. Azzouz, S.: Moisture diffusivity and drying kinetic equation of convective drying of grapes. J. Food Eng. 55, 323–330 (2002)

    Article  Google Scholar 

  20. Fr, J.M.; Foucat, L.; Bimbenet, J.J.; Bonazzi, C.: Modeling of moisture profiles in paddy rice during drying mapped with magnetic resonance imaging. Chem. Eng. J. 86, 173–178 (2002)

    Article  Google Scholar 

  21. Kang, W.; Lee, N.: Mathematical modeling to predict drying deformation and stress due to the differential shrinkage within a tree disk. Wood Sci. Technol. 36, 463–476 (2002). https://doi.org/10.1007/s00226-002-0153-5

    Article  Google Scholar 

  22. Di Matteo, M.; Cinquanta, L.; Galiero, G.; Crescitelli, S.: A mathematical model of mass transfer in spherical geometry: plum (Prunus domestica) drying. J. Food Eng. 58, 183–192 (2003). https://doi.org/10.1016/S0260-8774(02)00368-0

    Article  Google Scholar 

  23. Islam, R.; Ho, J.C.; Mujumdar, A.S.: Simulation of liquid diffusion-controlled drying of shrinking thin slabs subjected to multiple heat sources simulation of liquid diffusion-controlled. Dry. Technol. Int. J. 21, 413–438 (2003). https://doi.org/10.1081/DRT-120018455

    Article  Google Scholar 

  24. Ponsart, G.; Vasseur, J.; Frias, J.M.; Duquenoy, A.; Méot, J.M.: Modelling of stress due to shrinkage during drying of spaghetti. J. Food Eng. 57, 277–285 (2003)

    Article  Google Scholar 

  25. Kowalski, S.J.; Rybicki, A.: Drying induced stresses in a swelling porous wall. Transp. Porous Media 57, 35–48 (2004)

    Article  Google Scholar 

  26. Dufour, P.; Blanc, D.; Touré, Y.; Laurent, P.; Dufour, P.; Blanc, D.; Touré, Y.; Laurent, P.: Infrared drying process of an experimental water painting: model predictive control. Dry. Technol. 22, 269–284 (2009)

    Article  Google Scholar 

  27. Chemkhi, S.; Zagrouba, F.; Bellagi, A.: Mathematical model for drying of highly shrinkable media. Dry. Technol. 22, 1023–1039 (2004). https://doi.org/10.1081/DRT-120038578

    Article  Google Scholar 

  28. Perré, P.: École nationale du génie rural, des eaux et des forêts. Nancy, Montpellier (2004)

    Google Scholar 

  29. Musielak, G.; Kowalski, S.J.; Molin, W.: The identification of fracture in dried wood based on theoretical modelling and acoustic emission. Wood Sci. Technol. 38, 35–52 (2004). https://doi.org/10.1007/s00226-003-0211-7

    Article  Google Scholar 

  30. Perré, P.; Passard, J.: A physical and mechanical model able to predict the stress field in wood over a wide range of drying conditions. Dry. Technol. 22, 27–44 (2004). https://doi.org/10.1081/DRT-120028202

    Article  Google Scholar 

  31. Karim, M.A.; Hawlader, M.N.A.: Drying characteristics of banana: theoretical modelling and experimental validation. J. Food Eng. 70, 35–45 (2005). https://doi.org/10.1016/j.jfoodeng.2004.09.010

    Article  Google Scholar 

  32. Banaszak, J.; Kowalski, S.J.: Theoretical and experimental analysis of stresses and fractures in clay like materials during drying. Chem. Eng. Process. Process Intensif. 44, 497–503 (2005). https://doi.org/10.1016/j.cep.2004.06.012

    Article  Google Scholar 

  33. Ruiz-cabrera, M.A.; Foucat, L.; Bonny, J.M.; Renou, J.P.; Daudin, J.D.: Assessment of water diffusivity in gelatine gel from moisture profiles. I—Non-destructive measurement of 1D moisture profiles during drying from 2D nuclear magnetic resonance images. J. Food Eng. 68, 209–219 (2005). https://doi.org/10.1016/j.jfoodeng.2004.05.033

    Article  Google Scholar 

  34. Karlsson, M.; Stenström, S.: Static and dynamic modeling of cardboard drying part 2: simulations and experimental results. Dry. Technol. Int. J. 23, 165–186 (2005). https://doi.org/10.1081/DRT-200047951

    Article  Google Scholar 

  35. Karlsson, M.; Stenström, S.: Static and drying technology: annamic modeling of cardboard drying part 1: theoretical model. Dry. Technol. Int. J. 23, 143–163 (2005). https://doi.org/10.1081/DRT-200047954

    Article  Google Scholar 

  36. Mihoubi, D.; Bellagi, A.: Two-dimensional heat and mass transfer during drying of deformable media. Appl. Math. Model. 32, 303–314 (2006). https://doi.org/10.1016/j.apm.2006.12.003

    Article  MATH  Google Scholar 

  37. Soysal, Y.; Ôztekin, S.; Eren, Ö.: Microwave drying of parsley: modelling, kinetics, and energy aspects microwave drying of parsley: modelling, kinetics, and energy aspects. Biosyst. Eng. (2006). https://doi.org/10.1016/j.biosystemseng.2006.01.017

    Article  Google Scholar 

  38. Sharma, G.P.; Prasad, S.: Optimization of process parameters for microwave drying of garlic cloves. J. Food Eng. 75, 441–446 (2006). https://doi.org/10.1016/j.jfoodeng.2005.04.029

    Article  Google Scholar 

  39. Baini, R.; Langrish, T.A.G.: Choosing an appropriate drying model for intermittent and continuous drying of bananas. J. Food Eng. 79, 330–343 (2007). https://doi.org/10.1016/j.jfoodeng.2006.01.068

    Article  Google Scholar 

  40. Corzo, O.; Bracho, N.; Pereira, A.; Vásquez, A.: Application of correlation between Biot and Dincer numbers for determining moisture transfer parameters during the air drying of Coroba slices. J. Food Process. Preserv. 33, 340–355 (2008). https://doi.org/10.1111/j.1745-4549.2008.00345.x

    Article  Google Scholar 

  41. Bingol, G.; Pan, Z.; Roberts, J.S.; Devres, Y.O.; Balaban, M.O.: Mathematical modeling of microwave-assisted convective heating and drying of grapes. Int. J. Agric. Biol. Eng. 1, 46–54 (2008). https://doi.org/10.3965/j.issn.1934-6344.2008.02.046-054

    Article  Google Scholar 

  42. Silva, M.A.: Application to drying of porous media. Dry. Technol. Int. J. 18, 601–624 (2000). https://doi.org/10.1080/07373930008917728

    Article  Google Scholar 

  43. Khalloufi, S.; Almeida-rivera, C.; Bongers, P.: A fundamental approach and its experimental validation to simulate density as a function of moisture content during drying processes. J. Food Eng. 97, 177–187 (2010). https://doi.org/10.1016/j.jfoodeng.2009.10.007

    Article  Google Scholar 

  44. Márquez, C.A.; Michelis, A.D.: Comparison of drying kinetics for small fruits with and without particle shrinkage considerations. Food Bioprocess. Technol. 4, 1212–1218 (2011). https://doi.org/10.1007/s11947-009-0218-7

    Article  Google Scholar 

  45. Schössler, K.; Jäger, H.; Knorr, D.: Effect of continuous and intermittent ultrasound on drying time and effective diffusivity during convective drying of apple and red bell pepper. J. Food Eng. 108, 103–110 (2012). https://doi.org/10.1016/j.jfoodeng.2011.07.018

    Article  Google Scholar 

  46. Kaleta, A.; Górnicki, K.; Winiczenko, R.; Chojnacka, A.: Evaluation of drying models of apple (var. Ligol) dried in a fluidized bed dryer. Energy Convers. Manag. 67, 179–185 (2013). https://doi.org/10.1016/j.enconman.2012.11.011

    Article  Google Scholar 

  47. Curcio, S.; Aversa, M.: Influence of shrinkage on convective drying of fresh vegetables: a theoretical model. J. Food Eng. 123, 36–49 (2014). https://doi.org/10.1016/j.jfoodeng.2013.09.014

    Article  Google Scholar 

  48. Gulati, T.; Datta, A.K.: Mechanistic understanding of case-hardening and texture development during drying of food materials. J. Food Eng. 166, 119–138 (2015). https://doi.org/10.1016/j.jfoodeng.2015.05.031

    Article  Google Scholar 

  49. Rosa, D.P.; Cantú-Lozano, D.; Luna-Solano, G.; Polachini, T.C.; Telis-Romero, J.: Modelagem matemática da cinética de secagem de semente de laranja. Cienc. e Agrotecnologia. 39, 291–300 (2015). https://doi.org/10.1590/S1413-70542015000300011

    Article  Google Scholar 

  50. Llave, Y.; Takemori, K.; Fukuoka, M.; Takemori, T.; Tomita, H.; Sakai, N.: Mathematical modeling of shrinkage deformation in eggplant undergoing simultaneous heat and mass transfer during convection-oven roasting. J. Food Eng. 178, 124–136 (2016). https://doi.org/10.1016/j.jfoodeng.2016.01.013

    Article  Google Scholar 

  51. Alean, J.; Chejne, F.; Rojano, B.: Degradation of polyphenols during the cocoa drying process. J. Food Eng. 189, 99–105 (2016). https://doi.org/10.1016/j.jfoodeng.2016.05.026

    Article  Google Scholar 

  52. Defraeye, T.; Radu, A.: Convective drying of fruit: a deeper look at the air-material interface by conjugate modeling. Int. J. Heat Mass Transf. 108, 1610–1622 (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2017.01.002

    Article  Google Scholar 

  53. Deng, L.; Yang, X.; Mujumdar, A.S.; Zhao, J.; Wang, D.; Wang, J.; Gao, Z.; Xiao, H.: Red pepper (Capsicum annuum L.) drying: effects of different drying methods on drying kinetics, physicochemical properties, antioxidant capacity, and microstructure. Dry. Technol. (2017). https://doi.org/10.1080/07373937.2017.1361439

    Article  Google Scholar 

  54. Mahiuddin, M.; Khan, M.I.H.; Kumar, C.; Rahman, M.M.; Karim, M.A.: Shrinkage of food materials during drying: current status and challenges. Compr. Rev. Food Sci. Food Saf. 17, 1113–1126 (2018). https://doi.org/10.1111/1541-4337.12375

    Article  Google Scholar 

  55. Abdelouahab, N.B.; Gossard, A.; Rodts, S.; Coasne, B.; Coussot, P.: Convective drying of a porous medium with a paste cover. Eur. Phys. J. E 42, 11–14 (2019). https://doi.org/10.1140/epje/i2019-11829-4

    Article  Google Scholar 

  56. Zhou, X.; Ramaswamy, H.; Qu, Y.; Xu, R.; Wang, S.: Combined radio frequency-vacuum and hot air drying of kiwifruits: effect on drying uniformity, energy efficiency and product quality. Innov. Food Sci. Emerg. Technol. (2019). https://doi.org/10.1016/j.ifset.2019.102182

    Article  Google Scholar 

  57. Wei, S.; Wang, Z.; Wang, F.; Xie, W.; Chen, P.; Yang, D.: Simulation and experimental studies of heat and mass transfer in corn kernel during hot air drying. Food Bioprod. Process. 117, 360–372 (2019). https://doi.org/10.1016/j.fbp.2019.08.006

    Article  Google Scholar 

  58. Arul, G.P.; Shanmugam, S.; Veerappan, A.; Kumar, P.: Performance analysis of double-pass oscillating bed solar dryer for drying of non-parboiled paddy grains. Energy Sources Part A Recover. Util. Environ. Eff. 41, 418–426 (2019). https://doi.org/10.1080/15567036.2018.1520326

    Article  Google Scholar 

  59. Arul, G.P.; Shanmugam, S.; Veerappan, A.R.; Kumar, P.: Mathematical modeling and experimental studies on a dual inclined oscillating bed with double pass solar dryer for drying of non—parboiled paddy grains. Energy Sources Part A Recover. Util. Environ. Eff. (2019). https://doi.org/10.1080/15567036.2019.1670754

    Article  Google Scholar 

  60. Jingyun, L.; Huiling, Z.; Xiaoguang, Z.: Application and comparison of two mathematical models for simulating grain heat and mass transfer during in-bin drying. Int. J. Digit. Content Technol. Appl. 6, 200–208 (2012). https://doi.org/10.4156/jdcta.vol6.issue6.24

    Article  Google Scholar 

  61. Romdhana, H.; Lambert, C.; Goujot, D.; Courtois, F.: Model reduction technique for faster simulation of drying of spherical solid foods. J. Food Eng. 170, 125–135 (2015). https://doi.org/10.1016/j.jfoodeng.2015.09.021

    Article  Google Scholar 

  62. Tran, T.T.H.: Modelling of drying in packed bed by super heated steam. J. Mech. Eng. Res. Dev. 43, 135–142 (2020)

    Google Scholar 

  63. Albini, G.; Freire, F.B.; Freire, J.T.: Barley: effect of airflow reversal on fixed bed drying. Chem. Eng. Process. Process Intensif. 134, 97–104 (2018). https://doi.org/10.1016/j.cep.2018.11.001

    Article  Google Scholar 

  64. Koua, B.K.; Koffi, P.M.E.; Gbaha, P.: Evolution of shrinkage, real density, porosity, heat and mass transfer coefficients during indirect solar drying of cocoa beans. J. Saudi Soc. Agric. Sci. 18, 72–82 (2019). https://doi.org/10.1016/j.jssas.2017.01.002

    Article  Google Scholar 

  65. Madiouli, J.; Lecomte, D.; Nganya, T.; Chavez, S.; Sghaier, J.; Sammouda, H.: A method for determination of porosity change from shrinkage curves of deformable materials. Dry. Technol. 25, 621–628 (2007). https://doi.org/10.1080/07373930701227185

    Article  Google Scholar 

  66. Sghaier, J.; Messai, S.; Lecomte, D.; Belghith, A.: High temperature convective drying of a packed bed with humid air at different humidities. Am. J. Eng. Appl. Sci. 2, 61–69 (2013). https://doi.org/10.3844/ajeassp.2009.61.69

    Article  Google Scholar 

  67. Białobrzewski, I.; Zielinska, M.; Arun, S.M.; Markowski, M.: Heat and mass transfer during drying of a bed of shrinking particles—simulation for carrot cubes dried in a spout-fluidized-bed drier. Int. J. Heat Mass Transf. 51, 4704–4716 (2008). https://doi.org/10.1016/j.ijheatmasstransfer.2008.02.031

    Article  MATH  Google Scholar 

  68. Hashemi, G.; Mowla, D.; Kazemeini, M.: Moisture diffusivity and shrinkage of broad beans during bulk drying in an inert medium fluidized bed dryer assisted by dielectric heating. J. Food Eng. 92, 331–338 (2009). https://doi.org/10.1016/j.jfoodeng.2008.12.004

    Article  Google Scholar 

  69. Adegbie, S.K.; Kọrikọ, O.K.; Animasaun, I.L.: Melting heat transfer effects on stagnation point flow of micropolar fluid with variable dynamic viscosity and thermal conductivity at constant vortex viscosity. J. Niger. Math. Soc. 35, 34–47 (2016). https://doi.org/10.1016/j.jnnms.2015.06.004

    Article  MathSciNet  MATH  Google Scholar 

  70. Koriko, O.K.; Omowaye, A.J.; Animasaun, I.L.; Bamisaye, M.E.: Melting heat transfer and induced-magnetic field effects on the micropolar fluid flow towards stagnation point: boundary layer analysis. Int. J. Eng. Res. Afr. 29, 10–20 (2017)

    Article  Google Scholar 

  71. Motsa, S.S.; Animasaun, I.L.: Paired quasi-linearization analysis of heat transfer in unsteady mixed convection nanofluid containing both nanoparticles and gyrotactic microorganisms due to impulsive motion. J. Heat Transf. 138, 1–8 (2016). https://doi.org/10.1115/1.4034039

    Article  Google Scholar 

  72. Mahanthesh, B.; Shashikumar, N.S.; Gireesha, B.J.; Animasaun, I.L.: Effectiveness of Hall current and exponential heat source on unsteady heat transport of dusty TiO2-EO nanoliquid with nonlinear radiative heat. J. Comput. Des. Eng. 6, 551–561 (2019). https://doi.org/10.1016/j.jcde.2019.04.005

    Article  Google Scholar 

  73. Sandeep, N.; Animasaun, I.L.: Heat transfer in wall jet flow of magnetic-nanofluids with variable magnetic field. Alex. Eng. J. 56, 263–269 (2017). https://doi.org/10.1016/j.aej.2016.12.019

    Article  Google Scholar 

  74. Madiouli, J.; Sghaier, J.; Lecomte, D.; Sammouda, H.: Determination of porosity change from shrinkage curves during drying of food material To cite this version: HAL Id: hal-01688419 determination of porosity change from shrinkage curves during drying of food material. Food Bioprod. Process. 90(1), 43–51 (2012)

    Article  Google Scholar 

  75. Whitaker, S.: Improved constraints for the principle of local thermal equilibrium. Ind. Eng. Chem. Res. 30, 983–997 (1991). https://doi.org/10.1021/ie00053a022

    Article  Google Scholar 

  76. Messai, S.; Sghaier, J.; Belghith, A.: Mathematical modeling of a packed bed drying with humid air and superheated steam. J. Porous Media 14, 169–177 (2011). https://doi.org/10.1615/jpormedia.v14.i2.50

    Article  Google Scholar 

  77. Mihoubi, D.; Bellagi, A.: Modeling of heat and moisture transfers with stress-strain formation during convective air drying of deformable media. Heat Mass Transf. und Stoffuebertragung. 48, 1697–1705 (2012). https://doi.org/10.1007/s00231-012-1014-x

    Article  Google Scholar 

  78. van Meel, D.A.: Adiabatic convection batch drying with recirculation of air. Chem. Eng. Sci. 9, 36–44 (1958)

    Article  Google Scholar 

  79. Bahammou, Y.; Tagnamas, Z.; Lamharrar, A.; Idlimam, A.: Thin-layer solar drying characteristics of Moroccan horehound leaves (Marrubium vulgare L.) under natural and forced convection solar drying. Sol. Energy 188, 958–969 (2019). https://doi.org/10.1016/j.solener.2019.07.003

    Article  Google Scholar 

  80. Zhang, Y.; Hubler, M.: Role of early drying cracks in the shrinkage size effect of cement paste. J. Eng. Mech. 146, 04020128 (2020). https://doi.org/10.1061/(asce)em.1943-7889.0001861

    Article  Google Scholar 

  81. Janas, S.; Dzaomuho, P.; Verdin, E.; Jacquet, N.; Malumba, P.; Crine, M.; Bera, F.: Mathematical Modelization of Fixed-Bed Corn Drying and Experimental Validation. Elsevier, Amsterdam (2012)

    Google Scholar 

  82. Kandelousi, M.S.: Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition. Eur. Phys. J. Plus (2014). https://doi.org/10.1140/epjp/i2014-14248-2

    Article  Google Scholar 

  83. White, J.: CFD simulation of silica gel and water adsorbent beds used in adsorption cooling system (2012)

  84. Akpinar, E.K.: Drying of mint leaves in a solar dryer and under open sun: modelling, performance analyses. Energy Convers. Manag. 51, 2407–2418 (2010). https://doi.org/10.1016/j.enconman.2010.05.005

    Article  Google Scholar 

  85. Yang, W.; Zhang, J.; Cheng, H.: The study of flow characteristics of curved microchannel. Appl. Therm. Eng. 25, 1894–1907 (2005). https://doi.org/10.1016/j.applthermaleng.2004.12.001

    Article  Google Scholar 

  86. Gunhan, T.; Demir, V.; Hancioglu, E.; Hepbasli, A.: Mathematical modelling of drying of bay leaves. Energy Convers. Manag. 46, 1667–1679 (2005). https://doi.org/10.1016/j.enconman.2004.10.001

    Article  Google Scholar 

  87. Sheikholeslami, M.; Ganji, D.D.: Heat transfer improvement in a double pipe heat exchanger by means of perforated turbulators. Energy Convers. Manag. 127, 112–123 (2016). https://doi.org/10.1016/j.enconman.2016.08.090

    Article  Google Scholar 

  88. Hepbasli, A.; Akdemir, O.: Energy and exergy analysis of a ground source (geothermal) heat pump system. Energy Convers. Manag. 45, 737–753 (2004). https://doi.org/10.1016/S0196-8904(03)00185-7

    Article  Google Scholar 

  89. Prado, M.M.; Sartori, D.J.M.: Simultaneous heat and mass transfer in packed bed drying of seeds having a mucilage coating. Braz. J. Chem. Eng. 25, 39–50 (2008). https://doi.org/10.1590/S0104-66322008000100006

    Article  Google Scholar 

  90. Reddy, B.S.; Chakraverty, A.: Equilibrium moisture characteristics of raw and parboiled paddy, brown ride, and bran. Dry. Technol. 22, 837–851 (2004). https://doi.org/10.1081/DRT-120034266

    Article  Google Scholar 

  91. Sagar, V.R.; Kumar, P.S.: Recent advances in drying and dehydration of fruits and vegetables: a review. J. Food Sci. Technol. 47, 15–26 (2010)

    Article  Google Scholar 

  92. Banu, K.; Ismail, E.; Ertekin, F.K.: Modelling bulk density, porosity and shrinkage of quince during drying: the effect of drying method. J. Food Eng. 85, 340–349 (2008). https://doi.org/10.1016/j.jfoodeng.2007.07.030

    Article  Google Scholar 

  93. Kaya, A.; Aydin, O.; Demirtaş, C.: Drying kinetics of red delicious apple. Biosyst. Eng. 96, 517–524 (2007). https://doi.org/10.1016/j.biosystemseng.2006.12.009

    Article  Google Scholar 

  94. Moreira, R.; Figueiredo, A.; Sereno, A.: Shrinkage of apple disks during drying by warm air convection and freeze drying. Dry. Technol. 18, 279–294 (2000). https://doi.org/10.1080/07373930008917704

    Article  Google Scholar 

  95. Rungsiyopas, M.; Ruiz, T.: Modelling of the shape effect on the drying shrinkage of wet granular materials. Chem. Eng. Res. Des. 132, 295–302 (2018). https://doi.org/10.1016/j.cherd.2018.01.038

    Article  Google Scholar 

  96. Dehghannya, J.; Bozorghi, S.; Heshmati, M.K.: Low temperature hot air drying of potato cubes subjected to osmotic dehydration and intermittent microwave: drying kinetics, energy consumption and product quality indexes. Heat Mass Transf. und Stoffuebertragung. 54, 929–954 (2018). https://doi.org/10.1007/s00231-017-2202-5

    Article  Google Scholar 

  97. Aprajeeta, J.; Gopirajah, R.; Anandharamakrishnan, C.: Shrinkage and porosity effects on heat and mass transfer during potato drying. J. Food Eng. 144, 119–128 (2015). https://doi.org/10.1016/j.jfoodeng.2014.08.004

    Article  Google Scholar 

  98. Mariela, M.; Pacheco, J.G.: Shrinkage phenomenon in cherries during osmotic dehydration. Ann. Food Sci. Technol. 21, 19–30 (2020)

    Google Scholar 

  99. Mayor, L.; Sereno, A.M.: Modelling shrinkage during convective drying of food materials: a review. J. Food Eng. 61, 373–386 (2004). https://doi.org/10.1016/S0260-8774(03)00144-4

    Article  Google Scholar 

  100. Guine, R.P.F.: Influence of drying method on density and porosity of pears. Food Bioprod. Process. 84, 179–185 (2006). https://doi.org/10.1205/fbp.05106

    Article  Google Scholar 

  101. Srikiatden, J.; Roberts, J.S.: Predicting moisture profiles in potato and carrot during convective hot air drying using isothermally measured effective diffusivity. J. Food Eng. 84, 516–525 (2008). https://doi.org/10.1016/j.jfoodeng.2007.06.009

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to express their sincere appreciation to the research team that we are a part of and to the Energy and Thermal Transfers Laboratory, Faculty of Sciences of Tunis for their assistance in laboratory experiments.

Author information

Authors and Affiliations

  1. Research Laboratory of Thermal and Thermodynamic of Industrial Processes (LRTTPI), National Engineering School of Monastir, University of Monastir, Monastir, Tunisia

    Amal Kraiem, Jamel Madiouli & Jalila Sghaier

  2. Department of Mechanical Engineering, ISSAT, University of Kairouan, Kairouan, Tunisia

    Jamel Madiouli

  3. Chemical Engineering Department, King Khalid University, PO Box 394, Abha, 61411, Kingdom of Saudi Arabia

    Ihab Shigidi

Authors
  1. Amal Kraiem
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jamel Madiouli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jalila Sghaier
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ihab Shigidi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amal Kraiem.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kraiem, A., Madiouli, J., Sghaier, J. et al. Significance of Bed Shrinkage on Heat and Mass Transfer During the Transport Phenomenon of Humid Air. Arab J Sci Eng 46, 6085–6099 (2021). https://doi.org/10.1007/s13369-021-05444-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-021-05444-7

Keywords

Search

Navigation