[ Original ]
Journal of Korea Technical Association of the Pulp and Paper Industry - Vol. 52, No. 3, pp.77-89
ISSN: 0253-3200 (Print)
Print publication date 30 Jun 2020
Received 11 May 2020 Revised 09 Jun 2020 Accepted 11 Jun 2020

# Heat Transfer Characteristics in Horizontal Rectangular Channel of Multi-Channel Cylinder Dryer

Lijie Qiao1, ; Jixian Dong2, ; Zhuozhi Yang3 ; Sha Wang4 ; Huan Liu4 ; Bo Wang5 ; Lingbo Kong2,
1College of Mechanical and Electrical Engineering, Shaanxi University of Science & Technology, Xi’an, Shaanxi Province, 710021, People’s Republic of China, Lecturer.
2College of Mechanical and Electrical Engineering, Shaanxi University of Science & Technology, Xi’an, Shaanxi Province, 710021, People’s Republic of China, Professor.
3College of Flight Technology, Civil Aviation Flight University of China, Guanghan, Sichuan Province, 618307, People’s Republic of China, Lecturer.
4College of Mechanical and Electrical Engineering, Shaanxi University of Science & Technology, Xi’an, Shaanxi Province, 710021, People’s Republic of China, Student.
5College of Mechanical and Electrical Engineering, Shaanxi University of Science & Technology, Xi’an, Shaanxi Province, 710021, People’s Republic of China, Senior Experimentalist.

Correspondence to: E-mail: qiaolijie@sust.edu.cn (Address: College of Mechanical and Electrical Engineering, Shaanxi University of Science & Technology, Xi’an, Shaanxi Province, 710021, People’s Republic of China) Co-corresponding Author :‡ E-mail: djx@sust.edu.cn, lbkong@sust.edu.cn (Address: College of Mechanical and Electrical Engineering, Shaanxi University of Science & Technology, Xi’an, Shaanxi Province, 710021, People’s Republic of China)

## Abstract

The multi-channel cylinder dryer (MCD) for drying paper may be a promising solution to the energy consumption in paper drying. However, energy consumption is related to the heat transfer characteristics of the steam condensation process. The investigation of heat transfer coefficient (HTC) in horizontal rectangular channel of MCD was experimentally performed in this paper. And the changes of overall HTC, condensation HTC and HTC of cooling water side were explored under different condensing conditions. The results showed that the overall HTC increased with the increasing of the Nusselt number of cooling water, Reynolds number of cooling water and mass flow rate of cooling water. And the condensation HTC will increase with the increasing mass flow rate of cooling water and Reynolds number of cooling water, however, there is a fluctuation of the condensation HTC changing with Reynolds number of cooling water increasing. A better heat transfer performance can be achieved by the increase of steam mass flux, while excessive pressure drop can be avoided by setting a reasonable steam mass flux, 24 kg·m-2·s-1.

## Keywords:

Paper drying, multi-channel cylinder dryer, horizontal rectangular channel, heat transfer coefficient, condensation heat transfer coefficient

## 1. Introduction

The heat transfer of cylinder dryer used in traditional paper drying was realized by steam condensation, and considerable heat will generate due to the release of latent heat.1-3) However, the thermal resistance in the dryer is one of the most important problems hindering the effective transfer of heat.4,5) The working thermal resistance of the cylinder dryer is mainly composed of the thermal resistance generated by the condensed water layer, the thermal resistance generated by the thickness of the dryer wall, and the thermal resistance from the outer surface of the dryer to the wet paper web. The thermal resistance generated by the thickness of the dryer wall is affected by thermal conductivity and thickness of the wall, which can be regarded as constant. Therefore, the thermal resistance from the condensate layer and from sheet-to-dryer should be further studied. Corresponding to the thermal resistance, the total heat transfer coefficient (HTC) includes three parts: condensation HTC of condensate in dryer side, thermal conductivity of dryer wall and HTC from dryer outer web.

The condensate evacuation technology based on different principles were proposed in previous studies.4-9) The siphon technology is a good method due to its effective condensate removal effect.6-11) However, affected by the higher rotational force, siphon’s drainage capacity will reach its limit when facing high paper machine speed. Different from the siphon principle, a new device named axial spoiler bars installed in the dryer can improve the heat transfer efficiency7,9-11) through increasing the turbulence. And the heat transfer efficiency of dryer will be improved through the condensate layer to the dryer shell.

Although a series of technological transformations were conducted, the accumulation of water in the cylinder dryer has not been effectively resolved. Multi-channel cylinder dryer (MCD) is a new type of cylinder dryer proposed to solve the condensate accumulation of traditional cylinder dryers,12,13) as shown in Fig. 1, simultaneously it reduces the thermal resistance generated by the condensed water layer in the dryer. The incoming steam is restricted to flow in the small channel along the axial direction of the inner wall of the dryer, and the condensed water is pushed out of the dryer by the subsequent steam, and there is no water accumulation in the dryer. Compared with the traditional dryer, MCD significantly improves the condensate accumulation, and the condensation HTC of it is nearly 7 to 20 times14,15) larger than that of a conventional dryer.

The schematic diagram of traditional dryer and MCD.

It is obvious that a gas-liquid two-phase mixed flow formed in the small channel due to the generation of condensation, and its heat transfer characteristics are relatively complicated.14) On the one hand, the drying efficiency of MCD will be affected by the characteristics of steam condensation,14,15) so analyzing the characteristics of steam condensation is of great significance to improve the heat transfer performance, and many relationships have been obtained in previous studies.16-20) On the other hand, the heat transfer coefficients in horizontal channels were studied in the literatures.21-23) Gu et al.21) investigated the condensation characteristic of refrigerant fluoroolefin R1234ze(E) in horizontal circular, square and triangle mini-channels numerically. It showed that the heat transfer coefficients of the square or triangle tube were larger than that of the circular tube under the same external perimeter. The factors, including steam mass flux, system pressure, and channel aspect ratio, affecting steam-side heat transfer and pressure drop were explored by Choi et al.14) and Shin et al.15) through conducting experiments in the channel of the multi-channel dryer. In addition to considering the steam quality, Yan et al.18) also observed the flow pattern in the steam channel.

The contribution of the cooling-side HTC to the total HTC was ignored in the previous studies. However, the comprehensive consideration of HTC from the cooling-side and the condensate layer is important for the study of MCD heat transfer, which is included in this study. For the drying process of the dryer, there is convective heat transfer of the fluid (air flow) on the surface of the dryer, and the Nusselt number (Nu) of the cooling side fluid is a key parameter that affects the convective heat transfer of the cooling side.22) Coolant Reynolds number (Rec) and Prandtl number (Pr) are important parameters affecting Nu. Rec reflects the degree of turbulence of cooling water, and the study of Rec is meaningful due to convective heat transfer can be promoted by adjusting the degree of turbulence. The more sufficient the turbulence of the cooling water was, the better the convection heat transfer was. Rec is so important in determining condensation behavior, that it is convenient to express the HTC in terms of Rec.23) Simultaneously, Pr reflects the influence of the physical properties of the cooling medium on the convective heat transfer process. Cheng et al.22) and Ma et al.23) studied the influence of Rec of coolant, mass flow rate of coolant, steam mass flux and non-condensable gas ratio on steam condensation HTC and the total HTC of rectangular channel filled with steam / nitrogen mixture. It showed that higher coolant Reynolds number and corresponding coolant HTC brings about greater overall HTC.

The object of this paper is to explore the influence of Nusselt number, Reynolds number, mass flow rate of cooling water and steam mass flux on heat transfer coefficient based on experimental studies.

## 2. Materials and Methods

### 2.1 Experimental setup

The experimental apparatus used in this study consisted of three primary sections, as shown in Fig. 2, the test section, the steam loop and the cooling water loop. The test section is the core of the experimental system, in which the steam condensed and released the heat to the cooling water, and the cooling water was circulated in its loop for cooling the steam in the test section.

The schematic diagram of the experimental setup.

In steam loop, the saturated steam is generated by an electronic boiler heating the deionized water for preventing possible incrustation. Subsequently the steam entered the test section and condensed to form a two-phase flow, which would be completely condensed in the sub-cooler. And it is convenient to measure the mass flux of the condensate by a turbine flowmeter. Meanwhile, the sub-cooler prevented the steam from damaging subsequent flowmeters. Finally, the condensate returned to the condensate tank for recycling.

In order to cool the steam, water is pumped from the cooling water tank into the test section and flowed countercurrent to absorb the heat released from the steam side. The mass flow rate at the inlet of the cooling water channel and the temperature difference of cooling water between the inlet and outlet were measured. After exiting the channel, the cooling water flowed through a water chiller to release the absorbed heat for keeping the temperature of water tank nearly isothermal. And then the cooling water is returned to the water tank for the storage and circulation.

### 2.2 Measuring devices and uncertainty

The test section is consisted of three plates bolted together, as presented in Fig. 3. The middle plate was milled by aluminum with grooved rectangular channels on both sides. The steam and cooling water in two different parallel channels flowed in the opposite direction. The steam channel was covered with a transparent quartz glass plate for the observation, and the cooling water channel is covered with a stainless-steel plate for seal. And the experimental system was insulated well to prevent the heat loss. The effective length of the channels is 800 mm. As shown in Fig. 3(b), the height and the width of the steam channel cross-section were 4.5 mm and 13.5 mm.

Schematic diagram of the test section.

Temperature and pressure were measured by T-type thermocouples and manometers. Four thermocouples were installed in the inlets and outlets of two channels, respectively. The temperature of the cooling water was measured by seven thermocouples (T-type: -200~350℃) arranged along the channel with 100 mm adjacent distance, and six thermocouples (T-type: -200~350℃) were evenly embedded in the wall between the two channels to measure surface temperature, at 140 mm intervals as well. One pressure transmitter (PX 409-150GV: 0-1,034 kPa) is used to measure the steam inlet pressure, one differential pressure transmitter (PX409-2.5GI: 0-17.2 kPa) for the pressure drop on the steam side, and two turbine flow meters were used to the measurement of the steam flow (FTB1411: 2.3-11.3 LPM) and the coolant flow (FLR1009-BR-D: 50-500 LPM). In addition, the data acquisition instrument (LR8400, HIOKI, Japan) was set to record the temperature, pressure and flow in the section every 20 ms, and all experimental data points were measured under steadystate conditions.

### 2.3 Data reduction

Five main variables involved in the test were the steam mass flux G (ranges from 5 kg·m-2·s-1 to 40 kg·m-2·s-1), and the next four variables all about cooling water, mass flow rate mc (ranges from 56.16 kg·h-1 to 532.8 kg·h-1), Reynolds number Rec (ranges from 1,925.3 to 11,682.4), Nusselt number Nuc (ranges from 9.91 to 92.59), and Prandtl number Prc (ranges from 3.5997 to 5.9855).

2.3.1 Thermal equilibrium

The absorbed heat by the cooling water was derived from a thermal equilibrium on the water channel as Eq. 1:

 ${Q}_{\mathrm{c}}={C}_{\mathrm{p}}{m}_{\mathrm{c}}\left({T}_{\mathrm{c}\mathrm{o}}-{T}_{\mathrm{c}\mathrm{i}}\right)$ [1]

In which mc is the mass flow rate of the cooling water, Cp is the specific heat of the cooling water. Tco and Tci are the outlet and inlet temperature of cooling water, respectively.

The released heat from the steam was calculated as follows:

 ${Q}_{\mathrm{s}}={A}_{\mathrm{s}}{h}_{\mathrm{s}}\left({T}_{\mathrm{s}}-{T}_{\mathrm{w}}\right)$ [2]

In which As is the surface area of the heat transfer, hs is the average condensation heat transfer coefficient of the steam channel. Ts is the average steam temperature, and Tw is the average wall temperature between the steam channel and the cooling water channel.

Only when the thermal equilibrium between the absorbed heat and the released heat is approximately within ±10%, the experimental data is considered useful and is acquired. In this experiment, the heat transfer rate between the two channels can be considered as the absorbed heat by the cooling water.

2.3.2 Heat transfer coefficients

The heat transfer characteristic were reported in terms of HTC of the cooling water channel hc, condensation HTC hs and overall HTC K.

The cooling water flowed without changing phase, and the Reynolds number Rec varied about from 2.0×103 to 1.2×104 during the experiment. The HTC of the cooling water channel was calculated by the Gnielinski correlation24):

 ${h}_{\mathrm{c}}=\frac{N{u}_{\mathrm{c}}{\lambda }_{\mathrm{c}}}{{d}_{\mathrm{c}}}$ [3]
 $N{u}_{\mathrm{c}}=\frac{\left(f/8\right)\left(R{e}_{\mathrm{c}}-1000\right)P{r}_{\mathrm{c}}}{1+12.7\sqrt{f/8}\left({\mathit{Pr}}_{\mathrm{c}}^{2/3}-1\right)}\left[1+{\left(\frac{{d}_{\mathrm{c}}}{{l}_{\mathrm{c}}}\right)}^{\frac{2}{3}}\right]{C}_{\mathrm{t}}$ [4]
 $R{e}_{\mathrm{c}}=\frac{{\rho }_{\mathrm{c}}{u}_{\mathrm{c}}{d}_{\mathrm{c}}}{{\mu }_{\mathrm{c}}}$ [5]
 ${C}_{\mathrm{t}}={\left(\frac{p{r}_{\mathrm{c}}}{p{r}_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}}\right)}^{0.01}$ [6]
 $f={\left(1.82\mathrm{l}\mathrm{o}\mathrm{g}R{e}_{\mathrm{c}}-1.64\right)}^{-2}$ [7]

Where λc, ρc and μc represented the thermal conductivity, density and kinematic viscosity of cooling water, respectively. dc and lc represented the characteristic dimension of cooling water channel. Prc represented the Prandtl number of cooling water, and Prwall wall temperature was the Prandtl number at the wall temperature. uc represented the velocity of cooling water.

The local condensation HTC of any minor test segment can be expressed as:

 ${h}_{\mathrm{s},\mathrm{i}}=\frac{{Q}_{\mathrm{s},\mathrm{i}}}{{A}_{\mathrm{i}}\left({\overline{T}}_{\mathrm{s},\mathrm{i}}-{\overline{T}}_{\mathrm{w},\mathrm{i}}\right)}=\frac{{q}_{\mathrm{s},\mathrm{i}}}{{\overline{T}}_{\mathrm{s},\mathrm{i}}-{\overline{T}}_{\mathrm{w},\mathrm{i}}}$ [8]

In which hs,i, Qs,i, Ai and qs,i represented condensation HTC, heat transfer rate, area and heat flux of each minor segment, respectively. ${\overline{T}}_{\mathrm{s},\mathrm{i}},{\overline{T}}_{\mathrm{w},\mathrm{i}}$ was temperature of steam and cooling water in each minor segment. In each minor segment, the heat transfer rate absorbed by cooling water was approximately equal to the heat transfer rate released from the steam.

The average condensation HTC hs of the steam channel side was expressed as:

 ${h}_{\mathrm{s}}=\int \frac{{h}_{\mathrm{s},\mathrm{i}}dl}{l}\approx \frac{1}{l}\sum _{i=1}^{n}{h}_{\mathrm{s},\mathrm{i}}∆l$ [9]

Where l was the length of the channel.

Finally, in the light of the whole thermal resistance analysis on the convective heat transfer process in steam channel, cooling water channel and on the thermal conduction of the metal wall between both channels, the overall HTC can be calculated by:

 $K=1/\left(\frac{1}{{h}_{\mathrm{s}}}+\frac{\delta }{\lambda }+\frac{1}{{h}_{\mathrm{c}}}\right)$ [10]

where δ was the wall thickness and λ was the thermal conductivity of aluminum metal.

## 3. Results and Discussion

### 3.1 Temperature distribution and heat transfer rate

The temperature and pressure were measured by T-type thermocouples and manometers in this paper. The temperature distributions were depicted in Fig. 4. Tsi, Tci, Tco, Twi and Two represented temperature of steam inlet, cooling water inlet/outlet and wall surface inlet/outlet. Fig. 4(a) showed that experimentally measured temperature rose with the increasing of steam mass flux with constant inlet temperature and mass flow rate of cooling water, due to an increase in heat carried by steam. However, other temperatures declined as the cooling water mass flow rate increased with constant steam temperature and mass flux, due to the effective absorption of heat by increasing cooling water, as shown in Fig. 4(b).

Temperature distributions with changes in steam mass flux and mass flow rate of cooling water.

The influence of steam inlet mass flux and Reynolds number of cooling water on variations of heat transfer rate were shown in Fig. 5. It was found that the heat transfer rate increased with the increasing of steam mass flux, as shown in Fig. 5(a). And the heat transfer rate increases by 100.8% with increasing Reynolds number of cooling water from 1,925.3 to 11,682.4, as shown in Fig. 5(b). An increase in Reynolds number represented better turbulence, which meant a stronger heat transfer ability in the cooling water channel under the present test condition.

Development of heat transfer rate with changes in steam mass flux and Reynolds number of cooling water.

### 3.2 Influence of parameters of cooling water side on cooling water heat transfer coefficient and overall heat transfer coefficient

The influences of four parameters of cooling water side, Rec, Prc, Nuc and mass flow rate, on heat transfer coefficient were studied in this section.

The effect of Nusselt number on heat transfer performance were explored in this paper, as shown in Fig. 6, under the condition of the steam mass flux was 30 kg·m-2·s-1 and the steam temperature was 120°C. It was shown that Nuc strengthened the heat transfer process on the cooling water side, and the total HTC increases accordingly. However, as Nuc increased to the maximum, the HTC of cooling water side increased by 780% and total HTC increased by 546%. Obviously, the HTC of cooling water side increased more rapidly than the increase of total HTC. Based on Eq. 3, Nuc was a key factor affecting the convective heat transfer coefficient of cooling water. From Eq. 4, both Prc and Rec can affect Nuc. Among them, Prc reflects the influence of physical properties of cooling water on the heat transfer process. As revealed in Fig. 7(a), Nusselt number Nuc increased with the increase of Reynolds number Rec. The reason for the increase of Nuc was that as Rec increased, the more sufficient the turbulence of the cooling water was, the better the convection heat transfer was. As for Prandtl number Prc, its increase also promoted the growth of Nuc, as displayed in Fig. 7(b). Since Prc=μc·Cpc /λc (where μc, Cpc and λc represented the kinematic viscosity, specific heat capacity and thermal conductivity of cooling water respectively), Prc characterized the effect of cooling water physical properties on heat transfer. The physical properties of the medium removing heat had a positive effect on heat transfer.

Effect of Nusselt number on heat transfer performance.

Variation of Nusselt number in cooling water side.

The cooling water’s mass flow rate, which used to reflect the cooling water side thermal resistance, actually simulated the cooling load of wet paper webs with different moisture contents. The variation of the heat transfer performance with mass flow rate of cooling water was depicted in Fig. 8. With the increase of mass flow rate of cooling water, both the HTC of cooling water side and total HTC increased. However, as mass flow rate of cooling water became larger, the effect on the HTC of cooling water side was becoming more significant and the growth tendency was relatively faster. The convective heat transfer between the cooling water and the wall surface increased as the mass flow rate of cooling water increased. Due to the larger flow rate, the average temperature of the cooling water became lower after heating, and the temperature difference between the wall surface and the cooling water became larger. In the end, heat transfer was effectively promoted.

Effect of mass flow rate of cooling water on heat transfer performance.

### 3.3 Influence of steam mass flux and Reynolds number on the condensation heat transfer coefficient and overall heat transfer coefficient

The steam condenses and releases heat in the MCD, and transfers the heat to the wet paper web covering the outside of the dryer wall to drying the paper. Obviously, the steam mass flow rate directly reflects the heat consumption. The previous research shows that the steam mass flux is an important factor affecting the heat transfer in the horizontal channel.25,26) Reynolds number Rec reflects the degree of turbulence of cooling water, and the study of Rec is meaningful due to convective heat transfer can be promoted by adjusting the degree of turbulence. The more sufficient the turbulence of the cooling water was, the better the convection heat transfer was. Rec is so important in determining condensation behavior, that it is convenient to express the HTC in terms of Rec.

The influences of steam mass flux on HTC were shown in Figs. 9-10. Both the average condensation HTC and total HTC increased with the increase of steam mass flux as shown in Fig. 9. The steam mass flux resulted in larger temperature difference and heat flux as shown in Fig. 10. On the one hand, as the steam mass flux increased from 5 kg·m-2·s-1 to 24 kg·m-2·s-1, the average heat flux increased while the average temperature difference decreased. According to Fourier’s law, the average condensation HTC should decrease. On the other hand, as the steam mass flux increased from 24 kg·m-2·s-1 to 40 kg·m-2·s-1, the average heat flux increases by 71.3%, but the average temperature difference increases by 30.5%. Obviously, the heat flux increased more rapidly than the increase of temperature difference, which still leading to the increase of condensation HTC. As a result, the growth tendency of both the average condensation HTC and the total HTC were relatively slower. As the increased steam mass flux enhanced the condensation heat transfer process in the steam side, the overall heat transfer was also improved and the total HTC rose correspondingly. In consequence, it can be concluded that the increase of steam mass flux resulted in better heat transfer performance.

Variation of heat transfer coefficient with steam mass flux.

Variation of temperature difference and heat flux with steam mass flux.

In particular, the present data was notably same as the results of Yan et al.18) In Yan’s studies, at a steam mass flux of 20-40 kg·m-2·s-1, slug flow and wavy flow were frequent over most of the mass flux region. Therefore, when the steam mass flux was 24 kg·m-2·s-1, the slug flow and wave flow increased the disturbance of the steam phase, thereby increasing the relative surface roughness between the two-phase interface, and correspondingly increased the friction between steam and condensate, resulting in a larger two-phase flow pressure drop. If the two-phase flow pressure drop in the steam condensation process is greater, it indicates that the greater the frictional resistance that the steam overcomes during the heat transfer in the channel, the more energy is consumed. It is conceivable that for multi-channel dryers to dry paper, the more energy required. Therefore, choosing a reasonable steam mass flux (G is 24 kg·m-2·s-1) can avoid excessive pressure drop.

The influences of steam mass flux and Rec number on HTC were shown in Figs. 11-12. As presented in Fig. 11, The condensation HTC and total HTC increased with the increase of Rec. As described in Fig. 12, the heat flux increased by 101%, but the temperature difference increased by 81%, as the Reynolds number of cooling water increased from 1,925.3 to 11,682.4. Therefore, still according to Fourier’s law, the heat flux increased more rapidly than the increase of temperature difference, which still leading to the increase of condensation HTC. However, the heat transfer coefficient of the cooling water fluctuated, which was due to the large variation in the Reynolds number. As the Reynolds number changed, the fluid had experienced laminar flow, transition flow, turbulence, and fully developed turbulence, resulting in extremely instable flow fields. This instability made the shearing effect between the wall surface and the cooling water sometimes strong and sometimes weak. On the one hand, when the shear action was strong, the heat transfer caused by turbulence is enhanced. On the other hand, when the shearing effect was weak, the cooling water layer became thicker, which caused the thermal resistance to increase and the heat transfer to weaken. As a result, it can be found that as the Reynolds number increased, the total heat transfer was increased, and the total HTC was increased accordingly.

Variation of heat transfer coefficient with Reynolds number.

Variation of temperature difference and heat flux with Reynolds number.

## 4. Conclusions

This paper experimentally investigated the heat transfer performance involved steam condensation in the horizontal rectangular channel of a multichannel cylinder dryer. The influence of Nusselt number, mass flow rate of cooling water, steam mass flux and Reynolds number on heat transfer coefficient was examined.

• 1) Higher Nusselt number of cooling water and corresponding HTC of cooling water side brought about greater overall HTC, resulted from the effects of Reynolds number and Prandtl number of cooling water. The change of Prc indicated that the research on the physical properties of the medium removing heat was positive. Increasing mass flow rate of cooling water caused stronger turbulence and higher interfacial shear stress, and led to the increase of the condensation HTC and overall HTC.
• 2) The increase of steam mass flux resulted in better heat transfer performance. It was noteworthy that, when the steam mass flux was 24 kg·m-2·s-1, the occurrence of slug flow and wave flow caused a larger pressure drop causing greater friction resistance. Therefore the more energy was required to overcome the greater frictional resistance. Thus, choosing a reasonable steam mass flux (G was 24 kg·m-2·s-1) can avoid excessive pressure drop.
• 3) As Reynolds number increased, the general trend of the condensation HTC increased because the growth rate of the heat flux was higher than that of the heat transfer temperature difference. The fluctuation of the condensation HTC was due to the change of the Reynolds number causing the instability of the flow state. In addition, as the Reynolds number increased, the total heat transfer was increased, and the total HTC was also increased accordingly.

## Nomenclature

 A : area, m2 Cp : specific heat capacity, kJ·(kg·K)-1 D : difference d : diameter, m G : mass flux, kg·m-2·s-1 m : mass flow rate, kg·h-1 h : heat transfer coefficient, kW·m-2·K-1 K : total heat transfer coefficient, kW·m-2·K-1 Nu : Nusselt number Pr : Prandtl number Q : heat transfer rate, kW q : heat flux, kW· m-2 Re : Reynolds number T : temperature, °C $\overline{T}$ : average temperature, °C u : velocity, m·s-1

## Greek symbols

 δ : wall thickness, m λ : thermal conductivity, W·(m·K)-1 μ : viscosity, N·s·m-2 ρ : density, kg·m-3

## Subscripts

 c : cooling water i : inlet o : outlet s : steam w : wall

## Abbreviation

 HTC : heat transfer coefficient MCD : multi-channel cylinder dryer

## Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 51375286 and 21808135), Shaanxi Provincial Technology Innovation Guidance Project (Fund) (Grant No. 2018HJCG-10), Shaanxi Provincial Key Research and Development Project (Grant No. 2020GY-105).

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### Fig. 1.

The schematic diagram of traditional dryer and MCD.

### Fig. 2.

The schematic diagram of the experimental setup.

### Fig. 3.

Schematic diagram of the test section.

### Fig. 4.

Temperature distributions with changes in steam mass flux and mass flow rate of cooling water.

### Fig. 5.

Development of heat transfer rate with changes in steam mass flux and Reynolds number of cooling water.

### Fig. 6.

Effect of Nusselt number on heat transfer performance.

### Fig. 7.

Variation of Nusselt number in cooling water side.

### Fig. 8.

Effect of mass flow rate of cooling water on heat transfer performance.

### Fig. 9.

Variation of heat transfer coefficient with steam mass flux.

### Fig. 10.

Variation of temperature difference and heat flux with steam mass flux.

### Fig. 11.

Variation of heat transfer coefficient with Reynolds number.

### Fig. 12.

Variation of temperature difference and heat flux with Reynolds number.