MEMS Thermal Boundary Layer Flow Sensors

Xiang zheng Tu

A thermal boundary layer flow sensor is a heated micromachined sensor resided on a side wall of a tube, which is used to measure the velocity of a fluid flowing through the tube. It can be described more detail by referencing the above picture.

The picture shows a fluid such as air flowing through a tube, for example, a manifold of a mass flow meter. A MEMS sensor is resided on the side wall of the tube. The sensor consists of a thermal insulating bridge, a resistor heater, and two thermopiles. The bridge is heated up to a temperature higher than the fluid temperature by applying a current passing through the heater. So not only a velocity boundary layer is formed on the wall, but also a thermal boundary layer is formed on the surface of the sensor.

Newton’s Law of cooling states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings, which. can be expressed by the equation:

                                                        q_s = h (T_s -T)                                    (1)

where q_s is the heat flux from the bridge of the sensor, h is the convection coefficient, and Ts and T∞ are the temperatures of the bridge and the fluid, respectively.

About heat transfer close to walls in laminar flows, André Lévêque introduced the very reasonable assumption that for fluid flows of large Prandtl number, the temperature transition from surface to free stream takes place across a very thin region close to the surface. Therefore, in this region the change in velocity can be considered linear with normal distance from the surface.

According to André Lévêque’s assumption, the velocity of the fluid is zero at the wall and the velocity profile is approximated as being linear very close to the wall. As a result, the heat transfer from the surface of the bridge to the flow stream adjacent to the surface is by pure conduction. Thus, the convection coefficient can be expressed as:

                             h = q_s / ((T_s -T) = -k (ծT / ծY)_y=0 ((T_s - T)                (2)

where k is the thermal conductivity coefficient of the fluid.

Energy equation for flow over an isothermal flat plate has been solved by Blasius for numerous values of Prandtl number. For Pr>0.6, the nondimensional temperature gradient at the surface was found to be expressed as:

                           k (ծT / ծY)_y=0 = 0.332 Pr ^1/3 ((T_s -T)   (u /x)^1/2           (3)

Substituting this relation into equation (2) leads to

                                     h = 0.332 Pr ^1/3 k (u /x) ^1/2                                   (4)

That is, the convection coefficient h or the heat flux q_s is proportional to (u) ^1/2. It can be concluded that the heat lose or the temperature change of the heated bride of the sensor is caused by the flows of the fluid. The velocity of the flows can be deduced by measuring the temperature change of the bridge.

In order to measure the change of the temperature of the bridge two thermopiles are arranged on the two opposite sides of the heater of the sensor. They are composed of several thermocouples connected in series. Each thermocouple consists of an aluminum stripe and a polysilicon stripe, which are connected together. The Seebeck effect drives the two different stripes to generate a voltage related to a temperature difference.

Generally, MEMS thermal boundary flow sensors are miniaturized to allow maximal spatial resolution, minimal power consumption, highly dynamic response, and negligible flow interference. Particularly, the rugged design of the sensors minimizes the disturbance to the flow stream and provides an accurate reading of both smooth and turbulent flows. With such excellent performance the sensors are especially favorable for air mass flow meter applications.