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Effect of Shrinkage in Convective Drying of Spherical Food Material: A Numerical Solution

  • Research Article-Mechanical Engineering
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Abstract

A computational model is generated to analyse the influence of shrinkage on convective drying problems. The object considered here is cranberry which is assumed as 100% spherical. The drying air temperatures were considered from 313 to 348 K. There were four models used in this study, namely one-dimensional models without and with shrinkage, two-dimensional models without and with shrinkage. A finite difference scheme was used to discretize the heat and mass transport equations. Four separate computer codes were written in MATLAB to solve the discretized equations. The Arrhenius model is used to couple the heat and moisture transport equations and solve them simultaneously. The Gauss–Seidel iterative method was used to solve the equations. An empirical shrinkage model was used to calculate the shrinkage effect. The temperature and moisture distributions of cranberry were obtained with drying time. Moisture distributions without and with shrinkage results were calculated and compared to identify the effect of shrinkage. The cranberry lost a maximum of 35% of its size during drying. There was not much variation found in the results between 1- and 2D models. The maximum difference in centre moisture content of cranberry without shrinkage model was 56%, and the difference in mean moisture content was 49.2%. The numerical outcomes were validated with experimental data, and the model with shrinkage was a good fit with them than without shrinkage. Therefore, shrinkage needs to be considered in convective drying phenomena.

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Abbreviations

c :

Specific heat (kJ/kgK)

db :

Dry basis

dr :

Radial step (m)

D :

Moisture diffusivity (m2/s)

D 0 :

Pre-exponential factor (m2/s)

h :

Heat transfer coefficients (W/m2K)

h m :

Mass transfer coefficient (m/s)

k :

Thermal conductivity (W/mK)

Le:

Lewis number

M, MC :

Moisture content (kg/kg of db)

n :

Grid points

r, R :

Radius (m)

Δr :

Radial step

t :

Time (s)

Δt :

Time step (s)

T :

Temperature (K)

V :

Volume (m3)

x, y :

Coordinates

α :

Thermal diffusivity (m2/s)

ϕ :

Polar angle

Δϕ :

Increments in polar space

ρ :

Density (kg/m3)

Ɵ :

Azimuthal angle

a :

Air

d :

Dry air

i :

Grid in radial direction

j :

Grid in polar direction

n :

Property at surface

old:

Property at earlier time step

va:

Property of vapour in air

0:

Initial condition

References

  1. Mujumdar, A.M.: Handbook of Industrial Drying, 3rd edn. Taylor and Francis group, CRC Press, Boca Raton, FL (2006)

    Book  Google Scholar 

  2. Yuill, D.P., Fenton, D.L., Cramm, K.P., Enck, H.J., Fisher, D.S., Murphy, W.E.: Chapter 19, Thermal Properties of Foods. ASHRAE Handbook Refrigeration, SI, 1791 Tullie Circle, N.E., Atlanta, GA 30329, (2018). www.ashrae.org

  3. Jayapragasam, P.; Bideau, P.L.; Loulou, T.: Luikov’s analytical solution with complex eigenvalues in intensive drying. Transp. Porous Med. 130, 923–946 (2019). https://doi.org/10.1007/s11242-019-01348-1

    Article  MathSciNet  Google Scholar 

  4. Castro, A.M.; Mayorga, E.Y.; Moreno, F.L.: Mathematical modelling of convective drying of feijoa (Acca sellowiana Berg) slices. J. Food Eng. 252, 44–52 (2019). https://doi.org/10.1016/j.jfoodeng.2019.02.007

    Article  Google Scholar 

  5. Dhalsamant, K.; Tripathy, P.P.; Shrivastava, S.L.: Heat transfer analysis during mixed-mode solar drying of potato cylinders incorporating shrinkage: numerical simulation and experimental validation. Food Bioprod. Process. 109, 107–121 (2018). https://doi.org/10.1016/j.fbp.2018.03.005

    Article  Google Scholar 

  6. Defraeye, T.; Nicolaï, B.; Mannes, D.; Aregawi, W.; Verboven, P.; Derome, D.: Probing inside fruit slices during convective drying by quantitative neutron imaging. J. Food Eng. 178, 198–202 (2016). https://doi.org/10.1016/j.jfoodeng.2016.01.023

    Article  Google Scholar 

  7. Abhay, L.; Chandramohan, V.P.; Raju, V.R.K.; Anil, K.: Development of Indirect Type Solar Dryer and Experiments for Estimation of Drying Parameters of Apple and Watermelon. Therm Sci Eng Prog 16, 100477 (2020). https://doi.org/10.1016/j.tsep.2020.100477

    Article  Google Scholar 

  8. Beyhaghi, S.; Xu, Z.; Pillai, K.M.: Achieving the inside–outside coupling during network simulation of isothermal drying of a porous medium in a turbulent flow. Transp. Porous Med. 114, 823–842 (2016). https://doi.org/10.1007/s11242-016-0746-3

    Article  MathSciNet  Google Scholar 

  9. Arunsandeep, G.; Abhay, L.; Chandramohan, V.P.; Raju, V.R.K.; Reddy, S.K.: A numerical model for drying of spherical object in an indirect type solar dryer and estimating the drying time at different moisture level and air temperature. Int. J. Green Energy 15(3), 189–200 (2018). https://doi.org/10.1080/15435075.2018.1433181

    Article  Google Scholar 

  10. Lamrani, B.; Draoui, A.: Modelling and simulation of a hybrid solar-electrical dryer of wood integrated with latent heat thermal energy storage system. Therm. Sci. Eng. Prog. 18, 100545 (2020). https://doi.org/10.1016/j.tsep.2020.100545

    Article  Google Scholar 

  11. Sychevskii, V.A.: Heat and mass transfer in convective wood-drying plants. J. Eng. Phys. Thermophy. 91, 705–711 (2018). https://doi.org/10.1007/s10891-018-1793-0

    Article  Google Scholar 

  12. Ambethkar, V.; Srivastava, M.K.: Numerical study of transient 2-D compressible flow with heat and mass transfer using the finite volume method. Int. J. Comput. Methods Eng. Sci. Mech. 19(1), 31–41 (2017). https://doi.org/10.1080/15502287.2017.1366597

    Article  MathSciNet  Google Scholar 

  13. Süfer, Ö.; Palazoğlu, T.K.: A study on hot-air drying of pomegranate. J. Therm. Anal. Calorim. 137, 1981–1990 (2019). https://doi.org/10.1007/s10973-019-08102-1

    Article  Google Scholar 

  14. Chandramohan, V.P.: Experimental analysis and simultaneous heat and moisture transfer with coupled CFD model for convective drying of moist object. Int. J. Comput. Methods Eng. Sci. Mech. 17(1), 59–71 (2016). https://doi.org/10.1080/15502287.2016.1147506

    Article  MathSciNet  Google Scholar 

  15. Thiery, J.; Keita, E.; Rodts, S.; Murias, D.C.; Kodger, T.; Pegoraro, A.; Coussot, P.: Drying kinetics of deformable and cracking nano-porous gels. Eur. Phys. J. E. 39, 117 (2016). https://doi.org/10.1140/epje/i2016-16117-3

    Article  Google Scholar 

  16. Abhay, B.L.; Chandramohan, V.P.; Raju, V.R.K.: Energy and exergy analysis on drying of banana using indirect type natural convection solar dryer. Heat Transf. Eng. 41(6–7), 551–561 (2020). https://doi.org/10.1080/01457632.2018.1546804

    Article  Google Scholar 

  17. 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(5), 1113–1126 (2018). https://doi.org/10.1111/1541-4337.12375

    Article  Google Scholar 

  18. Chandramohan, V.P.; Talukdar, P.: Three dimensional numerical modeling of simultaneous heat and moisture transfer in a moist object subjected to convective drying. Int. J. Heat Mass Transf. 53, 4638–4650 (2010). https://doi.org/10.1016/j.ijheatmasstransfer.2010.06.029

    Article  MATH  Google Scholar 

  19. Arunsandeep, G.; Chandramohan, V.P.: Numerical solution for determining the temperature and moisture distribution of rectangular, cylindrical and spherical objects during drying. J. Eng. Phys. Thermophys. 91(4), 895–906 (2018). https://doi.org/10.1007/s10891-018-1814-z

    Article  Google Scholar 

  20. Zhang, L., Bhatti, M.M., Michaelides, E.E.: Electro-magnetohydrodynamic flow and heat transfer of a third-grade fluid using a Darcy–Brinkman–Forchheimer model. Int. J. Numer. Methods Heat Fluid Flow 0961–5539 (2020). https://www.emerald.com/insight/0961-5539.htm

  21. Afzal, Q.; Akram, S.; Ellahi, R., et al.: Thermal and concentration convection in nanofluids for peristaltic flow of magneto couple stress fluid in a nonuniform channel. J. Therm. Anal. Calorim. 144, 2203–2218 (2021). https://doi.org/10.1007/s10973-020-10340-7

    Article  Google Scholar 

  22. Ochoa, M.R.; Kesseler, A.G.; Pirone, B.N.; Marquez, C.A.; De Michelis, A.: Analysis of shrinkage phenomenon of whole sweet cherry fruits (Prunus avium) during convective dehydration with very simple models. J. Food Eng. 79(2), 657–661 (2007). https://doi.org/10.1016/j.jfoodeng.2006.02.025

    Article  Google Scholar 

  23. Fernando, W.J.N.; Ahmad, A.L.; Shukor, S.R.A.; Lok, Y.H.: A model for constant temperature drying rates of case hardened slices of papaya and garlic. J. Food Eng. 88, 229–238 (2008). https://doi.org/10.1016/j.jfoodeng.2008.02.008

    Article  Google Scholar 

  24. Zielinska, M.; Ropelewska, E.; Zapotoczny, P.: Effects of freezing and hot air drying on the physical, morphological and thermal properties of cranberries (Vaccinium macrocarpon). Food Bioprod. Process. 110, 40–49 (2018). https://doi.org/10.1016/j.fbp.2018.04.006

    Article  Google Scholar 

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Acknowledgements

The authors thank the Department of Mechanical Engineering, NIT Warangal, India, for financing this work. The approved number is: NITW/MED/Head/2015/408 dated 3rd December 2015.

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Authors and Affiliations

  1. Mechanical Engineering Department, National Institute of Technology Warangal, Warangal, Telangana, 506004, India

    Mukul Kumar Goyal, Saurabh Avinash Ture & V. P. Chandramohan

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  1. Mukul Kumar Goyal
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  2. Saurabh Avinash Ture
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  3. V. P. Chandramohan
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Correspondence to V. P. Chandramohan.

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Goyal, M.K., Ture, S.A. & Chandramohan, V.P. Effect of Shrinkage in Convective Drying of Spherical Food Material: A Numerical Solution. Arab J Sci Eng 46, 12283–12298 (2021). https://doi.org/10.1007/s13369-021-05957-1

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  • DOI: https://doi.org/10.1007/s13369-021-05957-1

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