A mass flow meter employs discrete chip-type temperature sensors
to sense a fluid flow rate. The sensor can be a semiconductor chip
such as SiC or silicon, or thin film tungsten on an AlN substrate.
The sensors can be distributed symmetrically with respect to the
conduit through which the fluid flows, and can be connected in a
four-sensor bridge circuit for accurate flow rate monitoring. An
output from the mass flow meter can be used to control the fluid
1. A mass flow meter (MFM) structure, comprising: a conduit for
conducting a fluid flow, and at least four mutually spaced temperature
sensors disposed to sense the temperature of a fluid flowing within
said conduit and arranged in upstream and downstream pairs along
said conduit, with the sensors of each pair located the same distance
along the conduits length and symmetrically on opposite sides of
the conduit from each other, said sensors connected in a 4-sensor
bridge circuit to sense the mass flow rate of a fluid flowing through
2. The MFM structure of claim 1 wherein said sensors are discrete
and are distributed symmetrically with respect to said conduit.
3. The MFM structure of claim 1 said sensors comprising semiconductor
4. The MFM structure of claim 3 said sensors comprising SiC chips.
5. The MFM structure of claim 4 further comprising a SiC oxide
interfacing between said SiC chips and said conduit.
6. The MFM structure of claim 3 said sensors comprising silicon
7. The MFM structure of claim 6 further comprising a silicon oxide
interfacing between said silicon chips and said conduit.
8. The MFM structure of claim 1 further comprising an electrically
insulative film enclosing said sensors, and a circuit on the exterior
of said film and extending through the film to contact said sensors.
9. The MFM structure of claim 1 wherein said sensors are mounted
to said conduit by respective first layers on said sensors and conduit
of a material selected from the group comprising TiW and Ni, and
respective second layers on said sensors and conduit of Au, with
said sensor and conduit second layers bonded to each other.
10. The MFM structure of claim 9 wherein said sensors comprise
semiconductor chips, further comprising an oxide of said semiconductor
interfacing between said sensors and said sensor first layers.
11. The MFM structure of claim 1 said sensors comprising thin
film tungsten layers on respective AlN substrates.
13. The MFM structure of claim 1 said bridge circuit including
extended leads between said upstream and downstream sensors long
enough to be substantially non-thermoconductive.
14. The MFM structure of claim 1 wherein said sensors include
respective AlN substrates that are mounted to said conduit.
15. The MFM structure of claim 1 further comprising electronic
circuitry for actuating said sensors and determining the mass flow
rate of a fluid flowing through said conduit from said sensors.
16. The MFM structure of claim 15 wherein said electronic circuitry
operates without amplification of the sensor outputs.
17. The MFM structure of claim 15 further comprising a control
valve governing the fluid flow through said conduit under the control
of said circuitry.
18. The MFM structure of claim 1 wherein said sensors are mounted
inside said conduit on protective shields and protected from the
environment within the conduit by said shields.
19. A mass flow meter (MFM) comprising: a conduit for conducting
a fluid flow, a plurality of temperature sensors disposed to sense
the temperature of a fluid flowing through said conduit and arranged
in upstream and downstream pairs along said conduit, with the sensors
of each pair located the same distance along the conduit's length
and symmetrically on opposite sides of the conduit from each other,
each sensor comprising an AlN substrate bearing a temperature sensing
circuit, and electronic circuitry for actuating said sensors and
determining from said sensors the mass flow rate of a fluid flowing
through said conduit.
20. The MFM of claim 19 said temperature sensing circuits comprising
respective thin film tungsten layers on said AlN substrates.
21. The MFM of claim 19 wherein each AlN substrate is mounted
to the outer surface of said conduit to conduct heat from said conduit
to its respective temperature sensing circuit.
22. The MFM of claim 19 further comprising a control valve governing
the fluid flow through said conduit under the control of said circuitry.
23. A fluid mass flow meter (MFM), comprising: a conduit for conducting
a fluid flow, a plurality of discrete temperature sensor carried
by to said conduit to sense the temperature of a fluid within said
conduit and arranged in upstream and downstream pairs along said
conduit, with the sensors of each pair located the same distance
along the conduit's length and symmetrically on opposite sides of
the conduit from each other, and electronic circuitry for actuating
said at least one sensor and sensing the mass flow rate of a fluid
flowing through said conduit from said sensors.
24. The MFM of claim 23 each said sensor comprising a semiconductor
25. The MFM of claim 24 each said semiconductor chip comprising
a SiC chip.
26. The MFM of claim 25 further comprising a SiC oxide interfacing
between each SiC chip and said conduit.
27. The MFM of claim 24 each said semiconductor chip comprising
a silicon chip.
28. The MFM of claim 27 further comprising a silicon oxide interfacing
between each silicon chip and said conduit.
29. The MFM of claim 23 each said sensor comprising a thin film
tungsten layer on a respective AlN substrate.
30. The MFM of claim 23 further comprising an electrically insulative
film enclosing each said sensor, and a circuit on the other side
of said film and extending through the film to contact each sensor.
31. The MFM of claim 23 wherein each said sensor is mounted to
said conduit by respective layers on said sensor and conduit of
a material selected from the group comprising TiW and Ni, and respective
second layers on said sensor and said conduit of Au, with said sensor
and conduit second layers bonded to each other.
32. The MFM of claim 31 wherein each said sensor comprises a respective
semiconductor chip, further comprising an oxide of said semiconductor
interfacing between said sensor and said first sensor layer.
33. The MFM of claim 23 wherein said electric circuitry senses
the temperature within said conduit as a function of the sensor
34. The MFM of claim 23 wherein each said sensor is mounted to
the outer surface of said conduit in thermal communication with
a fluid flowing through the conduit.
35. The MFM of claim 23 wherein each said sensor is mounted within
a respective opening in a wall of said conduit.
36. The MFM of claim 23 wherein each said sensor is mounted to
an inner surface of said conduit.
37. The MFM of claim 23 wherein each said sensor is mounted inside
said conduit on a protective shield and protected by said shield
from the environment within said conduit.
38. The MFM of claim 23 wherein each said sensor projects into
the interior of said conduit.
40. The MFM of claim 23 wherein said temperature sensors that
are electrically connected in a bridge circuit.
42. The MFM of claim 23 further comprising a control valve governing
the fluid flow through said conduit under the control of said circuitry.
43. A method of forming a temperature sensor, comprising: bonding
a plurality of discrete temperature sensors to a conduit in upstream
and downstream sensor pairs, with the sensors of each pair located
the same distance along the conduit's length and symmetrically on
opposite sides of the conduit from each other, and electrically
connecting each said sensor to sense the temperature of a fluid
flowing through said conduit.
44. The method of claim 43 wherein each said temperature sensor
is bonded to said conduit through a thermally conductive insulator.
47. The method of claim 43 said electrically connecting step comprising
connecting said upstream and downstream temperature sensors in a
4 sensor bridge network.
48. The method of claim 43 further comprising using said sensed
temperature as an indication of the mass flow rate of a fluid flowing
through said conduit, and controlling said fluid flow rate as a
function of the indicated mass flow rate.
49. The MFM structure of claim 1 wherein said sensors are connected
directly to each other in said bridge circuit.
50. The MFM of claim 40 wherein said sensors are connected directly
to each other in said bridge circuit.
51. The method of claim 47 wherein said sensors are connected
directly to each other in said bridge circuit.
 This application claims the benefit of provisional application
Ser. No. 60/392380 filed Jun. 28 2002.
BACKGROUND OF THE INVENTION
 1. Field of the Invention
 This invention relates to mass flow meters, and more particularly
to chip-type temperature sensors and four-sensor bridge circuits
for mass flow meters.
 2. Description of the Related Art
 Numerous different methods are employed to measure the flow
rate of gases and liquids. They can generally be divided into two
categories: those that measure volumetric flow, and those that measure
 An example of a volumetric flow meter is a tapered tube
through which the gas or liquid travels, displacing a float in the
tube. When there is no flow, the float rests at the bottom of the
tube, sealing its narrower end. As the fluid flows through the tube,
the float rises proportionally to the volumetric fluid flow.
 A principal problem with volumetric flow meters relates
to the measurement of gas flow rate. Changes in the pressure or
temperature of the gas can cause inaccuracies in the flow measurements.
 Mass flow meters (MFMS) are conventionally used to operate
a valve which controls the flow rate of a fluid through a conduit;
the combined MFM and valve is referred to as a mass flow controller
(MFC). These devices are used in many systems requiring precise
control of gas or liquid flow rate, such as in the semiconductor
processing industry to deliver gases whose atoms are used to grow
or dope semiconductor materials, where gas flow rates are crucial
yield parameters. MFCs for the semiconductor industry are discussed
in general in "Results from the workshop on Mass flow measurement
and control for the semiconductor industry", National Institute
of Standards and Technology (NIST), on May 15-16 2000 results
published Jul. 20 2000. An advantage of MFCs over volumetric flow
measurement is that mass flow is less susceptible to accuracy errors
due to variations in line pressure and temperature. Known types
of MFCs include immersible thermal MFCs, thermal MFCs, and differential
 Thermal MFCs are the most commonly used type of MFC in the
semiconductor processing industry. They can be made from relatively
inexpensive components, and provide a good compromise between price
and performance. With immersible MFCs, one or more sensors are located
directly in the flow stream, while with capillary tube MFCs a capillary
tube parallels the main fluid conduit, and one or more sensors are
provided on the outside of the tube.
 In immersible thermal MFCs, an immersed temperature sensor
also acts as a heater, heating up as electric current passes through
it. The temperature sensor remains at some known constant temperature
when the fluid is not flowing. A flowing fluid reduces the sensed
temperature, due to the fluid's carrying heat away from it. The
magnitude of the sensed temperature drop is proportional to the
fluid's mass flow rate. The sensor may be encapsulated for applications
where there is a concern about the sensor material contaminating
the flowing fluid stream, or itself being contaminated by the fluid.
 In an alternate submersible thermal MFC, a heater is immersed
upstream and a temperature sensor downstream. The amount by which
the fluid temperature at the sensor location rises due to operation
of the upstream heater can be correlated with the fluid's mass flow
 In capillary tube thermal MFCs, a known fraction of the
incoming flow stream is directed through a heated capillary tube,
while the remainder of the flow stream by-passes the capillary tube.
The tube is heated by metal wire that is wound around its outer
surface at an upstream location, with a temperature sensing winding
at a downstream location. Platinum wire is typically used because
its resistance change, as a function of temperature, is well known,
allowing it to act as both a heater and a temperature sensor. Some
MFC manufacturers use thin film platinum resistance temperature
devices, consisting of a thin layer of platinum on a thin film insulator
(typically alumina) that is deposited onto the outer surface of
the capillary tube. The platinum thin film layer changes resistance
as a function of temperature.
 The gas diverted through the capillary tube absorbs some
of the heat from the upstream windings. If no gas is flowing, the
tube will be heated uniformly and the up and downstream sensors
will sense equal temperatures. Once the gas begins to flow through
the tube, its heat absorption capacity cools the upstream portion
of the tube while heating the downstream portion; the temperature
differential increases with increasing gas flow. On-board or remotely
located electronics provide an excitation voltage or current for
the sensors, and also monitor the sensor response. For example,
if a current is applied, the voltage across the winding is monitored
so that the winding's resistance is known. Since the resistance
of the sensor varies as a known function of temperature, the temperature
at the sensor can be determined from its current and voltage.
 Thermal MFCs can be either constant current or constant
temperature devices. In a constant current device, the temperature
sensors are electrically connected as two of the resistive elements
in a bridge circuit; the other elements are passive resistors. The
constant excitation current is converted to heat by the sensor resistances,
providing a uniform temperature gradient along the capillary tube.
 In a constant temperature device, the sensors are again
connected in a two-sensor bridge circuit, but the MFC electronics
provide a constant voltage rather than a constant current to the
bridge circuit. A fluid flowing through the tube causes a reduction
in the temperature of the upstream sensor, which reduces its resistance
(for a positive temperature coefficient sensor), causing more current
to flow through it. The increase in excitation current causes the
sensor to give off more heat, which replaces the heat lost to the
fluid. The additional current is proportional to the fluid's mass
flow rate. Platinum is typically used as the sensing element.
 While they are in widespread use, presently available MFCs
suffer from one or more of the following characteristics: relatively
high temperature sensor drift, low sensitivity, long response times,
waste associated with the difficulty of handling ultra-fine platinum
wire during manufacture, additional electronics required to quantify
the electrical responses of low sensitivity temperature sensors,
and errors resulting from the circuitry for low sensitivity temperature
sensors, when used in conjunction with high sensitivity sensors.
SUMMARY OF THE INVENTION
 In one aspect of the present invention, at least four mutually
spaced temperature sensors are disposed to sense the temperature
of a fluid flowing through a conduit, and connected in a four-sensor
bridge circuit to provide an indication of the fluid's mass flow
rate. The sensors are discrete and distributed symmetrically with
respect to the conduit, preferably with a pair of sensors on opposite
side of the conduit at each of two locations along the flow path.
 In another aspect of the invention, the temperature sensors
are discrete chip-type elements. Options for the sensors include
semiconductor materials such as SiC or silicon, with an oxide interfacing
between the chip and the conduit for electrically conductive conduits,
and a thin film tungsten layer on an AlN substrate. The sensors
can be enclosed by an electrically insulative film, with a circuit
on the other side of the film extending through the film to contact
the sensors. The sensors can be mounted to the conduit by means
of TiW or Ni layers on both the sensor and conduit, each supporting
a layer of Au. Various sensor positions can be used, including on
the conduit's outer surface, on an inner conduit surface, within
openings in the conduit wall, or projecting into the interior of
 The chip-type sensor enables multiple sensors to be symmetrically
positioned around the conduit, either at a single location or at
multiple locations along the fluid flow path. The symmetrical placement
enables a more accurate temperature sensing, and is useful for both
four-sensor bridge circuits and other MFM configurations employing
one or more sensor pairs.
 The described MFM can be used to govern the fluid flow through
the conduit by applying its output to a flow control valve for the
 These and other features and advantages of the invention
will be apparent to those skilled in the art from the following
detailed description, taken together with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
 FIG. 1 is a simplified sectional view of a capillary tube
MFM in accordance with the invention;
 FIG. 2 is a schematic diagram of a four-sensor bridge circuit
that provides a MFM output in response to the sensors of FIG. 1;
 FIG. 3 is a graph illustrating the linear relationship of
the temperature between the upstream and downstream sensors to the
 FIG. 4 is a simplified combined perspective view and schematic
diagram of chip-type temperature sensors arranged in a MFM four-sensor
bridge in accordance with the invention;
 FIG. 5 is a sectional view of the structure illustrated
in FIG. 4 with the addition of an insulative sleeve around the
 FIG. 6 is a perspective view of an alternate chip-type sensor
configuration, with a thin film tungsten sensor on an AlN substrate;
 FIG. 7 is a simplified sectional view of a sensor chip mounted
to the interior wall of a fluid conduit;
 FIG. 8 is a simplified sectional view and schematic diagram
of a sensor mounted within an opening in a fluid conduit;
 FIG. 9a is a sectional view of a MFM sensor mounted within
an environmental shield in the interior of a conduit;
 FIG. 9b is a sectional view taken along the section line
9b-9b of FIG. 9a;
 FIG. 10 is a sectional view of a sensor in accordance with
an embodiment of the invention immersed within a fluid flow tube;
 FIG. 11 is a simplified sectional view of a MFC system incorporating
a MFM of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
 A capillary tube MFM in accordance with one embodiment of
the invention is illustrated in FIG. 1. A minor portion of a fluid
flow, either gas or liquid, through a main conduit 2 is diverted
to a capillary tube 4; the main conduit and capillary tube structure
can be conventional. The cross-sections of the main conduit and
capillary tube are precisely machined in a conventional manner to
assure their fluid flow rates are equal. However, instead of the
platinum wire windings previously provided around the capillary
tube, a pair of chip-type temperature sensors U1 and U2 are provided
at an upstream location along the tube, and another pair of chip-type
sensors D1 and D2 at a downstream location along the tube. The sensors
of each pair are preferably positioned symmetrically at 180.degree.
intervals, on opposite sides of the tube. This allows for a more
accurate sensing of the fluid temperature within the tube, in case
the fluid temperature varies slightly from one side of the tube
to the other. For example, if the sensors were located along a horizontal
portion of the capillary tube rather than a vertical portion as
shown, rising heat would make the upper sensor detect a slightly
higher temperature, and the lower sensor a slightly lower temperature.
The symmetrical sensor placements tend to cancel out such discrepancies,
and also to enable a more uniform introduction of heat into the
conduit. The capillary tube wall has a high thermal conductivity,
so that the fluid temperature within the tube is accurately transmitted
to the sensors; stainless steel is commonly used for this purpose.
 FIG. 2 illustrates a four-sensor bridge circuit used to
sense the mass flow rate of a fluid through the capillary tube of
FIG. 1. The bridge circuit is organized into left and right branches,
with each branch having upper and lower sections. The left branch
includes a pair of the upstream and downstream sensors, with the
upstream sensor U2 in its upper section and the downstream sensor
D2 in its lower section. The right branch also includes a pair of
up and downstream sensors, but their relative positions within the
branch are reversed; the downstream sensor D1 is in the upper section,
while the upstream sensor U1 is in the lower section.
 An actuating current from a current source I1 is fed into
the top of the bridge, with current flowing out of the bridge through
a resistor R to a ground reference. The bridge outputs are the voltages
Vo1 and Vo2 at the connections between D1 and U1 in the right branch,
and between U2 and D2 in the left branch, respectively.
 Each sensor has the same structure, and accordingly the
same temperature coefficient of resistance. A fluid flowing through
the capillary tube tends to transfer heat from the upstream sensors
U1 and U2 to the downstream sensor D1 and D2. Accordingly, for sensors
with a positive temperature coefficient of resistance, this will
result in a higher resistance for D1/D2 than for U1/U2. The total
resistance of the bridge's left branch will remain equal to the
total resistance of its right branch, and equal currents will flow
through each branch. However, because of the differences in individual
resistance levels, the upper section of the right branch will experience
a greater voltage drop across D1 than the voltage drop across the
lower section's U1 while conversely the upper section of the left
branch will experience a lower voltage drop across U2 than the voltage
drop across D2 in its lower section. Thus, Vo1 will be at a higher
voltage level than Vo2 with the voltage differential representing
the mass flow rate.
 The circuit of FIG. 2 achieves a higher degree of sensitivity
than prior two-sensor bridge circuits, since Vo2 drops in addition
to Vo1 rising in response to fluid flow, thus producing a compound
effect. It has been found that a useful monitoring of mass flow
rate can be achieved with this circuit without amplifying the sensor
 FIG. 3 illustrates the modeled output voltage differential
as a function of the temperature difference between upstream and
downstream sensors for a four-sensor bridge circuit. The curve is
substantially linear, so that only two points along the curve need
be determined to know the flow rate over the full linear range,
avoiding the need for a more complicated equation that might have
to be embedded in a microprocessor microchip.
 FIG. 4 illustrates an arrangement of chip-type temperature
sensors on the fluid conduit 4 in accordance with the invention.
SiC and silicon chips are preferred; they have similar sensitivities
in the positive regions of their temperature coefficients of resistance.
SiC is capable of a higher operating temperature without diffusion
than is silicon. Other semiconductor materials may also be employed,
but in general they tend to be harder to use, do not form native
oxides, and are no more sensitive than SiC or silicon. Electrical
contact pads 6 are provided as metallization layers on opposite
ends of each chip, and enable the connection of electrical leads
to the chips so that excitation voltages or currents can be applied,
and the response of the chips monitored.
 The lead wire arrangement shown in FIG. 4 corresponds to
the four-element bridge circuit of FIG. 2 with one end of upstream
chip U1 connected by lead 8 to the downstream end of the downstream
chip D2 the upstream end of the other upstream chip U2 connected
by lead 10 to the downstream end of the other downstream chip D1
the facing ends of U1 and D1 connected together by lead 12 the
facing ends of U2 and D2 connected together by lead 14 I1 applied
to lead 10 resistor R connected to lead 8 Vo1 taken from lead
12 and Vo2 taken from lead 14. Although leads 12 and 14 are illustrated
as being short, in practice their lengths would be considerably
extended, such as by connecting them to pin-out electronics. This
can increase the thermal path length between the connected chips
to a point at which the leads can be considered substantially non-thermally
conductive for purposes of mass flow rate monitoring, thus preventing
an additional thermal path between the chips that would interfere
with the measurements. The other leads would be arranged in a similar
 FIG. 5 is a not-to-scale sectional view illustrating how
the symmetrically arranged chips U1 and U2 can be bonded to the
conduit 4. Electrically insulating but thermally conductive layers
16-1 and 16-2 are formed on the faces of U1 and U2 respectively,
to allow the electrically conductive chips to be in direct contact
with the stainless steel conduit 4 and bonding material, without
creating an electrical short circuit. The electrically insulating
layers 16-1 and 16-2 can be monolithically integrated, deposited
or bonded onto the chip sensors. With SiC or silicon used for the
sensors, the electrically insulating layers are preferably formed
by oxidizing the surfaces of the chips that are to face the conduit.
 A thermally conductive bonding material 18 adheres the chip-type
sensors to the conduit. If the bonding material, typically a solder,
will not adhere directly to the chip oxide and conduit material,
a suitable intermediary bonding material is first deposited onto
these surfaces. In FIG. 5 the bonding material 18 is eutectic gold/tin
solder, which will not adhere directly to the electrically insulating
oxide layers 16-1 and 16-2 or to the stainless steel tube 4. To
produce a good bond, layers 20-1 and 20-2 of TiW or Ni, preferably
about 400-1500 Angstroms thick, are deposited on the upper and lower
chip oxide layers 16-1 and 16-2 respectively. A similar TiW or
Ni layer 20-3 is deposited around the outer surface of the tube
4. Gold (Au) layers 22-1 22-2 and 22-3 preferably about 4000-25000
Angstroms thick, are then deposited on the intermediate TiW or Ni
layers 20-1 20-2 and 20-3 respectively. The eutectic gold/tin
solder 18 which adheres to the Au surfaces, can then be applied
to bond the two chips U1 and U2 to opposite sides of the tube 4.
Gold is a preferred bonding material because it has a very high
thermal conductivity and does not readily oxidize. Numerous solders
are available for gold-to-gold bonding.
 For further protection of the overall assembly, and to provide
additional support to hold the sensors in place, the assembly can
be shielded in an insulative sleeve 24 such as the flexible polyimide
film provided under the trademark KAPTON.RTM. by E.I. DuPont de
Nemours and Company. Contact pad metallizations 26 are deposited
or printed on the outer surface of the sleeve in alignment with
the sensor contacts. When the assembly is heated, the contact metal
26 migrates through the sleeve to mate with the sensor contacts,
thus providing a vehicle for external electrical access to the sensors.
 Another advantageous sensor chip configuration, illustrated
in FIG. 6 consists of a tungsten thin film 28 deposited as the
sensor element on an insulating AlN substrate 30. The tungsten conductor
preferably traces a serpentine pattern on the substrate 30 for even
heat distribution when a heating current is applied to it, and terminates
at each end in a pair of spaced contact pads 32. Tungsten provides
a high degree of thermal sensitivity, and can tolerate a wide temperature
range when used in conjunction with an AlN substrate because of
their closely matched temperature coefficients of expansion. The
thin film tungsten layer is generally about 10-1000 microns thick.
Such a temperature sensor is the subject of copending patent application
Ser. No. ______ filed on the same date as the present application
in the name of James D. Parsons, one of the present inventors.
 FIG. 7 illustrates the positioning of a sensor 34 in accordance
with the invention along an interior wall of the conduit 4. The
sensor is bonded to the wall in a manner similar to an exterior
sensor, with or without the addition of an electrically insulating
layer between the sensor and conduit wall as determined by the type
of material used for the sensor. Sensor lead wires 36 can be brought
out through a remote location of the conduit, or directly through
bushings in the conduit wall. The placement of a sensor inside the
conduit as illustrated allows for very rapid and accurate tracking
of the temperature of the fluid flowing through the conduit, but
requires that neither the sensor nor the bonding material be reactive
with the fluid.
 Refer now to FIG. 8 another alternative for mounting a
sensor 36 is illustrated, with the sensor bonded within an opening
in the wall of conduit 4 so that its surface facing the conduit
interior is directly heated by the fluid. The sensor contacts 38
are on its exterior surface and easily accessible. The sensor, and
the conduit opening within which it fits, should be small enough
that the sensor does not protrude too far into the conduit, and
a good bond can be obtained around its periphery to hold the sensor
in place and prevent fluid loss from the conduit.
 The sensor can be part of a four-element bridge as described
above, either the upstream or downstream element of a two-sensor
MFM, or operate by itself in a single-sensor MFM. A current source
I2 is shown directing a current through the sensor, with a voltmeter
40 monitoring the sensor's voltage response to the applied current.
A comparison of the applied current and measured voltage yields
the sensor's resistance; this can be compared with either its resistance
at zero flow, or with the resistance of an up or downstream sensor,
to determine the fluid mass flow rate within the conduit.
 To prevent the fluid from reacting with the sensor or its
bonding materials, this preserving the sensor and/or preventing
contamination of the fluid, a chip-type sensor 42 depicted in FIGS.
9a and 9b can be mounted to the interior of a protective shield
44 that forms a closed compartment within the conduit 4 sealed
off from fluid flowing through the conduit. For a stainless steel
conduit, the shield 44 would preferably also be stainless steel.
Lead wires 46 can extend up from the sensor, through bushings (not
shown) in the conduit wall.
 FIG. 10 illustrates an immersible type thermal MFM in which
a semiconductor or thermistor chip-type sensor 48 is held in the
fluid flow stream within the conduit 4 at the end of a ceramic die
substrate 50. The substrate bears electrical leads 52 formed from
thin layers of deposited metal, which allow an excitation voltage
or current to be applied to the sensor 48 and also allow on-board
or remotely located MFM electronics to monitor the sensor's resistance.
 FIG. 11 illustrates an MFC which utilizes the immersible
MFM of FIG. 10 although it can also be used with any of the other
MFM embodiments contemplated by the invention. A flow control valve
54 is located upstream from the immersed sensor 48 with the sensor's
voltage-current characteristics monitored by an electronics package
56 via the lead traces (not shown) on substrate 50. An electrical
interface 58 on the exterior of a housing 60 for the MFC system
provides electrical inputs and outputs to the system. The electronics
56 provide a signal to the valve control actuator 62 via lead wires
64 to control the operation of the valve in response to the detected
fluid mass flow rate, allowing the flow rate to be maintained at
a desired level despite disturbances such as upstream or downstream
line pressure or temperature variations.
 While particular embodiments of the invention have been
shown and described, numerous variations and alternate embodiments
will occur to those skilled in the art. Accordingly, it is intended
that the invention be limited only in terms of the appended claims.