Three Dimensional (3D) Modeling of Heat and Mass Transfer during Microwave Drying of Potatoes

Huacheng Zhu1,2,Tushar Gulati1 and Ashim K. Datta1

1Department of Biological and Environmental Engineering, Cornell University, Ithaca, NY 2 Institute of Applied Electromagnetics, Sichuan University, Chengdu, China

Microwave drying of fruits and vegetables has been found to result in large textural changes in the product such as puffing, crack formation and even burning due to the inhomogeneous heating of the microwaves.

Microwave drying of potatoes is a complex interplay of mass, momentum and energy transport.

Three phases are considered in the system: solid (skeleton), liquid (water) and gas (water vapor and air).

Concentration of different species was solved for using the Transport of Dilute Species module (for liquid water) and Maxwell-Stefan Diffusion model (for vapor and air) together with Darcy Law (to calculate Gas Pressure).

Microwave oven worked in 10% power level (Cycle Way). Shrinkage effects have been ignored.

Modeling Framework

Potatoes treated as a porous material

Transport Model

• Conservation of energy – Bulk flow – Conduction – Phase change

• Conservation of mass – Water: bulk flow, capillary flow

and phase change – Gas (air, vapor): bulk flow phase

change, binary diffusion

• Conservation of momentum – Darcy’s flow

The microwave oven works in a cycle way

Total sample’s average water saturation with drying time

Tushar Gulati 175 Riley Robb Hall

Email: th237@cornell.edu Ph: 607-255-2871

Ashim Datta 208 Riley Robb Hall

Email: akd1@cornell.edu Ph: 607-255-2482

Conclusions

A mechanistic approach that predicts the microwave drying process of potatoes has been developed.

The model could aid in predicting key quality attributes associated with the microwave drying process.

Geometry & COMSOL Implementation

Results

Boundary Conditions - Forced convection heat

transfer - Moisture loss through

evaporation

COMSOL Implementation - Electromagnetic - Transport of Dilute Species - Transport of Concentrated Species - Heat Transfer in Fluids - Darcy Law

The coupled Electromagnetic and Transport Model developed above was solved in COMSOL Multiphysics 4.3a to obtain the moisture content and mass fraction of vapor.

Calculated surface mass fraction of vapor in the first microwave heating cycle

0s 2s 7s 12s 17s 22s

Calculated surface water saturation with drying time

0s 44s 88s 132s 176s 220s

Microwave oven model GE JES738WJ02

Potato Sample size 1cm³

Introduction

Electromagnetic Model

• Maxwell’s Equations – Faraday’s Law of Induction – Ampere’s Law – Gauss Law for electricity – Gauss Law for magnetism

• Power Dissipation – Poynting Theorm

Governing Equations

¶cw

¶t+ v

w- v

s( ) ×Ñcw

+ cwÑ×v

w= Ñ× D

wÑc

w( ) - I

Conservation of Mass

Water:

¶cv

¶t+ v

g- v

s( ) ×Ñcg

+ cgÑ×v

g= Ñ× jS

g

C2

rg

MaM

vD

eff ,gÑx

v

æ

èçç

ö

ø÷÷

+ I

¶cg

¶t+ v

g- v

s( ) ×Ñcg

+ cgÑ×v

g= IGas:

Vapor:

¶

¶tå

i=s,w,v,a

cic

p,iT( )é

ëê

ù

ûú+ å

i=w,v,a

vi- v

s( ) ×Ñ cic

p,iT( ) + å

i=w,v,a

cic

p,iT Ñ×v

i( ) - cp,w

TÑ× DcÑc

w( ) = Ñ keffÑT( ) - lI

Conservation of Energy

Darcy’s Law: (water and gas)

vi- v

s= -

kik

r ,i

Sif

im

i

ÑP

Conservation of Momentum

Maxwell’s Equation

0 *

( ) 0

0

j

j

E H

H E

E

H

Faraday’s Law of Induction:

Ampere’s Law:

Gauss Law for electricity:

Gauss Law for magnetism:

Poynting Theorm:

0

1( , ) ''( *)

2P T x E E

Power Dissipation Huacheng Zhu

175 Riley Robb Hall Email: hz78@cornell.edu

Ph: 607-255-2871