A detailed understanding of the flow of a liquid metal in a rectangular duct subject to a strong transverse magnetic field is vital in a number of engineering applications, notably for proposed blanket technologies for fusion reactors. Fusion reactors offer the potential for clean base-load energy and their development is now entering an engineering phase where the practical means by which the energy released can be converted into useful heat must be addressed. To such ends, this article considers the convective heat transfer processes for fully developed laminar magnetohydrodynamic (MHD) flows in rectangular ducts of the kind proposed in some blanket designs. Analytical solutions which incorporate the nonuniformity of peripheral temperature and heat flux and the effect of volumetric heating, are developed as functions of magnetic field strength and duct aspect ratio. A distinct feature of these MHD problems, not yet addressed in the literature, is that unlike the conventional characterization of heat transfer by a Nusselt number, it is necessary to generalize the concept to vectors and matrices of Nusselt coefficients, due to the extreme anisotropy of both the flow and heating. The new analytical results presented here capture more complex heat transfer behavior than non-MHD flows and in particular characterize the importance of aspect ratio. The importance of these new results lie not only in the improved understanding of this complex process but also in the provision of characterizations of convective heat transfer which underpin progress toward systems scale simulations of fusion blanket technology which will be vital for the realization of practical fusion reactors.

References

References
1.
Wong
,
C.
,
Malang
,
S.
,
Sawan
,
M.
,
Dagher
,
M.
,
Smolentsev
,
S.
,
Merrill
,
B.
,
Youssef
,
M.
,
Reyes
,
S.
,
Sze
,
D. K.
,
Morley
,
N. B.
,
Sharafat
,
S.
,
Calderoni
,
P.
,
Sviatoslavsky
,
G.
,
Kurtz, R. Fogarty
,
P.
,
Zinkle
,
S.
, and
Abdou
,
M.
,
2006
, “
An Overview of Dual Coolant Pb–17Li Breeder First Wall and Blanket Concept Development for the Us Iter-Tbm Design
,”
Fusion Eng. Des.
,
81
(
1–7
), pp.
461
467
.
2.
Smolentsev
,
S.
,
Moreau
,
R.
,
Bühler
,
L.
, and
Mistrangelo
,
C.
,
2010
, “
MHD Thermofluid Issues of Liquid-Metal Blankets: Phenomena and Advances
,”
Fusion Eng. Des.
,
85
(
7–9
), pp.
1196
1205
.
3.
Patel
,
A.
,
Pulugundla
,
G.
,
Smolentsev
,
S.
,
Abdou
,
M.
, and
Bhattacharyay
,
R.
,
2018
, “
Validation of Numerical Solvers for Liquid Metal Flow in a Complex Geometry in the Presence of a Strong Magnetic Field
,”
Theor. Comput. Fluid Dyn.
,
32
(
2
), pp.
165
178
.
4.
Gajbhiye
,
N. L.
,
Throvagunta
,
P.
, and
Eswaran
,
V.
,
2018
, “
Validation and Verification of a Robust 3D Mhd Code
,”
Fusion Eng. Des.
,
128
, pp.
7
22
.
5.
Shercliff
,
J.
,
1953
, “
Steady Motion of Conducting Fluids in Pipes Under Transverse Magnetic Fields
,”
Math. Proc. Cambridge Philos. Soc.
,
49
(
1
), pp.
136
144
.
6.
Hunt
,
J. C. R.
,
1965
, “
Magnetohydrodynamic Flow in Rectangular Ducts
,”
J. Fluid Mech.
,
21
(
4
), pp. 577–590.
7.
Wolfendale
,
M. J.
, and
Bluck
,
M. J.
,
2015
, “
A Coupled Systems Code-CFD MHD Solver for Fusion Blanket Design
,”
Fusion Eng. Des.
,
98
, pp.
1902
1906
.
8.
Bluck
,
M.
, and
Wolfendale
,
M.
,
2015
, “
An Analytical Solution to Electromagnetically Coupled Duct Flow in MHD
,”
J. Fluid Mech.
,
771
, pp.
595
623
.
9.
Bluck
,
M. J.
,
Wolfendale
,
M. J.
, and
Marquis
,
A. J.
,
2015
, “
An Analytical Solution to the Heat Transfer Problem in Shercliff Flow
,”
Int. J. Heat Mass Transfer
,
86
, pp.
542
549
.
10.
Bluck
,
M. J.
, and
Wolfendale
,
M. J.
,
2017
, “
An Analytical Solution to the Heat Transfer Problem in Thick-Walled Hunt Flow
,”
Int. J. Heat Fluid Flow
,
64
, pp.
103
111
.
11.
Blūms
,
E.
,
Mikhaĭlov
,
Y.
, and
Ozols
,
R.
,
1987
,
Heat and Mass Transfer in MHD Flows
,
World Scientific Publishing
, Teaneck, NJ.
12.
Zniber
,
K.
,
Oubarra
,
A.
, and
Lahjomri
,
J.
,
2005
, “
Analytical Solution to the Problem of Heat Transfer in an MHD Flow Inside a Channel With Prescribed Sinusoidal Wall Heat Flux
,”
Energy Convers. Manage.
,
46
(
7–8
), pp.
1147
1163
.
13.
Ying
,
A.
,
Lavine
,
A.
, and
Tillack
,
M.
,
1989
, “
The Effect of Hartmann and Side Layers on Heat Transfer in Magnetohydrodynamic Flow
,”
Fusion Technol.
,
15
(2P2B), pp. 1169–1173.
14.
Sidorenkov
,
S.
,
Hua
,
T.
, and
Araseki
,
H.
,
1995
, “
Magnetohydrodynamics and Heat Transfer Benchmark Problems for Liquid-Metal Flow in Rectangular Ducts
,”
Fusion Eng. Des.
,
27
, pp.
711
718
.
15.
Takase
,
K.
, and
Hasan
,
M.
,
1995
, “
Heat Transfer Characteristics of Rectangular Coolant Channels With Various Aspect Ratios in the Plasma-Facing Components Under Fully Developed MHD Laminar Flow
,” 16th
IEEE/NPSS
Symposium Fusion Engineering
, Champaign, IL, Oct. 2–5, pp.
1538
1541
.
16.
Tezer-Sezgin
,
M.
,
1994
, “
Boundary Element Method Solution of MHD Flow in a Rectangular Duct
,”
Int. J. Numer. Methods Fluids
,
18
(
10
), pp.
937
952
.
17.
Al-Khawaja
,
M. J.
, and
Selmi
,
M.
,
2009
, “
Numerical Solutions of Two Heat Transfer Limits of MFM Square Duct Flow Using Matlab Program
,”
Int. J. Comput. Methods Eng. Sci. Mech.
,
10
(
1
), pp.
102
107
.
18.
Al-Khawaja
,
M.
, and
Selmi
,
M.
,
2006
, “
Highly Accurate Solutions of a Laminar Square Duct Flow in a Transverse Magnetic Field With Heat Transfer Using Spectral Method
,”
ASME J. Heat Transfer
,
128
(
4
), pp.
413
417
.
19.
Lahjomri
,
J.
,
Zniber
,
K.
,
Oubarra
,
A.
, and
Alemany
,
A.
,
2003
, “
Heat Transfer by Laminar Hartmann's Flow in Thermal Entrance Region With Uniform Wall Heat Flux: The Graetz Problem Extended
,”
Energy Convers. Manage.
,
44
(
1
), pp.
11
34
.
20.
Shahmardan
,
M. M.
,
Norouzi
,
M.
,
Kayhani
,
M. H.
, and
Amiri Delouei
,
A.
,
2012
, “
An Exact Analytical Solution for Convective Heat Transfer in Rectangular Ducts
,”
J. Zhejiang Univ., Sci. A
,
13
(
10
), pp.
768
781
.
You do not currently have access to this content.