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Numerical simulation of forced convection in a duct subjected to microwave heating

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Abstract

In this paper, forced convection in a rectangular duct subjected to microwave heating is investigated. Three types of non-Newtonian liquids flowing through the duct are considered, specifically, apple sauce, skim milk, and tomato sauce. A finite difference time domain method is used to solve Maxwell’s equations simulating the electromagnetic field. The three-dimensional temperature field is determined by solving the coupled momentum, energy, and Maxwell’s equations. Numerical results show that the heating pattern strongly depends on the dielectric properties of the fluid in the duct and the geometry of the microwave heating system.

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Abbreviations

A :

area (m2)

C p :

specific heat capacity (J/(kg K))

c :

phase velocity of the electromagnetic propagation wave (m/s)

E :

electric field intensity (V/m)

f :

frequency of the incident wave (Hz)

h :

effective heat transfer coefficient (W/(m2 K))

H :

magnetic field intensity (A/m)

L :

standard deviation of temperature (°C)

k :

thermal conductivity (W/(m K))

m :

fluid consistency coefficient, (Pa sn)

n :

flow behavior index

N t :

number of time steps

p :

pressure (Pa)

q :

electromagnetic heat generation intensity (W/m3)

Q :

volume flow rate (m3/s)

T :

temperature (°C)

t :

time (s)

tan δ:

loss tangent

w :

velocity component in the z direction (m/s)

W :

width of the cavity (m)

ZTE :

wave impedance (Ω)

η:

apparent viscosity (Pa s)

ε:

electric permittivity (F/m)

ɛ′:

dielectric constant

ɛ′′:

effective loss factor

λ g :

wave length in the cavity (m)

μ:

magnetic permeability (H/m)

ρ:

density (kg/m3)

σ:

electric conductivity (S/m)

τ:

instantaneous value

∞:

ambient condition

0:

free space, air

inc:

incident plane

in:

inlet

x, y, z :

coordinate system of the applicator

X, Y, Z :

coordinate system of the microwave cavity

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Acknowledgements

The authors acknowledge with gratitude a USDA grant that provided support for this work and the assistance of the Food Rheology Laboratory at North Carolina State University. The calibrations of the fluid consistency coefficients and the flow behavior indexes for the non-Newtonian liquids considered in this study by Ms. S. Ramsey are greatly appreciated.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC, 27695-7910, USA

    J. Zhu & A. V. Kuznetsov

  2. Department of Food Science, North Carolina State University, Raleigh, NC, 27695-7624, USA

    K. P. Sandeep

Authors
  1. J. Zhu
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  2. A. V. Kuznetsov
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  3. K. P. Sandeep
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Corresponding author

Correspondence to A. V. Kuznetsov.

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Zhu, J., Kuznetsov, A.V. & Sandeep, K.P. Numerical simulation of forced convection in a duct subjected to microwave heating. Heat Mass Transfer 43, 255–264 (2007). https://doi.org/10.1007/s00231-006-0105-y

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  • DOI: https://doi.org/10.1007/s00231-006-0105-y

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