Numerical simulation of forced convection in a duct subjected to microwave heating
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DOI: 10.1007/s002310060105y
 Cite this article as:
 Zhu, J., Kuznetsov, A.V. & Sandeep, K.P. Heat Mass Transfer (2007) 43: 255. doi:10.1007/s002310060105y
Abstract
In this paper, forced convection in a rectangular duct subjected to microwave heating is investigated. Three types of nonNewtonian 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 threedimensional 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)
Superscripts
 τ

instantaneous value
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