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An experimental study was carried out to investigate the effects of inlet pressure, sample thickness, initial sample temperature, and temperature sensor location on the surface heat flux, surface temperature, and surface ultrafast cooling rate using stainless steel samples of diameter 27 mm and thickness (mm) 8.5, 13, 17.5, and 22, respectively. Inlet pressure was varied from 0.2 MPa to 1.8 MPa, while sample initial temperature varied from 600°C to 900°C. Beck’s sequential function specification method was utilized to estimate surface heat flux and surface temperature. Inlet pressure has a positive effect on surface heat flux (SHF) within a critical value of pressure. Thickness of the sample affects the maximum achieved SHF negatively. Surface heat flux as high as 0.4024 MW/m^{2} was estimated for a thickness of 8.5 mm. Insulation effects of vapor film become apparent in the sample initial temperature range of 900°C causing reduction in surface heat flux and cooling rate of the sample. A sensor location near to quenched surface is found to be a better choice to visualize the effects of spray parameters on surface heat flux and surface temperature. Cooling rate showed a profound increase for an inlet pressure of 0.8 MPa.

Water spray quenching of metals got a lot of attention due to its very high cooling efficiency. The traditional laminar quenching has low cooling rates in the range of 30°C/s^{2} heat flux [

Metal quenching is classified as ill-posed inverse heat conduction problem (IHCP). Direct chill (DC) casting is used to prepare the nonferrous metal ingots for the sheet metal rolling. In DC casting, heat transfer from the molten metal to the cooling water takes place through the outer solidified layer. Spray cooling derives large amount of heat by the evaporation of liquid droplets that are impinged upon a heated surface. In IHCP, boundary condition, that is, surface heat flux, of the quenched surface is to be estimated from the temperature measurements made at an arbitrary location inside the metal. Inside metal temperature histories are used due to practical difficulty to install and insulate the temperature sensor in the boundary of metal, associated with IHTP [

The mechanical properties of steel are directly related to microstructure of the steel which in return directly depend on the finish roll temperature and rate of cooling. In a typical production line of run out table of steel industry, the strips are reheated to a hot rolling temperature close to 900°C and then cooled down to coiling temperature of 600°C [

Current study focused on effects of inlet spray pressure, thickness of the sample, initial sample temperature, and sensor location on surface heat flux, surface temperature, and cooling rate during ultrafast inverse heat conduction from stainless steel plate utilizing Beck’s sequential function specification method with one interior point temperature history.

The effect of variation of inlet pressure on the mean volume diameter (MVD) can be determined by the following equation [

A direct problem is a common problem with known governing equation along with material properties involved in the equation. Initial and boundary conditions are per specified. The aim of the direct problem is to determine the field variable. On the other hand, in an inverse problem, a part of the usual description is not given and to be found. In inverse problem, some experimental data are given to estimate the unknown part of the usual description of the problem. Inverse problem can be categorized as a boundary inverse problem, coefficient inverse problem, and retrospective inverse problem. Present study deals with a boundary inverse problem. In a boundary inverse problem, boundary heat flux at

In order to estimate the surface heat flux history during the quenching process of metal sample, it is necessary to make a mathematical model of the heat conduction process. In present study, the quenched target was taken as homogeneous, isotropic, and flat. A mathematical illustration of the inverse heat conduction problem is given as [

The objective is to find

At this point, let us introduce a new sensitivity coefficient, defined as

For

The experimental setup used in this research was comprised of three main systems, namely, fluid supply system, instrument system, and heating system, as shown in Figure

Sketch of experimental facility.

Fluid delivery system (FSS) consisted of a spray nozzle supplied by Spray Systems Co. Ltd. FSS was equipped with a CDL3-36 non-self-priming vertical multistage centrifugal pump with a head of 152 m. It can work in the fluid working temperature limits of −15°C to +120°C.

Coriolis mass flow meter (ZLJ series) had been used in the fluid delivery system to measure the mass flow rate of the fluid during spraying process. FSS had also been provided with a pressure sensor (0

Instrumentation system includes all of the necessary electronic equipment to drive the FSS, to power heaters, and to acquire necessary measurements. It consists of a data acquisition system installed in personal computer, thermocouples installed at different geometrical locations inside the stainless steel sample, and FSS delivery system to monitor the temperature variations.

The primary component of hot surface is a stainless steel sample (cylindrical shape) with a diameter

Details of cylindrical stainless steel samples: (a) stainless steel sample, (b) holder assembly, (c) red hot sample before quenching, and (d) sample after quenching.

In present work, we studied 1D spray heat transfer from top surface of the heater so cylindrical surface of the heater was insulated with ceramic tube and bottom surface was insulated with fiber glass insulation. Benson burner with natural gas was used to heat up the block to desire high temperature (100~900°C).

It is obvious that the flow rate of the water through nozzle increases with the increase in the inlet pressure. The increase in the mass flow rate is exponential as shown in Figure

Variation of mass flow rate with inlet pressure.

Variation of droplet velocity with inlet pressure.

Variation in droplet size with inlet pressure.

Variation of Weber number as a function of inlet pressure.

In order to study the effect of inlet nozzle pressure on surface heat flux during spray cooling of stainless steel block of ^{2}, 0.2563 MW/m^{2}, and 0.4024 MW/m^{2,} respectively. At inlet pressure of 1.3 MPa, the MSHF decreases to 0.3577 MW/m^{2}. The decrease in the MSHF at high inlet pressure of the fluid can be explained by considering the effect of inlet pressure on mean velocity,

Variation of surface heat flux with inlet pressure.

Variation of maximum surface heat flux as a function of inlet pressure.

Figure

Variation of surface temperature with inlet pressure.

Effect of inlet pressure on cooling rate.

The amount of heat content in any plate depends upon its dimension and initial temperature. In the present study, heat transfer is considered along the thickness of the plate, and in another direction it is supposed to be negligible. Hence, the plate thickness decides the heat content in the present case.

It is shown in Figures ^{2}, 0.2667 MW/m^{2}, 0.257 MW/m^{2,} and 0.2101 MW/m^{2,} respectively, showing decrease in surface flux (Figure

Variation of surface heat flux with thickness of the sample.

Variation of maximum surface heat flux with thickness of the sample.

The real-time surface temperature plots for

Variation of surface temperature with thickness of the sample.

As explained earlier, cooling rate decreases with increasing thickness of a sample. Cooling rates of 558.71°C/s, 289.11°C/s, 160.02°C/s, and 156.95°C/s are achieved for

Effect of thickness sample on surface cooling rate.

Surface heat flux for four different initial sample temperatures was estimated under constant inlet pressure of 1 MPa for a sample of ^{2}< 433900 W/m^{2}< 497800 W/m^{2,} while, for initial sample temperature of 900°C, a corresponding decrease in maximum achieved heat flux was observed, that is, 471100 W/m^{2}. The trend of maximum surface flux variation for different initial sample temperatures is represented in Figure

Variation of surface heat flux with initial average sample temperature.

Variation of surface heat flux with initial sample temperature.

Variation of surface temperature with initial average sample temperature.

Variation of cooling rate with initial sample temperature.

Though in present study we consider ID heat conduction but in real world no ideal thermal insulation exists which can totally prevent heat conduction from cylindrical and bottom surface of the cylinder. The temperature response at the surface from an interior point has an obvious dependence on the location of the temperature sensor. Estimated surface heat flux from the temperature response from different vertical locations from the sprayed cooled surface is shown in Figure

Estimation of surface heat flux from different sensor locations.

Variation of surface heat flux with different sensor locations.

Estimation of surface temperature from different sensor locations.

Variation of cooling rate with different sensor locations.

As it is clear from Figures

Effect of inlet pressure on surface cooling rate.

Effect of initial average body temperature on surface cooling rate.

Present study was focused on determining the effects of inlet pressure, sample thickness, and sensor location on surface heat flux, surface temperature, and cooling rate during water quenching of stainless steel. Inverse heat conduction ill-posed Beck’s sequential function specification linear method was used to estimate the time-varying surface heat flux and surface temperature of the quenched sample. A prior study was carried out to determine the effect of the inlet pressure on mass flow rate, mean spray velocity, inlet velocity, droplet size, and Weber number (

cooling rates in the ultrafast cooling range were achieved with water spray cooling during quenching of the stainless steel samples;

maximum achieved surface heat flux increases with increase in inlet pressure, but this increase in surface heat flux is limited to a critical value of inlet pressure depending on a balance between the mean spray velocity and droplet size;

maximum achieved surface heat flux decreases with an increase in the thickness of the sample. In other words thickness of the plate has inverse relation with surface heat flux during quenching of the metal samples;

vapor film effects become dominant in the initial sample range of 900°C, causing a corresponding decrease in the maximum surface heat flux and cooling rate of the sample;

temperature sensor location near to quenched surface is a better choice to better understand the effects of spray parameters on the surface flux, surface temperature, and surface cooling rates;

the increase in inlet pressure increases cooling rate of the surface of the sample to a certain critical value of the inlet pressure depending on the individual characteristics of the nozzle to be used. Above the critical value of inlet pressure, cooling rate of the surface has decreasing trend;

surface cooling rate increases with increasing surface super heat.

The authors declarethat there is no conflict of interests regarding the publication of this paper.

The authors are grateful for the support of the State Key Development Program for Basic Research of China (Grant no. 2012CB720403), the National Natural Science Foundation of China (no. 50906102), and the Natural Science Foundation of Chongqing, China (no. CSTC2011jjA90015).