Heat transfer analysis procedure is presented for two-temperature gaseous plasma. Analysis is based on laminar flow of singly-ionized, quasineutral plasma with variable properties. Sheath analysis is described for species in accelerating field, decelerating field, emitted from wall, and recombining at wall

Bose, T. K.

English

NASA Technical Reports Server

December 1972	 B72-10707 
S	 NASA TECH BRIEF 
NASA Pasadena Office
	
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Computation of Laminar Heat Transfer from Gaseous 
Plasmas in Electromagnetic Fields 
S
Electrode erosion in plasma-propulsion and power-
generation devices can be caused by intense heat flux, 
especially at the anode. In the past, methods for com-
puting anode heat fluxes were limited to boundary-
layer flows of high-temperature gaseous plasmas in 
the absence of magnetic fields; much of the earlier 
work relating to plasmas was confined to reentry 
problems. 
A comparatively general analysis of heat transfer 
for a two-temperature gaseous plasma in the presence 
of electromagnetic fields has been developed; it is 
available in report form. The analysis is based on 
laminar flow of a singly-ionized, quasineutral plasma 
with variable properties. The total velocity of the 
electrons is considered to be the sum of the mass-
averaged directed velocity of the gas mixture plus an 
ambipolar-diffusion velocity resulting from the con-
centration gradient of the electrons plus a field veloc-
ity of the electrons in an electromagnetic field; the 
field velocity for ions is assumed to be negligible. It 
is shown that the Nusselt number is a function of six 
different dimensionless parameters compared to two 
parameters for a nonionized, low-temperature gas 
flow without applied electromagnetic fields. The total 
heat flux to the wall consists of the convective heat 
flux (which can be computed from Nusselt's relations) 
plus additional terms representing energy loss or gain 
at the sheath edge near the surface. 
A sheath analysis is described for a species (1) in 
an accelerating field, (2) in a decelerating field, (3) 
emitted from the wall, and (4) recombining at the 
wall. Expressions for energy loss or gain terms are
then obtained for special cases of a cathode, an anode, 
and some other surfaces. To show the importance of 
different nondimensional parameters on convective 
heat flux, a simple heat-transfer model consisting of 
flow between parallel flat plates is then considered. 
The current is assumed to be uniformly distributed, 
and thermophysical properties are assumed to be con-
stant; additionally, the, temperatures of each of the 
species are taken to be equal. The distribution of the 
gas temperature between electrodes is found to be 
dependent upon a dimensionless variable which is 
proportional to the current, and on another dirnen-' 
sionless variable which is inversely proportional to 
the cathode temperature and directly proportional to 
the ratio of thermal to electrical conductivity. 
The ratio of the anode-to-cathode surface temper-
atures is important; for a typical value of the ratio of 
these temperatures, it is shown that an independent 
adjustment of the value of both the dimensionless 
variables noted above leads to a reversal in the sign 
of the convective heat transfer at the cathode. In the 
physical sense, the reversal in the convective heat flux 
to and from the cathode is brought about by a change 
in the joule heating which influences the temper-
ature gradient at the surface. 
Note: 
The following document may be obtained from: 
National Technical Information Service 
Springfield, Virginia 22151 
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(continued overleaf) 
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https://ntrs.nasa.gov/search.jsp?R=19720000706 2020-03-17T03:43:21+00:00Z
Reference:	 Source: Tarit Kumar Bose of 
JPL Technical Report 32-1447 (N71-14062),	 Caltech/JPL 
Laminar Flow Heat Transfer from a Gaseous 	 under contract to 
Plasma at Elevated Electron Temperature
	 NASA Pasadena Office 
in the Presence of Electromagnetic Fields.
	 (NPO-11725)
. 
I 
-1O7O7 Category 03


Computation of laminar heat transfer from gaseous plasmas in electromagnetic fields

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