Nonintrusive measurements of the internal heat transfer coefficient in the core of a randomly packed bed of uniform spherical particles are made. Under steady, fully-developed flow the spherical particles are subjected to a step-change in volumetric heat generation rate via induction heating. The fluid temperature response is measured. The internal heat transfer coefficient is determined by comparing the results of a numerical simulation based on volume averaging theory (VAT) with the experimental results. The only information needed is the basic material and geometric properties, the flow rate, and the fluid temperature response data. The computational procedure alleviates the need for solid and fluid phase temperature measurements within the porous medium. The internal heat transfer coefficient is determined in the core of a packed bed, and expressed in terms of the Nusselt number, over a Reynolds number range of 20 to 500. The Nusselt number and Reynolds number are based on the VAT scale hydraulic diameter, $dh=4ɛ/S$. The results compare favorably to those of other researchers and are seen to be independent of particle diameter. The success of this method, in determining the internal heat transfer coefficient in the core of a randomly packed bed of uniform spheres, suggests that it can be used to determine the internal heat transfer coefficient in other porous media.

## References

1.
Kays
,
W. M.
, and
London
,
A. L.
, 1950, “
Heat Transfer and Flow Friction Characteristics of Some Compact Heat Exchanger Surfaces, Part 1—Test System and Procedure
,”
Trans. ASME
,
72
, pp.
1075
1085
.
2.
Kays
,
W. M.
, and
London
,
A. L.
, 1984,
Compact Heat Exchangers
,
McGraw-Hill
,
New York
.
3.
Hausen
,
H.
, 1929, “
Theory of Heat Exchange in Regenerators
,”
Zeitschrift fur Angewandte Mathematik und Mechanik
,
9
, pp.
173
200
.
4.
Schumann
,
T. E. W.
, 1929, “
Heat Transfer: A Liquid Flowing Through a Porous Prism
,”
J. Franklin Inst.
,
28
, pp.
405
416
.
5.
Locke
,
G. L.
, 1950, “
Heat Transfer and Flow Friction Characteristics of Porous Solids
,” Technical Report TR No.10,
Stanford University
, California.
6.
Kohlmayer
,
G. F.
, 1968, “
An Indirect Curve Matching Method for Transient Matrix Heat-Transfer Testing in the Low NTU-Range
,”
Int. J. Heat Mass Transfer
,
14
, pp.
567
581
.
7.
Kohlmayer
,
G. F.
, 1968, “
Extension of Maximum Slope Method to Arbitrary Upstream Fluid Temperature Change
,”
Trans. ASME J. Heat Transfer
,
90
, pp.
130
134
.
8.
Rodriguez
,
J. I.
, and
Mills
,
A. F.
, 1990, “
Analysis of the Single-Blow Transient Testing Technique for Perforated Plate Heat Exchangers
,”
Int. J. Heat Mass Transfer
,
33(9)
, pp.
1969
1976
.
9.
Liang
,
C. Y.
, and
Yang
,
W. J.
, 1975, “
Modified Single-Blow Technique for Performance Evaluation on Heat Transfer Surfaces
,”
J. Heat Transfer
,
97
, pp.
16
21
.
10.
Stang
,
J. H.
, and
Bush
,
J. E.
, 1974, “
The Periodic Method for Testing Compact Heat Exchanger Surfaces
,”
J. Eng. Power
,
96A
(
2
), pp.
87
94
.
11.
Younis
,
L. B.
, and
Viskanta
,
R.
, 1993, “
Experimental Determination of the Volumetric Heat Transfer Coefficient Between Stream of Air and Ceramic Foam
,”
Int. J. Heat Mass Transfer
,
36(6)
, pp.
1425
1434
.
12.
Nie
,
X.
,
Besant
,
R. W.
,
Evitts
,
R. W.
, and
Bolster
,
J.
, 2011, “
A New Technique to Determine Convection Coefficients with Flow Through Particle Beds
,”
Trans. ASME J. Heat Transfer
,
133
(
4
), p.
041601
.
13.
Jones
,
S.
, and
Catton
,
I.
, 1998, “
Non-Intrusive Heat Transfer Coefficient Determination in Highly Porous Metal/Ceramic Foams
,” HTD-Vol. 361-5, Proceedings of the ASME Heat Transfer Division, ASME, Vol. 5.
14.
Rhee
,
S. J.
, 1977, “
Natural Convection Heat Transfer in Beds of Inductively Heat Particles
,” M.S. thesis, University of California, Los Angeles, pp.
23
25
.
15.
Somerton
,
C. W.
, 1982, “
Natural Convection and Boiling in Porous Media
,” Ph.D. thesis, University of California, Los Angeles, pp.
50
–53, 140–
142
.
16.
Cherng
,
J. C.
, 1978, “
Effect of Bottom Cooling on Natural Convection in Beds of Inductively Heated Particles
,” M.S. thesis, University of California, Los Angeles.
17.
Mills
,
A. F.
, 1999,
Heat Transfer
,
Prentice-Hall
,
.
18.
Incropera
,
F. P.
,
Dewitt
,
D. P.
,
Lavine
,
A.
, and
Bergman
,
T. L.
, 2007,
Fundamentals of Heat and Mass Transfer
,
John Wiley & Sons
,
Hoboken, NJ
.
19.
Benenati
,
R. F.
, and
Brosilow
,
C. B.
, 1962, “
Void Fraction Distribution in Beds of Spheres
,”
AIChE J.
8
(
3
), pp.
359
361
.
20.
H.
Martin
, 1978, “
Low Peclet Number Particle-to-Fluid Heat and Mass Transfer in Packed Beds
,”
Chem. Eng. Sci.
,
33
, pp.
913
919
.
21.
Achenbach
,
E.
, 1995, “
Heat and Flow Characteristics of Packed Beds
,”
Exp. Therm. Fluid Sci.
,
10
, pp.
17
27
.
22.
Ziółkowska
,
I.
, and
Ziółkowski
,
D.
, 1988, “
Fluid Flow Inside Packed Beds
,”
Chem. Eng. Process
,
23
, pp.
137
164
.
23.
Schlunder
,
E. U.
, 1978, “
Transport Phenomena in Packed Bed Reactors
,”
Chemical Reaction Engineering Reviews-Houston, American Chemical Society Symposium Series
,
D
,
Luss
and
V. W.
Weekman
, eds., Vol.
72
, pp.
110
161
.
24.
Fiers
,
B.
,
Ferschneider
,
G.
, and
Maillet
,
D.
, 2010, “
Reduced Model for Characterization of Solid Wall Effects for Transient Thermal Dispersion in Granular Porous Media
,”
Int. J. Heat Mass Transfer
,
53(25–26)
, pp.
5962
5975
.
25.
Scheidegger
,
A. E.
, 1957,
The Physics of Flow through Porous Media
,
University Toronto Press
.
26.
Travkin
,
V. S.
, and
Catton
,
I.
, 2001, “
Transport Phenomena in Heterogeneous Media Based on Volume Averaging Theory
,”
,
34
, pp.
1
144
.
27.
Viskanta
,
V.
, 1995, “
Modeling of Transport Phenomena in Porous Media Using a Two-Energy Equation Model
,” ASME/JSME Thermal Engineering Conference, Vol.
3
.
28.
Wakao
,
N.
,
Kato
,
K.
, 1969, “
Effective Thermal Conductivity of Packed Beds
,”
J. Chem. Eng. Jpn
,
2(1)
, pp.
24
33
.
29.
Whitaker
,
S.
, 1972, “
Forced Convection Heat Transfer Correlations for Flow in Pipes, Past Flat Plates, Single Cylinders, Single Spheres, and for Flow in Packed Beds and Tube Bundles
,”
AIChE J.
,
18(2)
, pp.
361
371
.
30.
Kar
,
K. K.
, and
Dybbs
,
A.
, 1982, “
Internal Heat Transfer Coefficients of Porous Metals
,”
Heat Transfer in Porous Media
,
J. V.
Beck
, and
L. S.
Yao
, eds.,
ASME
,
New York
, Vol.
22
, pp.
81
91
.
31.
Rajkumar
,
M.
, 1993, “
Theoretical and Experimental Studies of Heat Transfer in Transpired Porous Ceramics
,” M.S.M.E. thesis, Purdue University, West Lafayette, IN.
32.
Galitseysky
,
B. M.
, and
Moshaev
,
A. P.
, 1993, “
Heat Transfer and Hydraulic Resistance in Porous Systems
,”
Experimental Heat Transfer, Fluid Mechanics and Thermodynamics
,
Kelleher
M. D.
,
Sreehivasan
K. R.
,
Shah
R. K.
and
Toshi
Y.
eds., pp.
1569
1576
.
33.
Kokorev
,
L. S.
,
Subbotin
,
V. I.
,
Fedoseev
,
V. N.
,
Charitonov
,
V. V.
, and
Vosokobojnikov
,
V. V.
, 1987, “
The Relationship between the Hydraulic Drag and Heat Transfer Coefficients in Porous Media
,”
High Temperature.
,
25
, pp.
92
96
.
34.
Gortyshov
,
Y. F.
,
Muravev
,
G. B.
, and
,
I. N.
, 1987, “
Experimental Study of Flow and Heat Exchange in Highly Porous Structures
,”
J. Eng. Phys. Thermophys.
,
53(3)
, pp.
987
990
.
35.
Spalding
,
D. B.
,
Taborek
,
J.
, and
Armstrong
,
R.C.
, 1983,
Heat Exchanger Design Handbook
,
Hemisphere Publishing Corporation
,
New York
.
36.
Anzelius
,
A.
, 1926, “
Uber Erwarmung Vermittels Durchstromender Medien
,”
Z. Angew. Math. Mech.
6
,
291
294