Abstract
To investigate the combined influence of Hall effect, ion slip, viscous dissipation and Joule heating on the fully developed laminar MHD channel heat transfer, the exact solution of the energy equation is derived assuming a constant wall heat flux, finely segmented electrodes and a small magnetic Reynolds number. It is concluded that there can be a substantial difference, depending upon Hartmann number, electric field intensity and Brinkman number, between the Nusselt number considering the Hall effect and that neglecting it. Representative results are presented in diagrams and in tables.
Zusammenfassung
Um den Gesamteinflu\ des Hall-Effekts, Ionenschlupfes, der viskosen Dissipation and Jouleschen ErwÄrmung auf die laminare WÄrmeübertragung in einem MHD-Kanal zu untersuchen, ist die exakte Lösung der Energiegleichung abgeleitet, wobei man konstante WÄrmestromdichte an der Kanalwand, unendlich fein segmentierte Elektroden und kleine magnetische Reynolds-Zahl annimmt. Es ist festgestellt, da\ abhÄngig von der Hart mann-Zahl, elektrischen FeldstÄrke und Brinkman-Zahl ein wesentlicher Unterschied zwischen der Nusselt-Zahl, die den Hall-Effekt berücksichtigt, und der, die ihn vernachlÄssigt, bestehen kann. Typische Ergebnisse sind in den Bildern und Tabellen dargestellt.
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Abbreviations
- A:
-
channel cross section
- B:
-
magnetic induction
- Br:
-
Brinkman number
- E:
-
electric field
- Ec:
-
Eckert number
- Ha:
-
Hartmann number
- Nu:
-
Nusselt number
- Pe:
-
Peclet number
- Pr:
-
Prandtl Number
- Q:
-
heat generation function, Eq. (12)
- Re:
-
Reynolds number
- T:
-
temperature
- c:
-
half channel height
- cp :
-
specific heat at constant pressure
- f:
-
mass fraction of unionized particles
- h:
-
specific enthalpy
- j:
-
current density
- p:
-
pressure
- q:
-
heat flux
- t:
-
time
- v:
-
velocity
- x,y,z:
-
cartesian coordinate
- Βe :
-
Hall parameter
- ΒI :
-
ion slip parameter
- δij :
-
Dirac delta function
- η:
-
dynamic viscosity
- λ:
-
thermal conductivity
- Μ:
-
magnetic permeability
- Ν:
-
kinematic viscosity
- ρ:
-
mass density
- ρe :
-
charge density
- σ:
-
electrical conductivity
- Τ:
-
shear stress tensor
- Φ:
-
dissipation function
- c:
-
conduction
- j:
-
Joule heating, Eq. (14)
- m:
-
mean value
- mag:
-
magnetic
- q:
-
heat flux, Eq. (14)
- ref:
-
reference value
- v:
-
viscous dissipation, Eq. (14)
- w:
-
wall
- x,y,z:
-
cartesian coordinate direction
- →:
-
vector
- +:
-
substantial quantity, Eqs. (2) and (3)
- ′:
-
reduced quantity, Eqs. (9c) and (10)
- −:
-
dimensionless quantity, Eq. (10)
References
Perlmutter, M.; Siegel, R.: Heat transfer to an electrically conducting fluid flowing in a channel with a transverse magnetic field. NASA TN D-875 (1961)
Eraslan, A.H.: Temperature distributions in MHD channels with Hall effect. AIAA J. 7 (1969) 186/188
Sutton, G.W.; Sherman, A.: Engineering Magnetohydrodynamics. New York: McGraw-Hill (1965)
Javeri, V.: Influence of Hall effect and ion slip on velocity and temperature fields in an MHD channel. WÄrme- u. Stoffübertragung 7 (1974) 226/235
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Javeri, V. Combined influence of Hall effect, ion slip, viscous dissipation and Joule heating on MHD heat transfer in a channel. Wärme- und Stoffübertragung 8, 193–202 (1975). https://doi.org/10.1007/BF01681561
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DOI: https://doi.org/10.1007/BF01681561