Abstract

In the manufacture of propellants, drying is a crucial step in which liquid solvents are extracted from the propellants' microstructure in order to impart the desired physical and chemical qualities. Therefore, the prediction of the effective diffusivity, a fundamental characteristic defining the rate of solvent transfer during vacuum drying of propellants, is particularly valuable for determining optimal drying conditions in the operation of drying systems and optimizing the drying process. This paper presents an elegant way to estimate the lumped value of the effective diffusivity for the mass transfer process in the course of drying propellants. Analytical solutions for the effective diffusivity at planar, cylindrical, and spherical geometries are obtained. These solutions are used to investigate effects of the propellant geometry on the drying process. Using experimental data for the transient moisture content, it becomes possible to determine geometries, which should be preferred for a given function of the mass flux.

References

1.
Figiel
,
A.
, and
Michalska
,
A.
,
2016
, “
Overall Quality of Fruits and Vegetables Products Affected by the Drying Processes With the Assistance of Vacuum-Microwaves
,”
Int. J. Mol. Sci.
,
18
(
1
), p.
71
.10.3390/ijms18010071
2.
Puttalingappa
,
Y. J.
,
Natarajan
,
V.
,
Varghese
,
T.
, and
Naik
,
M.
,
2022
, “
Effect of Microwave-Assisted Vacuum Drying on the Drying Kinetics and Quality Parameters of Moringa Oleifera Leaves
,”
J. Food Process Eng.
,
45
(
8
), p.
14054
.10.1111/jfpe.14054
3.
Kim
,
S. S.
, and
Bhowmik
,
S. R.
,
1995
, “
Effective Moisture Diffusivity of Plain Yoghurt Undergoing Microwave Vacuum Drying
,”
J. Food Eng.
,
24
(
1
), pp.
137
148
.10.1016/0260-8774(94)P1614-4
4.
Tikhonov
,
A. N.
, and
Samarskii
,
A. A.
,
1963
,
Equations of Mathematical Physics
,
Pergamon Press
, New York.
5.
Crank
,
J.
,
1975
,
The Mathematics of Diffusion
,
Oxford University Press
, Oxford, UK.
6.
Deen
,
W. M.
,
1998
,
Analysis of Transport Phenomena
,
Oxford University Press
, Oxford, UK.
7.
Kulish
,
V. V.
,
2010
,
Partial Differential Equations
,
Pearson
,
Singapore
.
8.
Colton
,
D.
,
Ewing
,
R.
, and
Rundell
,
W.
,
1992
,
Inverse Problems in Partial Differential Equations
,
SIAM
,
Philadelphia, PA
.
9.
Engl
,
H. W.
,
Rundell
,
W.
, eds.,
1994
,
Inverse Problems in Diffusion Processes
,
Philadelphia
,
SIAM, Philadelphia, PA
.
10.
Isakov
,
V.
,
1998
,
Inverse Problems in Partial Differential Equations
,
Springer
,
New York
.
11.
Kirsch
,
A.
,
1996
,
An Introduction to the Mathematical Theory of Inverse Problems
,
Springer
,
Berlin
.
12.
Tarantola
,
A.
,
2005
,
Inverse Problem Theory Methods Model Parameter Estimation
, SIAM, Philadelphia.
13.
Aster
,
R. C.
,
Borchers
,
B.
, and
Thurber
,
C. H.
,
2019
,
Parameter Estimation and Inverse Problems
, 3rd ed., SIAM, Philadelphia, PA.
14.
Vogel
,
C.
,
2002
,
Computational Methods for Inverse Problems
,
SIAM
,
Philadelphia, PA
.
15.
Lagarias
,
J. C.
,
Reeds
,
J. A.
,
Wright
,
M. H.
, and
Wright
,
P. E.
,
1998
, “
Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions
,”
SIAM J. Optim.
,
9
(
1
), pp.
112
147
.10.1137/S1052623496303470
16.
Abramowitz
,
M.
, and
Stegun
,
I. A.
,
1964
,
Handbook of Mathematical Functions
,
Dover
,
New York
.
17.
Poletkin
,
K.
, and
Kulish
,
V.
,
2012
, “
A Generalised Relation Between the Local Values of Temperature and the Corresponding Heat Flux in a One-Dimensional Semi-Infinite Domain With the Moving Boundary
,”
Int. J. Heat Mass Transfer
,
55
(
23–24
), pp.
6595
6599
.10.1016/j.ijheatmasstransfer.2012.06.067
18.
Kulish
,
V. V.
, and
Lage
,
J. L.
,
2000
, “
Diffusion Within a Porous Medium With Randomly Distributed Heat Sinks
,”
Int. J. Heat Mass Transfer
,
43
(
18
), pp.
3481
3496
.10.1016/S0017-9310(99)00385-3
19.
Kulish
,
V.
,
2020
, “
A Non-Field Analytical Method for Solving Energy Transport Equations
,”
ASME J. Heat Mass Transfer-Trans. ASME
,
142
(
4
), p.
042102
.10.1115/1.4046301
20.
Kulish
,
V. V.
, and
Lage
,
J. L.
,
2000
, “
Fractional-Diffusion Solutions for Transient Local Temperature and Heat Flux
,”
ASME J. Heat Mass Transfer-Trans. ASME
,
122
(
2
), pp.
372
376
.10.1115/1.521474
21.
Oldham
,
K. B.
, and
Spanier
,
J.
,
1974
,
The Fractional Calculus
,
Academic Press
,
New York & London
.
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