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

First Online: 10 March 2006 Received: 14 February 2005 Accepted: 06 February 2006 DOI :
10.1007/s00231-006-0105-y

Cite this article as: Zhu, J., Kuznetsov, A.V. & Sandeep, K.P. Heat Mass Transfer (2007) 43: 255. doi:10.1007/s00231-006-0105-y
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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.

List of symbols A area (m^{2} )

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/(m^{2} K))

H magnetic field intensity (A/m)

L standard deviation of temperature (°C)

k thermal conductivity (W/(m K))

m fluid consistency coefficient, (Pa s^{n} )

n flow behavior index

N _{t} number of time steps

p pressure (Pa)

q electromagnetic heat generation intensity (W/m^{3} )

Q volume flow rate (m^{3} /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)

Z_{TE} wave impedance (Ω)

Greek symbols 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/m^{3} )

σ electric conductivity (S/m)

Subscripts ∞ 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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Authors and Affiliations 1. Department of Mechanical and Aerospace Engineering North Carolina State University Raleigh USA 2. Department of Food Science North Carolina State University Raleigh USA