A High-Resolution Method for the Experimental Determination of the Heat Transfer Coefficients of Industrial Nozzle Systems in Heat Treatment Plants

Abstract

In industrial plants, metal strips are quenched using convective heat transfer. This involves accelerating gas through a nozzle system onto the material to be quenched, resulting in a fast and uniform cooling process. The efficiency of the heat transfer is determined by the specific nozzle system. The presented work is focussed on the analysis of the heat transfer by forced convection through impingement jets both theoretically and experimentally. A unique method for determining the forced convective heat transfer coefficient is described and its application to industrial size nozzle arrays of annealing-line cooling sections is presented.

1. Introduction

After metal strips are produced by primary forming and rolling, heat treatment processes are used to adjust the final product properties. Continuous annealing lines, as shown in Figure 1, are used for this process, alongside other heat treatment plants. The heating rates, tempering and the cooling rates determine the different phase fractions of the metals and establish their characteristic mechanical properties.

Due to the increased use of high-strength steels and Al7xxx aluminium grades, which require high cooling rates, quenching has been in the focus in recent years. Additionally, the large variations in cooling rates for different steel grades used worldwide require a high degree of flexibility for heat treatment plant engineering.

Gas cooling fulfils both requirements and can achieve cooling rates up to 150 K/(s∙mm) as a function of the strip thickness [2]. The convective heat transfer depends not only on the properties of the cooling gas, but also on the velocity and the degree of turbulence of the existing flow. These complex dependencies are summarised by the heat transfer coefficient for forced convection h_force.

The importance of global energy conservation has become evident, particularly since the release of the Intergovernmental Panel on Climate Change’s sixth global climate report [3]. Therefore, when designing and retrofitting cooling lines, it is essential to consider not only the required heat transfer coefficients but also the energy consumption of the line due to the necessary movement of the fluid. A cooling section that meets the specified cooling rates is effective, but not necessarily efficient. In the context of nozzle design, efficiency refers to achieving the specified cooling rates with as little effort and, therefore, energy input as possible. This effort can be measured in terms of energy input or manufacturing and maintenance costs. An efficient nozzle design is described as a system which requires minimal energy to generate high flow velocities and effective manufacture and maintain costs.

This article presents an experimental method for measuring heat transfer coefficients by forced convection of various industrial-size nozzle systems used for cooling sections of annealing lines. Usually, experimental studies are performed to determine the heat transfer coefficient by forced convection of various nozzle systems, supporting plant manufacturers in designing both new and existing plants. This article explains and compares the experimental method developed at the Department for Industrial Furnaces and Heat Engineering at RWTH Aachen University for slot and round nozzle systems with the studies of other authors.

2. Fundamentals

2.1. Convective Heat Transfer by Impingement Jet

Convection is the transfer of energy associated with the flow of material. There are two types of convection: forced convection and free convection. Forced convection is caused by external forces, for example by the use of a fan, while free convection is caused by forces within the fluid itself. In general, these are differences in density that cause buoyancy forces in the earth’s gravitational field. Convective heat transfer refers to the transfer of energy to a solid in the form of heat at a location where it has been transported by fluid flow. These phenomena include both the transfer of energy by molecular movement in the form of diffusion and the directional movement of particles. In conjunction with a temperature difference, convection leads to localised heat transfer, which is described by Newton’s law of cooling, as shown in Equation (1) [4]:

$$q_{\mathit{conv}}^{″}=h·\left(T_s-T_{\infty }\right)$$

(1)

with

h	as the heat transfer coefficient in W/(m2K);
$q_{\mathit{conv}}^{″}$	as the convective heat flow density in W/m2;
Ts	as the strip temperature in K;
T∞	as the fluid flow temperature in K.

To calculate the transferred heat flow, the heat flow density is multiplied by the transfer area according to Equation (2) [4]:

$${\dot{Q}}_{\mathit{conv}}=q_{\mathit{conv}}^{″}·A$$

(2)

with

${\dot{Q}}_{\mathit{conv}}$	as the convective heat flow in W;
A	as reference area in m2.

When determining the heat transfer coefficient for both free and forced convection, it is important to consider a large number of dependencies. These include the geometry of the body around which the flow passes, the surface properties of the body and the material properties of the fluid. Additionally, the flow conditions of the impingement jet, which are shown schematically in Figure 2, also have a significant influence on the heat transfer coefficient.

The impingement jet can be divided into three characteristic regions. First, there is a free jet region. After leaving the nozzle, the jet flows according to the given initial conditions. Under technical conditions, a turbulent flow structure is expected. The free jet spreads out as a result of mixing with the ambient fluid, forming a shear layer and subsequently slows down. As the distance to the wall surface decreases, the free jet transforms into a stagnant flow. The velocity is separated into a vertical component and a horizontal component. The vertical component is decelerated to a velocity of u = 0 m/s, while the horizontal component is accelerated to its maximum value. The stagnation region is identified by the stagnation point, where the total velocity is zero. The subsequent wall jet region has similar flow structures to the free jet. As the flow rate increases, it becomes a wider decrease in velocity. At some point, it encounters the other jet from the adjacent nozzle, forming a mixed region, and they flow out again. In the industrial furnace, the return flow is fed back to the fan and the cycle starts all over again [5].

2.2. Optimisation Approaches for Nozzle Systems

The challenges of optimising a nozzle system to achieve optimal heat transfer by forced convection have already been described by Martin [6]. Schnabel [7] and Hilgeroth [8] recommend the following three lengths as a basis for the nozzle design:

• Hydraulic diameter of the nozzle D_hyd;
• Nozzle-to-strip distance, nozzle height H;
• Nozzle-to-nozzle distance, nozzle pitch s.

All three parameters are strongly interrelated. To optimise the nozzle system, it is essential to keep one of the three parameters constant and adapt it to the boundary conditions of the technical specifications. Otherwise, reducing all parameters would lead to an increase in forced convective heat transfer due to the increasingly shorter flow path of the fluid. In case of a constant nozzle height, the following estimates result for the remaining two parameters:

$$D_{\mathit{hyd},\mathit{opt}}\approx \frac{1}{5}·H$$

(3)

$$s_{\mathit{opt}}\approx \frac{7}{5}·H$$

(4)

For round nozzles, the nozzle diameter is equal to the hydraulic diameter. In case of slot nozzles, where the slot length is significantly greater than the slot width W, the hydraulic diameter is calculated using D_hyd = 2 W. When optimising the nozzle opening area and nozzle pitch, the relative opening area A_rel is used to enable comparisons between different systems. The relative opening area describes the ratio of the absolute nozzle opening area A_nozzle to the area of the nozzle body A_total. The optimum values for the area of relative nozzle opening are the analytically determined suggested values [7].

$$\mathrm{Round} \mathrm{nozzle} \mathrm{field}:\hspace{1em}\hspace{1em}{A}_{\mathit{rel},\mathit{opt}}\approx 1.52\%$$

(5)

$$\mathrm{Slot} \mathrm{nozzle} \mathrm{field}:\hspace{1em}\hspace{1em}{A}_{\mathit{rel},\mathit{opt}}\approx 7.18\%$$

(6)

In addition to optimising for a defined heat transfer coefficient, it is also necessary to consider the effectiveness of the overall system. The area-related fluid power $P_f^{″}$ is used for this purpose. It is defined according to Equation (7):

$$P_f^{″}=∆p·C_c·u·A_{\mathit{rel}}$$

(7)

with

$∆p$	as the nozzle outlet pressure related to atmospheric pressure in Pa;
Cc	as the contraction coefficient;
u	as the flow velocity in m/s.

The contraction coefficient is calculated by dividing the contracted nozzle cross-section by the nozzle opening area. It is important to examine the coefficient for each specific nozzle in advance. The equations used to evaluate the effectiveness and efficiency of a nozzle system demonstrate that accurate temperature and pressure measurements, as well as a precise investigation of the flow conditions, are necessary for a holistic analysis.

2.3. Classification of the Present Method

Dimensionless numbers were introduced to make the results of experimental investigations by several authors comparable and to reduce the experimental scope. They are based on the general principle that the solution of a physical problem is independent of the chosen metric system and can be expressed by dimensionless parameters. In the context of heat transfer problems, the Nusselt number Nu was introduced according to Equation (8) [9]:

$$\mathit{Nu}=\frac{h·L}{\lambda }$$

(8)

with

L	as the characteristic length in m;
$\lambda$	as the thermal conductivity in W/(mK).

The Nusselt number is also dependent on the properties of the fluid being used, including its velocity, density, viscosity and heat capacity. These properties can also be summarised in dimensionless groups of numbers, specifically the Prandtl number Pr and the Reynolds number Re in case of forced convection. The local Nusselt number also depends on an empirical constant K based on the nozzle geometry. For forced convection, the local Nusselt number follows the dependence described in Equation (9) for a defined geometry.

$$\mathit{Nu}=f(K,\mathit{Re},\mathit{Pr})$$

(9)

The dimensionless Reynolds number, defined in Equation (10), characterises the existing flow by measuring the ratio of inertial and viscous forces. It is important for comparing different nozzles with varying flow characteristics.

$$\mathit{Re}=\frac{\rho ·u·L}{\mu }$$

(10)

with

ρ	as the fluid density in kg/m3;
μ	as the kinematic viscosity kg/ms.

Initial studies of the heat transfer coefficient on an unmoved flat plate using an impingement jet were conducted in the 1970s. Since then, several further investigations have been carried out by various authors. A selection of investigated slot nozzles is listed in

Table 1. Studies on determining the heat transfer coefficient for slot nozzle systems according to [10].

Author (Year)	Range of Validity			Principle
	H/W	s/W	Re
Hilgeroth (1965) [8]	5 to 36.5	19.8 to 73	7.6 × 104 to 5 × 105	Thermocouple, heated surface
Martin (1977) [6]	2 to 40	3.2 to 125	1500 to 4 × 104	Vaporisation, heated flow
Menzler (1992) [11]	2 to 31	6 to 47	5260 to 6.7 × 104	Thermocouple, heated surface

, while Table 2 lists a collection of investigated round nozzle systems. The studies presented were all conducted using different but comparable measurement principles and have different ranges of validity. The coefficients and their respective range of validity can be used to compare the different measurement methods used in these studies. The first coefficient for validity is the ratio between the nozzle-to-strip distance H and the width of the slot nozzle W, called the H/W ratio. The second coefficient for validity, s/W, describes the ratio between the nozzle-to-nozzle distance s and the width of the slot nozzle W. The third coefficient is the range for the Reynolds number Re for the measurements. For round nozzle systems, the coefficients change. The first coefficient H/D is the ratio between the nozzle-to-strip distance H and the hydraulic diameter of the round nozzle D. The second coefficient s/D describes the ratio between the nozzle-to-nozzle distance s and the hydraulic diameter D.

There are three main measurement principles as shown in Table 1 and Table 2: vaporisation by a heated flow, the use of liquid crystal techniques and the determination of the heated surface temperature by thermocouples or, newly, by IR-cameras.

Martin’s [6] experimental setup is based on a test method that measures a change in the water column. The integral heat transfer coefficient is determined from the measured integral mass transfer coefficient. Air flows onto a flat plate with concentric circles or individual rectangular elements consisting of a porous stone. It is important that each element on the plate is separate and has its own water chamber. A burette with an additional water supply is connected to the water chamber. To determine mass transport, the inlet tube of the water supply was closed and the water column in the burette was observed using a stopwatch. Investigating different nozzle geometries and fields require significant effort as it involves manufacturing a new porous plate and adapting the water supply. Huber [12] and Huang [13] use a method based on the liquid crystal technique to determine the convective heat transfer with round nozzle fields. The realignment of the crystal lattice produces a liquid crystal colour that reflects different wavelengths of light depending on the coating temperature. The colour differences are recorded using an RBG camera.

The most commonly used measuring principle is the direct measurement of the surface temperature with thermocouples. According to Rao [14], a copper plate can be used to distribute the heat from an external heat source homogeneously over a certain area. This method is suitable for determining the average heat transfer coefficient precisely, but not for resolving localised heat transfer phenomena. In this case, measuring the temperature of the surface with an infrared camera has the advantage that the strip surface temperature can be recorded for each pixel, as in Katti’s [15] study. Here, the resolution of the temperature profile depends on the camera resolution.

Table 2. Studies on determining the heat transfer coefficient for round nozzle systems according to [10].

Author (Year)	Range of Validity			Principle
	H/D	s/D	Re
Hilgeroth (1965) [8]	2 to 6	2 to 30.6	1.5 × 104 to 5 × 105	Thermocouple, heated surface
Martin (1977) [6]	2 to 12	4 to 14	2000 to 1 × 106	Vaporisation, heated flow
Florschuetz (1981) [16]	1 to 13	4 to 8	2500 to 7 × 104	Thermocouple
Kramer (1988) [17]	1.1 to 12.5	3 to 12.5	6500 to 5.2 × 104	Thermocouple, heated surface
Huber (1994) [12]	0.25 to 10	4 to 8	3500 to 2 × 104	Liquid crystal
Huang (1998) [13]	3	3.5 to 44.5	4.85 × 103 to 1.83 × 104	Liquid crystal
Katti (2008) [15]	1 to 3	2 to 6	3000 to 1 × 104	IR-camera, heated surface
Rao (2009) [14]	1 to 3	5 to 15	2500 to 7 × 104	Thermocouple, heated surface

Table 2. Studies on determining the heat transfer coefficient for round nozzle systems according to [10].

Author (Year)	Range of Validity			Principle
	H/D	s/D	Re
Hilgeroth (1965) [8]	2 to 6	2 to 30.6	1.5 × 104 to 5 × 105	Thermocouple, heated surface
Martin (1977) [6]	2 to 12	4 to 14	2000 to 1 × 106	Vaporisation, heated flow
Florschuetz (1981) [16]	1 to 13	4 to 8	2500 to 7 × 104	Thermocouple
Kramer (1988) [17]	1.1 to 12.5	3 to 12.5	6500 to 5.2 × 104	Thermocouple, heated surface
Huber (1994) [12]	0.25 to 10	4 to 8	3500 to 2 × 104	Liquid crystal
Huang (1998) [13]	3	3.5 to 44.5	4.85 × 103 to 1.83 × 104	Liquid crystal
Katti (2008) [15]	1 to 3	2 to 6	3000 to 1 × 104	IR-camera, heated surface
Rao (2009) [14]	1 to 3	5 to 15	2500 to 7 × 104	Thermocouple, heated surface

Various authors have used impingement jets for cooling, but with different experimental setups. These setups differ not only in the measuring principle, but also in the nozzle geometries and nozzle exit velocities investigated. The aim of this study is to investigate the fast cooling of metal strips as realistically as possible. This means that the size of the nozzle geometry is comparable to industrial applications, ensuring that practical nozzle exit speeds are achieved. To optimize an efficient nozzle system, it is necessary to measure the nozzle exit velocity and the strip surface temperature precisely. In addition, it is important to ensure that the nozzle configurations can be changed and adapted without significant additional effort.

3. Present Method for Determining the Heat Transfer Coefficient

3.1. Experimental Setup

The experimental setup for analysing the forced convective heat transfer of the impingement jet on a metal strip is shown in Figure 3. The forced heat transfer coefficient is calculated by performing an energy balance based on temperatures measured using an IR thermal camera (InfrTec GmbH Infrarotsensorik und Messtechnik, Dresden, Germany), as described in Section 3.2.

The test setup consists of a fan, an inlet section with a volume flow measurement, a distribution chamber, a variable nozzle array and a conductive heated strip. The fluid is drawn in by the fan, which can achieve a maximum pressure increase of Δp = 22,800 Pa at a maximum fan speed of r = 3000 min⁻¹. The maximum achievable volume flow is $\dot{V}$ = 15,000 m³/h, the maximum motor-connected load of the fan is P = 90 kW. The fan is connected to a tube that leads to the distribution chamber. Here, a volume flow measurement in the form of a Wilson measurement grid is included. The measurement grid has a diameter of D_grid = 388.8 mm. The inlet and outlet sections of the volume flow measurement are designed in accordance to DIN 5167 [18]. Accordingly, the length of the inlet section is five times larger than the grid diameter while the length of the outlet section is two and half times the grid diameter in order to ensure a fully developed undisturbed flow at the measuring point. Various nozzle systems can be easily installed onto the distribution chamber to analyse different nozzle geometries and nozzle pitches s. The nozzle box has a maximum area of 1480 × 1560 mm². Located above the nozzle field, there is a conductive heated strip with an area of 630 × 1160 mm² representing the impingement surface. The strip is resistance-heated via three transformers, each with an electrical power of P = 12.5 kVA. Each transformer provides an equal proportion of the total power. The distance between the electrically heated strip and the nozzle system H can be adjusted between H = 0 and 250 mm using an electric motor.

During the measurement, an impingement flow causes convective heat transfer that locally cools the strip. This, together with the electric heating of the strip, creates a specific temperature field. This temperature field is measured using an IR thermal camera. With a resolution of 640 × 480 pixels (total 307,200 pixel), it determines an individual temperature T_xy for each pixel. For the area of the heated strip and with a distance of 1.3 m between the camera lens and the strip, each pixel describes a strip area of 1.28 × 1.28 mm². Additional plates are mounted on all four sides of the strip to increase the impingement surface area. These plates extend the surface area to 930 × 1500 mm². Without these edge plates, the impinging flow would be diverted over the strip edges, potentially causing cooling on the top side of the strip and leading to incorrect temperature distribution measurements. To investigate edge effects, the edge plates of the strip can be removed. Edge effects in forced convection cooling refer to changes in heat transfer caused by flow at the edges of the strip. The temperature profiles at the edges may differ from those in the rest of the strip, depending on the nozzle system used.

The experimental setup is also equipped with Pitot tubes at the nozzle outlets and several pressure and temperature measuring points. The flow from the inlet section to the nozzle outlet can be characterised due to the multiple measurement points. This is particularly necessary for the exact determination of the fluid performance of each nozzle system. All measured data are continuously recorded. The measurement of the temperature distribution on the strip with the IR thermal camera is performed when the system has reached a steady state. At steady state, the energy for heating the strip is equal to all heat losses. The measured temperature distribution in the state of thermal equilibrium is used to calculate the forced convective heat transfer coefficient.

3.2. Measurement Principle

The dependencies of free and forced convective heat transfer can be found in Section 2. It is important to note that the heat transfer coefficient cannot be measured directly. In the present work, the heat transfer coefficients are determined with energy balances. The IR thermal camera is used to measure the temperature T_xy for each pixel of the heated strip in steady state. The supplied electrical energy $\dot{Q}$_gen corresponds to the dissipated heat losses $\dot{Q}$_losses of the sample, as shown in Equation (11):

$${\dot{Q}}_{\mathit{gen}}={\dot{Q}}_{\mathit{losse}}$$

(11)

The basic prerequisites for the validity of this energy balance are the properties of the heated strip. The strip made of CuNi44 has an almost constant electrical resistance in the temperature range of T = 0–600 °C. This allows easy calculations of the heat generated in the strip without having to consider changes in electrical resistance. Furthermore, CuNi44 has a constant thermal conductivity of λ = 21.5 W/(mK) in the temperature range of T = 0–300 °C. However, because of the strip’s thickness of t_strip = 0.1 mm, it can be considered as thermally thin (Bi = αL/λ ≪ 1 with L = t_strip = 0.1 mm). As a result, thermal conduction in the thickness direction is negligible. Accordingly, the heat losses consist of the heat conduction in the longitudinal and in the transversal direction as well as forced convection and radiation on the nozzle-facing side. On the nozzle averted side, heat losses occur due to free convection and radiation towards the surroundings. A schematic representation of the heat flow for one pixel is shown in Figure 4; Equation (12) shows the energy balance of all heat losses as stated in Equation (11).

$${\dot{Q}}_{\mathit{gen}}={\dot{Q}}_{\mathit{conv},\mathit{force}}+{\dot{Q}}_{\mathit{conv},\mathit{free}}+{\displaystyle \sum _{n=1}^2}{\dot{Q}}_{n,\mathit{rad}}+{\displaystyle \sum _{k=1}^4}{\dot{Q}}_{k,\mathit{cond}}$$

(12)

with

${\dot{Q}}_{\mathit{conv},\mathit{force}}$	as the forced convection heat flow in W;
${\dot{Q}}_{\mathit{conv},\mathit{free}}$	as the free convection heat flow in W;
${\dot{Q}}_{n,\mathit{rad}}$	as the radiation heat flow in W;
${\dot{Q}}_{k,\mathit{cond}}$	as the conduction heat flow in W.

The heat generated by the electrical energy in each pixel can be calculated based on Joule’s first law, Equation (13). Since the electrical resistance of the strip material is independent of temperature, the same power is generated in each pixel area. Therefore, the heat calculation can be simplified by dividing the total power by the number of pixels n_px:

$${\dot{Q}}_{\mathit{gen},\mathit{px}}=∆U_{\mathit{px}}·I\approx \frac{U·I}{n_{\mathit{px}}}$$

(13)

with

ΔUpx	as the voltage drop per pixel in V;
I	as the current in A;
U	as the voltage drop over the strip in V.

With the introduction of the pixel length Δx and pixel width Δy, the following expressions for the convective heat flows result according to Equation (1):

$${\dot{Q}}_{\mathit{conv},\mathit{force}}=h_{\mathit{force}}\cdot \left(T_{x,y}-T_{\mathit{fluid}}\right)\cdot ∆x∆y$$

(14)

$${\dot{Q}}_{\mathit{conv},\mathit{free}}=h_{\mathit{free}}\cdot \left(T_{x,y}-T_{\mathit{Fluid}}\right)\cdot ∆x∆y$$

(15)

The fluid temperature T_fluid is the reference temperature for the convective heat flow, while the ambient temperature T_∞ is used for the heat flow by radiation. The free convection heat transfer coefficient h_free is determined separately using the equation of the Nusselt number of an isothermal horizontal wall. An experimental check analogous to the energy balance is also conducted. To simplify the determination of the radiative heat flow, the strip is coated with a black, temperature-resistant paint. The emissivity of ε = 0.9 is included in the balance according to Schleupen’s results [19]. The terms for the radiative heat flow are as follows:

$${\dot{Q}}_{\mathit{rad},\mathit{top}}={\epsilon }_{\mathit{top}}\cdot \sigma \cdot \left(T_{x,y}^4-T_{\infty }^4\right)\cdot ∆x∆y$$

(16)

$${\dot{Q}}_{\mathit{rad},\mathit{bottom}}={\epsilon }_{\mathit{bottom}}\cdot \sigma \cdot \left(T_{x,y}^4-T_{\infty }^4\right)\cdot ∆x∆y$$

(17)

As mentioned, the conductive heat flow is considered in the longitudinal and transversal directions using the Equations (18)–(20) to calculate the energy balance. The purpose of this energy balance is to determine the forced convective heat transfer coefficient for each pixel. To achieve this, a MATLAB^® R2023a-based evaluation is carried out for all 307,200 pixels. This method allows for the determination of both the average heat transfer coefficient of defined areas and the precise local heat transfer coefficient.

$${\dot{Q}}_{\mathit{cond},x-1,y}=\frac{{\lambda }_{\mathit{strip}}}{∆x}\cdot \left(T_{x,y}-T_{x-1,y}\right)\cdot ∆y·t_{\mathit{strip}}$$

(18)

$${\dot{Q}}_{\mathit{cond},x+1,y}=\frac{{\lambda }_{\mathit{strip}}}{∆x}\cdot \left(T_{x,y}-T_{x+1,y}\right)\cdot ∆y·t_{\mathit{strip}}$$

(19)

$${\dot{Q}}_{\mathit{cond},x,y-1}=\frac{{\lambda }_{\mathit{strip}}}{∆y}\cdot \left(T_{x,y}-T_{x,y-1}\right)\cdot ∆x·t_{\mathit{strip}}$$

(20)

$${\dot{Q}}_{\mathit{cond},x,y+1}=\frac{{\lambda }_{\mathit{strip}}}{∆y}\cdot \left(T_{x,y}-T_{x,y+1}\right)\cdot ∆x·t_{\mathit{strip}}$$

(21)

3.3. Uncertainty of Measurement

In order to provide an estimate of the measurement deviation, a propagation of uncertainty of the calculated heat transfer coefficients was carried out using Equation (22):

$$\mathrm{\epsilon }y=\sqrt{{\displaystyle \sum _{i=1}^N}{\left(\frac{\partial F}{\partial x_i}·\epsilon x_i\right)}^2}$$

(22)

The measurement uncertainties (εy) of all identified quantities,

Table 3. Uncertainties of the quantities used to determine the Nusselt number.

Quantity	Measurement Range	Uncertainty
Current	0–2000 A	±2.0%
Voltage	0–12 V	±1.0%
Pixel temperature	60–200 °C	±1.0–3.3%
Ambient temperature	20–30 °C	±0.1%
Jet temperature	20–40 °C	±0.1%
Pixel length Δx	1.28 mm	±1.0%
Pixel width Δy	1.28 mm	±1.0%

, have been determined. F refers to the functions used to calculate the measured value, which corresponds to the terms of the energy balance from Section 3.2. The independent variables correspond to x_i and their uncertainties are considered as εx_i. The standard deviation resulting from the propagation of uncertainty in the experimentally determined heat transfer coefficient of forced convection h_force is given by ε_hforce ± 4.4%. The biggest influence on the deviation of the heat transfer coefficient is the temperature measurement of the pixels with the infrared camera. This highlights the importance of accurate camera alignment and regular calibration.

To ensure comparability with other authors, the uncertainty propagation of the determined heat transfer coefficient has been extended by determining the propagation of uncertainty of the Nusselt number according to Equations (8) and (22) and is estimated to be un_Nu = ±7.6%. In addition to the calculation of the uncertainty of the heat transfer coefficient ε_hforce = ±4.4%, the uncertainty of the characteristic length, which in this case corresponds to the nozzle diameter, and the uncertainty of the thermal conductivity of the used fluid were also considered. In particular, the thermal conductivity uncertainty has a major influence.

The thermal conductivity of the fluid being monitored cannot be measured directly. Instead, the ambient data, shown in

Table 4. Uncertainties of the measured quantities.

Quantity	Measurement Range	Uncertainty
Nozzle height H	16–120 mm	±0.1–0.3%
Nozzle pressure pNozzle	100–5000 Pa	±0.5–2%
Relative air humidity	40–60%	±1.5%
Ambient pressure	1027.7 hPa	±0.1%
Hydraulic diameter Dhyd	25 mm	±2.0%

, are measured and the corresponding thermal conductivity is obtained from the standard literature.

Additionally, the uncertainties of the quantities that are regarded as boundary conditions of the investigations must also be considered. This includes the measurement of the strip distance H, determination of the nozzle’s exit velocity u via the measured nozzle pressure p_nozzle and the influences on the fluid properties. These quantities and their uncertainties are listed in Table 4.

4. Results

A distinction is made between two investigations of nozzle systems for the application in heat treatment plants, the investigation of a single round nozzle and that of an array of round nozzles. The single nozzle study provides information on the performance of an impingement jet without the influence of how other nozzles, respectively, flow. A basic understanding of the characteristics of a single nozzle can, thus, be established for different nozzle exit velocities u and strip distances H.

However, as arrays of nozzles are typically used in heat treatment plants, it is necessary to extend the investigations from a single nozzle to an array of nozzles. Here, the interactions between the individual impingement jets can be studied and the arrangement of the individual nozzles can be optimised.

4.1. Single Nozzle

A single round nozzle with a hydraulic nozzle diameter of D_hyd = 25 mm and a nozzle length of L_nozzle = 80 mm was analysed. The strip distance is H = 50 mm and the nozzle box pressure p_nozzle = 1550 Pa, which corresponds to a nozzle exit velocity of u_nozzle = 52.6 m/s. This results in a Reynold number Re = 88,780, which corresponds to a fully turbulent flow.

Figure 5a shows the locally determined forced heat transfer coefficients per pixel. Figure 5b shows the forced heat transfer coefficients in the longitudinal direction through the centre of a single round nozzle at section A–A. The characteristic cooling pattern of a single round nozzle can be observed. A first maximum can be seen in the centre of the single round nozzle, which is subject to local variations. This is followed by a local minimum towards the nozzle wall, which is replaced by a second local maximum. The strong formation of two local maxima with increased heat transfer is typical for round nozzles. The distribution of the maxima and minima can be considered as rotationally symmetric.

However, the heat transfer distribution can also be visualised 3-dimensionally, Figure 6. The X- and Y-axes describe the longitudinal and transverse directions, analogous to Figure 5a. The Z-axis describes the heat transfer coefficient. This way of visualisation provides qualitative information about the flow conditions on the strip. For the single round nozzle, it is clearly possible to observe the primary and secondary maxima of the convective heat transfer resulting from the flow conditions. Also, the rotational symmetry is visible.

4.2. Nozzle Field

A round nozzle field consisting of 80 individual round nozzles with a hydraulic nozzle diameter of D_hyd = 25 mm and a nozzle length of L_nozzle = 30 mm was examined. The nozzles were arranged with a nozzle spacing of s = 100 mm. The chosen strip distance is H = 50 mm. The measured nozzle box pressure of p_nozzle = 1354 Pa corresponds to a nozzle outlet velocity of u_nozzle = 48.4 m/s, resulting in a Reynolds number of Re = 81.767. The calculated local heat transfer coefficients per pixel are shown in Figure 7a. The corresponding section A–A through the centre of the round nozzle field is illustrated in Figure 7b.

The local distribution of the forced heat transfer coefficients of the round nozzle system shows a clear influence of the impingement jets on each other. Each individual nozzle can be seen to have a local maximum. Low heat transfer coefficients can be seen where there are nozzle walls. Between the individual nozzles, in the mixed zone, the impingement jets from the surrounding nozzles meet and together form another honeycomb maximum.

5. Classification the Results

The results of the round nozzle field, Section 4.2, are compared with empirically determined equations established by other authors. As shown in Section 2.3, the model equations pertain to various geometric configurations and are, therefore, only partially comparable. Figure 8 compares the calculated mean heat transfer coefficients of forced convection for a round nozzle field according to various model equations with measurement results gathered with the presented method. A detailed description of all model equations can be found in Lenz [20].

The general correlation that the forced heat transfer coefficient increases less linearly with the nozzle exit velocity is evident for all models. The measurements also confirm this correlation. The measurement follows the Huber [12] model equation up to a nozzle exit velocity of u_nozzle = 50 m/s, after which the Kramer [17] model is the best approximation. The measurement show higher heat transfer coefficients than the Martin [6] model, but lower heat transfer coefficients than the Hilgeroth [8] model.

In general, the classification of the measurement results shows that both the measurement and the energy balancing for calculating the heat transfer coefficient are realistic and follow the recognised models of other authors. Noticeable differences are attributed to the different measurement methods. The Hilgeroth model predicts significantly higher heat transfer coefficients than all other models and the measurement. This can be explained by a significant change in the nozzle system compared to the other studies. Hilgeroth investigated a geometry consisting of round holes in parallel nozzle ribs through which air can flow. Accordingly, only a small space is available for the mixing zone with its backflows. The models of the other authors predict the same heat transfer coefficients as a function of the nozzle outlet velocity, taking geometric deviations into account.

The good agreement between the measurement and the Huber model is due to the short nozzle height of L = 30 mm. In his work, Huber analysed a perforated plate which, unlike Martin’s investigations, has no real nozzles. The length of Martin’s nozzles is unknown.

It is not possible to compare the local heat transfer coefficients from the measurement with the existing model equations. In the past, it was not possible to measure the temperature of the impact surface as accurately and with the same local resolution as it is possible today. The investigation methods with the local resolution are too different to be compared in a representative way.

6. Summary

The high-resolution method presented for determining the forced heat transfer coefficients on metal strips is used to more precisely design heat-treatment plants in order to increase the efficiency of nozzle fields. The method uses an IR thermal camera to measure the temperature distribution on a conductively heated strip as it is cooled by forced convection. The forced convective heat transfer is determined from the measured temperature distribution using an energy balance of all heat losses. Different local heat transfer coefficient distributions are presented, as well as the calculation method and the uncertainty of this measurement method.

Although there are many authors who discuss the design of nozzle systems, the applications can be very different. Smaller nozzle diameters and fields have been investigated more often in comparison to the experimental test setup presented, depending on the circumstances. However, the results can be transferred using dimensionless numbers. This work determines mean forced convection heat transfers that closely align with the equations according to Huber and Kramer. The present method can also be used to determine local heat transfer coefficients, but these cannot be compared with the work of other authors, as none have achieved this high resolution of 1.28 × 1.28 mm².

7. Outlook

To further accelerate the study of convective heat transfer, two additional measurement methods can be added to the experimental setup. These methods extend the setup, but always use the same setup base and analyse the same nozzle systems.

One upgrade is a special nozzle arrangement in which the flow for each individual nozzle can be adjusted independently. Thus, the convective heat transfer can be controlled for each nozzle, allowing the optimization of the resulting temperature gradients over the width and length of the strip. As a result, the temperature distribution can be optimized to improve the flatness of the steel strip during quenching. With the additional setup, it will be possible to study temperature gradients and how this affects flatness defects.

Both the basic setup and the upgrade of the individually adjustable nozzle field can be expanded to include laser measurement techniques. This allows a two-dimensional velocity vector field of the impact jets to be recorded using the particle image velocity (PIV) method. Flow and turbulence variables such as vorticity, turbulence level and Reynolds stress can, thus, be measured. This method enables a more detailed understanding of the flow conditions of the impingement jets and visualises the interactions of the individual impingement jets in a nozzle field. For this purpose, a corresponding laser shield was installed around the setup, which encloses the laser as well as the camera system.