Microfoil heat flow sensor (MHFS) theory

Measuring heat transfer across a rigid material such as stainless steel used to be done by measuring the temperature on both sides of the material; the inner and outer surfaces. Since the development of heat flux sensors, the heat transfer across a surface can be determined from measurement of temperature at the outer surface alone. The opposite sides of the stainless steel coupon will be at different temperatures creating a differential that can be measured. The MHFS (Model 20456-3, Rhopoint) was embedded into the copper stub along with Tc2 and Tc3 as

illustrated in Figure 3.11. The block sits in an ice bath maintained at 0°C. The MHFS has been described in detail previously by Aziz (2010) and Christian (2004). In this case, approximately 80 % of the fouled area was covered by the MHFS (the area of the sensor, 500 mm2, divided by the fouling area of the coupon, 625 mm2_{). The construction of the MHFS is shown in Figure 3.11}

(right).

The heat flux sensor is constructed with two temperature measuring elements, in this case chromel and alumel, physically separated by a thermal insulator. When the heat begins to

111 ‘transfer’ through thermoelectric material A, the thermal energy at J1 generates a small voltage.

Heat passes through the insulating material (thermal barrier) and a differential temperature is generated. Since the temperature differential is proportional to the voltage differential, the heat transfer rate can be directly read out as a function of voltage. Direct measurement of the heat flux through the coupon can thus be made.

Thermoelectric material “B” Thermoelectric material “A” Copper output leads Thermal barrier S Upper junction at T1 Upper junction at T2 + _

Figure 3.11: The copper stub positioned in the spring in the cooling block. The position of the MHFS, Tc2 and Tc3

are indicated (left). Schematic of the MHFS construction (Aziz 2008) (right).

To calculate the overall heat transfer coefficient (U) from the measured temperature and heat flow, kTB was calculated to find heat flux (q) according to Equation [3.4];

V T x q _B s s

_

_



Where q = heat flux (in kW m-2_{), }

s = sensor thermal conductivity (in kW m-1 K-1), xs = thickness

of the sensor (in m),  = a constant (in V-1_{), (T}

B) = a dimensionless temperature factor and V =

voltage output (in V). RdF supplied a calibration chart of the MHFS for .TB as a function of Cooling block 20 mm 30 mm Copper stub Tc3 Tc2 MHFS

112 temperature. A linear relationship between .TB and temperature was found over the temperature

range investigated (20 – 80˚C) The equation of this relationship was  = -0.001TB + 1.0274. TB

was approximated as Tc2. RdF gave the value of;

11.9 μV Btu-1 _ft-2 _hr-1 _{for the factor}



_

s s x . Thus, μV .hr ft Btu 9 . 11 1 2    s s x .

Conversion of Btu ft2_.h.μV-1 _{to SI units can be done by multiplying 11.9 by 3.154591 x 10}-3

which gives 0.000265 kW m-2 _μV-1_{. U was calculated from the recorded temperatures and the}

calculated heat flux according to:

2 Tc T q U av  _[3.5]

Where q is the heat flux, Tc2 is the temperature of the insulated thermocouple and Tav is the

average of Tc4 and Tc5 (see Figure 3.2). Figure 3.12 (a) shows Uc, the heat transfer coefficient of

a clean coupon, determined when the flow was increased and decreased at 70°C.The error associated with calculating Uc is in Table B.2 in the Appendix. As the flow rate is increased the

boundary layer thickness decreases and a higher heat flux should be measured. The MHFS detects a change in voltage thus the heat transfer coefficient can be seen to change with flow rate. There is an increase in Uc with the onset of flow. Figure 3.12 (b) illustrates the effect of the

flowing system on Tc2, Tav, and q within the first 100 s of rinsing. All sensor readings increase.

Undoubtedly heat is lost to the system and the surroundings. This effect is likely to be related to the stabilisation time of the system. At lower temperatures the duration of this effect would be shorter.

113 (a)

(b)

Figure 3.12: (a) Response of U the MHFS at different flow rates at 70°C; (b) Response of Tc2, Tc4 and Tc5 average

(TL av) and q readings during the first 100 s of rinsing.

Figure 3.13 illustrates characterisation of Uc when the MHFS was in contact with different media.

This was done to give as much background information on the behaviour of the MHFS as possible, to ensure the sensor was in contact with the coupon during experiments and there were no leaks. Actual cleaning behaviour (measured by plotting U values) can therefore be clearly identified. The response time of the MHFS in the ice bath in contact with either the general surroundings or the coupon in flowing and non-flowing conditions was characterised.

0.5 m s-1 _{0.4 m s}-1 _{0.26 m s}-1

0.26 m s-1

0.13 m s-1

114

Figure 3.13: Response time of the MHFS in ice under different conditions. A: MHFS in contact with surroundings; B: MHFS in contact with the coupon; C: MHFS in contact with the coupon when water is flowing through the test section at 70˚C, 0.26 m s-1_{; D: MHFS in contact with the coupon when flow stopped, E: MHFS in contact with the}

surroundings.

The phases identified in Figure 3.13 correspond to: A. MHFS response in contact with the surroundings,

B. MHFS response in contact with the coupon positioned within the test section (no flow), C. MHFS response in contact with the coupon positioned within the test section (flowing

system at 70°C),

D. MHFS response in contact with the coupon when the flow was stopped, E. MHFS response in contact with the surroundings.

When the MHFS is in contact with the general surroundings, U is measured at 0 kW m-2 _K-1_{. This}

illustrates effective cooling of the sensor to 0°C using the block, copper stub and the ice bath set up. Tc2 is cooling down in phase A and E. Then the sensor is in contact with the coupon during

B C D E

115 phase B and the Uc and Tc2 both increase and then decrease as the coupon is also cooled. At the

start of phase C, an increase in Uc, occurs for a similar duration as in Figure 3.13, and Uc then

becomes constant. When the flow is stopped Uc decreases and Tc2 remains at a constant

temperature.

To ensure that cooling the MHFS had minimal effect on the cleaning behaviour of yeast a comparison of two cases of cleaning 30°C, 0.4 m s-1, for the MHFS cooled and not cooled in ice was done at by plotting the average area vs. cleaning time, illustrated in Figure 3.14. The profiles appear similar; certainly within the error of the experiment.

Water rinsing of yeast slurry films that had been aged revealed a thinner film of deposit that could not be removed completely with water. Measuring complete removal of this thin film using chemical cleaning was not possible using heat transfer as the film was removed within a couple of seconds. As such the effect of chemical cleaning on wholly fouled coupons was investigated.

116

Figure 3.14: Removal behaviour of yeast at 0.4 m s-1_{, 30°C rinsed with 2 wt% Advantis 210 when the MHFS was}

cooled in ice and not cooled in ice.