Liquid Heat Transfer Research Articles

Experimental investigation of the intermittent spray heat transfer characteristics of nanofluids in single- and two-phase states

Traditional air-cooled cooling systems used in engineering vehicles consume significant energy and do not align well with future development trends. To address this problem, a single- and two-phase intermittent spray cooling technique for nanofluids was proposed in this study. The effects of the duty cycle and spray frequency on the heat transfer performance and surface temperature uniformity of intermittent spray were determined by experiments, and the thermal behaviour of intermittent spray with different mass fractions of Al2O3 nanofluids was compared in detail. The results revealed that when the spray frequency is constant, the heat transfer coefficient increases with an increase in duty cycle, but the cooling efficiency decreases. The spray frequency mainly affects the average heat transfer surface temperature and its uniformity. At 2.0 Hz, nanofluids with a mass fraction of 0.7 % exhibited the best intermittent spray performance, with an average heat transfer coefficient of 431.8 W/(m2·K). However, a continuous increase in the mass fraction of the nanofluids inhibited the heat transfer performance. The impact of droplets on the heat transfer surface, the liquid film heat transfer process, and the heat transfer characteristics of the nanofluid intermittent spray in the single- and two-phase states were further studied. The results revealed that the heat transfer of intermittent spray mainly depends on the properties and flow rate of the coolant in a single-phase state. Although the heat transfer performance of intermittent spray is evidently enhanced in the two-phase state, it still does not exceed that of continuous spray. These findings highlight the flexibility of nanofluid intermittent spray cooling in enhancing heat transfer control and can inform the development of energy-saving and intelligent cooling systems for engineering vehicles.

A prediction model based on data-driven method for velocity and heat transfer coefficient of falling-film liquid on horizontal tube

The prediction of liquid film velocity and heat transfer coefficient of horizontal-tube falling-film flow is important for the investigation and enhancement of the flow and heat transfer behavior. To date, the prediction mainly relies on semi-empirical-semi-theoretical formulas based on data fitting. This prediction method has many limitations and assumptions on working conditions, and the error is large when it is extended to practical applications. In this paper, a support vector regression machine prediction method based on sine cosine algorithm optimization is proposed to improve the prediction accuracy of the liquid film velocity and heat transfer coefficient. And the database was established by conducting horizontal-tube falling-film flow and heat transfer experiments. Results show that the support vector regression model has the best prediction performance with small sample size in comparison with other four machine learning methods and traditional correlation based on Least Square method. The RMSEs of liquid film prediction model and heat transfer prediction model are only 0.0281 and 0.0117 respectively. And the MAPEs are 8.58 and 2.63 respectively. The liquid film velocity and heat transfer coefficient were accurately predicted based on relevant parameters. The importance of these parameters was also analyzed.

Experimental investigation of the oscillation threshold to limit state operation of a single branch pulsating heat pipe

The study investigates the characteristics of oscillations and associated thermo-hydrodynamic phenomena for startup, limit state, and intermediate transitional behavior of a pulsating heat pipe (PHP) with the help of its single branch. Experiments are performed on a transparent single branch PHP (SBPHP) at different orientations, evaporator and condenser section temperatures using n-pentane as the working fluid. The entire two-phase flow behavior is recorded with the help of shadowgraph based high speed imaging synchronized in real-time domain with pressure data acquisition at evaporator end. Instability threshold is determined in terms of evaporator temperature at different tube orientations and condenser temperatures. The oscillation startup mechanism along with the associated intermittency is studied in detail. The SBPHP is found to have characteristic variations in oscillation amplitude and frequency as it undergoes a gradual transition from its oscillation threshold to limit state. The mechanism by which the limit state creeps-in and intumesces further is an intrinsic function of liquid-vapor distribution in SBPHP, which in turn depends on the applied boundary conditions. The operational limit is governed by evaporator dryout exceeding permissible limits marked by the steep rise in the dry length of evaporator. As SBPHP approaches or operates at its limit state, evaporator is found to have different regimes across its length, viz., mild convective evaporation combined with subcooled nucleate boiling, saturated nucleate boiling, forced convective boiling, film breakdown and permanent dryout. The liquid film distribution, pressure fluctuations, and heat transfer components in evaporator at the limit state have also been studied.

A method to partition boiling heat transfer mechanisms using synchronous through-substrate high-speed visual and infrared measurements

Heat transfer during boiling involves a variety of transport mechanisms. Available experimental techniques cannot yet fully delineate these mechanisms which has contributed to a long-standing, persistent challenge of constructing accurate mechanistic models for boiling. In this work, we develop a method to identify and distinguish between the individual heat transfer mechanisms that occur during boiling using synchronous, through-substrate, high-speed visual and infrared measurements. Local heat fluxes are deduced from temperature measurements and a synchronized set of binarized phase maps are obtained from processing high-speed visual measurements. Experimental pool boiling investigation of HFE-7100 fluid on an indium tin oxide surface revealed four distinct heat transfer signatures in the heat flux maps corresponding to liquid convection, contact line evaporation, vapor convection, and local microconvection due to rewetting during boiling. To classify these regions, pixel-wise binary and morphological operations are performed on the phase maps of the entire surface. In contrast with prior partitioning techniques which use standalone heat flux measurements, our synchronous high-resolution visualization enables the region classification around fine bubble footprints that otherwise would not be detected with heat flux maps alone. The heat fluxes and superheats are then partitioned into their underlying mechanisms using classified regions from the phase maps. Analysis of the nucleate boiling regime data shows that different mechanisms contribute in varying degrees to the overall heat transfer at different points along the boiling curve: for the surface-fluid combination studied, single-phase liquid heat transfer is the primary contributor at low heat fluxes while at high heat fluxes, contact line evaporation contributed the most. We further employ the experimental approach to partitioning dynamic processes resulting from step increases in heat input demonstrating its potential for investigating transient phenomena such as dryout. The experimental and post-processing method introduced in this study is the first to delineate partitioning between different heat transfer mechanism regions in the presence of multiple interacting bubbles over the entire surface throughout the boiling curve in both steady and transient operating conditions.

Study on the turbulent Prandtl number model for liquid metal flow and heat transfer in a narrow rectangular channel

In order to improve the core power density of liquid metal reactors, plate-type fuel assemblies are typically used, which have obvious advantages in heat transfer capacity. For the low Prandtl number fluid, the RANS turbulence model-based CFD method needs to be modified by inserting the turbulent Prandtl number model. This paper investigated the turbulent Prandtl number model for the turbulent heat transfer of liquid metal flow in a narrow rectangular channel. First, the existing turbulent Prandtl number models were summarized and classified as the local turbulence Prandtl number model and the global turbulence Prandtl number model. They were evaluated based on the experimental data. The results showed that the prediction results of each model are not ideal. Then, a typical numerical example was used to analyze the temperature field and flow field in the narrow gap of a narrow rectangular channel. It was shown that the entire flow region only includes the near-wall region and the transition region, and the transition region accounts for the main proportion. A semi-empirical local turbulence Prandtl number model was obtained by solving the turbulent transport equation, and the unknown coefficients were determined iteratively with the experimental data. The error was controlled within ±20%. Finally, the applicability of the newly proposed turbulent Prandtl number model was explored, and the results showed that it has good applicability for the different runner sizes and different liquid metal types. This study can provide a reference for the numerical simulation of turbulent heat transfer of metal liquid in the narrow rectangular channel.

Aligned Magnetohydrodynamics and Thermal Radiation Effects on Ternary Hybrid Nanofluids Over Vertical Plate with Nanoparticles Shape Containing Gyrotactic Microorganisms

Nowadays, challenges in development of heat transfer for various engineering fields including heat exchangers, electronics, chemical and bio-industry and others are crucial. Ternary hybrid nanofluids (THNF) as a new heat transfer liquids can be considered as effective medium for increment of heat and energy transport. In the case of THNF when three nanoparticles are added in the based fluid to enhance the transport processes. Dissimilar to the nanofluids (NF) and hybrid nanofluids (HNF) model that considers two types of nanoparticles, this studied consider the three types of nanoparticles in this work which are Aluminium Oxide (AI2O3), Copper (Cu), and Carbon Nanotube (CNT) with different shapes containing gyrotactic microorganisms. The objective is to find the effect of magnetohydrodynamics (MHD) and radiation to the steady of THNF flow past the vertical plate. The mathematical model has been formulated based on a combination Tiwari-Das and Buongiorno nanofluids model. The governing flow and heat transfer equations are simplified to the ordinary differential equations (ODEs) with the adaptation of conventional similarity transformations which are then evaluated by the bvp4c solver (MATLAB) to generate the numerical solutions. The solutions are visually represented through graphs and table to be easily observed. The results indicated that the effect of magnetic field parameter decrease the velocity and contrary in concentration, and microorganism profile while the temperature is increased in magnetic but contrary in radiation parameter . The concentration and density microorganism of THNF is increase with higher value in and but decrease in velocity and temperature. The spherical nanoparticle shape has a higher density, causing the skin friction of THNF to be lower compared to NF and HNF.

Experimental Cooling Performance Evaluation of Different Coolants for Data Centre

The direct liquid cooling (DLC) of the data center is becoming popular due to its higher heat removal from the computer chips. The direct liquid cooling method is more effective than the conventional air-cooling system and reduces the higher infrastructure and maintenance costs. The DLC reduces the chip failure rate drastically and increases the life of the data centers. Different liquids can be used as a coolant and some manufacturers are coming up with different coolants where the liquid has high thermal efficiency and is electrically non-conductive. In this article, a heat-transfer cold plate made of aluminum is designed and a different combination of heat-transfer liquids (Distilled water, Ethylene Glycol, and Polyethylene Glycol) is tested to find a comparatively better combination of heat-transfer liquid. It was observed that the combination of Ethylene Glycol and distilled water performs better than other combinations. It was also found that the coolant flow rate plays an important role in the cooling of the chips as well.

Temperature distribution evolution in zero-gap alkaline water electrolyzer: Experimental and modeling

Alkaline water electrolysis technology is currently the most prospective commercial choice for producing green hydrogen, however, accurately modeling the temperature distribution evolution inside the alkaline water electrolyzer is still a challenge, since the existence of strong coupling multi-physical fields among gas–liquid flow, electrochemistry and heat transfer. In this article, 3D simulation models of the zero-gap alkaline water electrolyzer are established considering the mutual coupling relationship among two-phase flow, electrochemistry and heat transfer as well as the bypass current effect to study the heat transfer property and temperature profiles under different electrolysis conditions. The simulation study is conducted for the electrolyzer consisting of five electrolysis cells. The voltage, temperature difference and gas production rate were measured experimentally and simulated well using the established models. It indicates that the average relative error is respectively 0.45% for the estimated cell voltage, 13% for the estimated outlet-inlet temperature difference of the cathode flow channel, and 1.18% for the estimated hydrogen production rate. The characteristics of temperature distribution evolution in the zero-gap alkaline water electrolyzer have been disclosed, accordingly the suitable heat management strategy has been suggested for the stable operation. The results would provide a useful guide on the optimization and design of large-scale alkaline water electrolyzer to implement long-term stable operation with low cost.

Optimization of simultaneous utilization of air and water flow in a hybrid cooling system for thermal management of a lithium-ion battery pack

The present study provides a simulation of a battery pack (BCK) comprising lithium-ion battery cells positioned within an air channel utilizing Finite Element Method (FEM). A tube containing a flowing liquid, which serves the purpose of cooling BCK, sits at center of the BCK. Laminar nanofluids (NFs) or water flow enters tube, and air flows inside channel. A transient investigation is conducted on BCK temperature, heat transfer coefficient (HTC), and air and liquid outlet temperatures by varying airflow rate (AFR). The results demonstrate that raising airflow decreases the BCK's average temperature (TAE) and maximum temperature (TMM). The TAE of the BCK is more sensitive to changes in flow rate. Furthermore, as the AFR increases, the HTC increases because liquid and air leaving the outlet are cooled. Using NFs instead of water in the tube causes the average and TMM of the BCK to decrease and the HTC to enhance. The results show that The TMM and the TAE of the BCK are increased until the first 25 min and then are reduced. Using NFs instead of water reduces the outlet air and water temperature when AFR is low. Using NFs for battery cooling typically results in better performance than water.

Flue gas waste heat affects algal liquid temperature for microalgal production in column photobioreactors

AbstractTo explore the effects of waste heat (50–170°C) from steel plant flue gas on the column photobioreactor algal liquid temperature for microalgal production, a flue gas‐microalgal liquid heat transfer model was developed that simulated the microalgal growth environment for flue‐gas carbon dioxide (CO2) fixation. The simulation results showed that the influence of high‐temperature flue gas weakened with the increasing microalgal liquid temperature due to enhanced evaporation and heat dissipation. Increasing the flue gas temperature and aeration rate resulted in a higher microalgal liquid temperature up to a maximum increase of 4.16°C at an ambient temperature of 25°C, an aeration rate of 2 L/min, and a flue gas temperature of 170°C. In an experiment on the effect of incubation temperature on the growth rate of microalgae, at an optimal temperature of 35°C, the Chlorella sp. PY‐ZU1 growth rate exhibited a remarkable increase of 104.7% compared to that at 42.5°C. Therefore, modulating the flue gas conditions can significantly increase the microalgal growth rate for CO2 fixation, making it a promising approach to increase biomass production for efficient carbon utilization.

Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field

Abstract A mathematical model is envisaged that discusses the motion of 3D nanofluids (NFs) with anisotropic slip influence magnetic field past a stretching sheet. The heat transportation phenomenon is analysed by melting effect, heat generation, and chemical reaction. The main motivation of this study is to analyse the behaviour of liquid motion and heat transfer (HT) of NFs because this study has huge applications in boiling, solar energy, and micropower generation, which are used in the engineering process. The physical governing partial differential equation is transformed into a coupled non-linear system of ordinary differential equations using suitable appropriate transformations. The translated equations are calculated using Runge–Kutta–Fehlberg method via shooting procedure. The physical characteristics of various parameters on velocities, concentration, and thermal fields are explored in detail. The HT is high in NFs when compared to pure or regular liquids for ascending values of heat source parameter and slip factor. Also, the skin friction coefficients via coordinate axes and rate of Nusselt number were analysed.

A Simple and Cost-Effective Technique to Monitor the Sublimation Flow During Primary Drying of Freeze-Drying Using Shelf Inlet/Outlet Temperature Difference or Chamber to Condenser Pressure Drop

As lyophilization continues to be a critical step in the manufacturing of sensitive biopharmaceuticals, challenges often arise during the scale up to commercial scale or the transfer from one manufacturing site to another. While data from the small-scale development of the lyophilization cycle is abundant it is typically much more difficult to extract important information from commercial scale cycles, due to the lack of process analytical technologies available on the commercial line. There is often a reluctance to include wireless temperature or pressure probes during GMP operations due to the additional contamination risk, and retrofitting equipment such as the TDLAS can be prohibitively expensive. Further, as products become more advanced, the cost of consuming the product or even the availability of material may limit the opportunities to run commercial scale trials. This paper presents two novel methods to garner critical cycle information to allow for the evaluation of cycle performance without the need for expensive analytical equipment, costly revalidation and line downtime. Critically, this can be achieved using commonly available temperature and capacitance probes on existing commercial scale equipment. The first method is a calorimetric method, based on quantifying the differences in heat transfer liquid temperature between the shelf inlet and shelf outlet. This change in temperature results from the on-going sublimation, an endo-thermic reaction occurring during lyophilization. The second method uses the differential pressure between the chamber and condenser resulting from the vapor flow from vial to condenser during primary drying. As stated by the authors both methods align well and provide valuable cycle characterization data.

Controlling gas–liquid flow and enhancing heat transfer in a T-junction microchannel by wettability-engineered walls

Characteristics of gas–liquid flow and heat transfer in a cross-flow T-junction microchannel with wettability-engineered walls are numerically investigated in this paper. The validated diffuse interface method is adopted for interface capture. First, the effects of wall wettability on bubble formation and transportation are studied. Three flow patterns are observed due to different combinations of the bottom and the top wall contact angles. On this basis, two methods are proposed to enhance the heat transfer. One is to increase the two-phase interfacial contact area by dividing the microchannel into three functional regions, which can promote the heat exchange at the two-phase interface. The other is to increase the velocity fluctuation intensity by alternating the contact angle along the channel, which can enhance mixing between the hot liquid layer adjacent to the wall and the cool liquid core. These two methods are applicative for steady and unsteady problems, respectively. The flow states, velocity vectors, and streamlines are used to analyze the fluid and thermal mixing mechanism. Meanwhile, a quantitative comparison of the wall temperature is made at a given wall heat flux. The obtained results can provide fresh insights into the gas–liquid flow control and the heat transfer enhancement in a microchannel, which are valuable for the design of microreactors and radiators.

Wavy Ice Patterns as a Result of Morphological Instability of an Ice–Water Interface with Allowance for the Convective–Conductive Heat Transfer Mechanism

In this research, the wavy ice patterns that form due to the evolution of morphological perturbations on the water–ice phase transition interface in the presence of a fluid flow are studied. The mathematical model of heat transport from a relatively warm fluid to a cold wall includes the mechanism of convective–conductive heat transfer in liquid and small sinusoidal perturbations of the water–ice interface. The analytical solutions describing the main state with a flat phase interface as well as its small morphological perturbations are derived. Namely, the migration velocity of perturbations and the dispersion relation are found. We show that the amplification rate of morphological perturbations changes its sign with variation of the wavenumber. This confirms the existence of two different crystallization regimes with (i) a stable (flat) interfacial boundary and (ii) a wavy interfacial boundary. The maximum of the amplification rate representing the most dangerous (quickly growing) perturbations is found. The theory is in agreement with experimental data.

Transient behavior of liquid film deposition and surface heat transfer upon cryogen-spray cooling coupled with cold air jet

Cryogen spray cooling (CSC) has become a promising auxiliary-cooling technique for laser dermatology, which recently enhanced by cold air jet (CSC-CAJ). However, the CAJ-to-spray interactions could worsen the CSC performance and associated liquid film behavior. In this study, the transient behavior of liquid film deposition and surface heat transfer of CSC-CAJ was investigated. A high-speed camera was used to capture the film intensity through Mie-scattering technique. Fast-response TFTC thermocouple was used to measure the transient surface temperature. The large eddy simulation (LES) was used to extract the vortical structure, while the discrete-phase model (DPM) and Eulerian wall film (EWF) were coupled for the spray process and the transient film modeling. The results showed that the CAJ significantly enhanced CAJ-to-spray mixing and mitigated the film thickness (i.e., 32 % reduction). The CSC-CAJ had asymmetric film coverage due to induced counter-rotating vortex-pairs (CRVP) from the CAJ-to-spray interaction, which laterally clustered the spray. It permitted fast evaporation with dominant CAJ at the spray-periphery while permitting fast evaporation with dominant spray at the spray-core. Consequently, the CSC-CAJ showed 75 % temperature increment at the windward side and 15 % temperature reduction with 60 % heat transfer coefficient enhancement at the impingement point. The experimental film intensity and simulated film thickness were linearly correlated and significantly influenced the surface temperature. The combined results affirmed the significant impact of the CAJ on the transient film deposition, which potentially helps promote advanced cooling technology.

Numerical investigation on heat transfer enhancement of spray cooling by surface structure optimization

A numerical model of spray cooling for enhanced surfaces in the non-boiling regime is created with deionized water as cooling medium. This model is validated by contrasting the simulated data with the corresponding experimental data, and the relative deviation is within 12 %. Compared with a smooth surface, the area of the enhanced surface is expanded, the cooling performance is significantly improved, but the surface temperature distribution is less uniform. Compared to the straight groove surface with the same area, the heat flux of the radial groove surface is higher because its surface structure is more conducive to the spreading and leaving of the liquid film. Studies of the effects of the structure parameters (groove width and groove number) of the radial groove surface on the heat transfer show that there is an optimal groove width (0.2 mm) and groove number (45) for the strongest cooling capacity, and both the velocity and thickness of the liquid film are significant factors in cooling performance. The faster the liquid film velocity, the thinner the liquid film and, thus, the better the heat transfer. Motivated by these findings, three novel enhanced surfaces are machined to increase liquid film fluidity and heat transfer area even further. The cooling performance of the three novel enhanced surfaces is further improved, and the slope groove surface acquires the strongest cooling capacity due to the acceleration of liquid film flow by gravity, although its heat transfer area is not the largest. Research on all enhanced surfaces indicates that thinner liquid film and faster liquid film flow should be the primary design goals of the enhanced surface, followed by an increase in heat transfer area.

Heat transfer characteristics in vertical tube condensers: Experimental investigation and numerical validation

The paper establishes a vertical steam condensation heat transfer experimental device to investigate the process of liquid film condensation heat transfer under the countercurrent heat transfer of a secondary coolant. An improved experimental method, integrating measurements and simulations, accurately calculates local heat transfer coefficients and heat flux. The validity of the data is confirmed through comparison with established condensation correlations, affirming the method's effectiveness. The correlations of previous research (i.e., Numrich, Carey, Oh, Lee, and Shah) demonstrate greater consistency with the experimental results, with mean relative deviations (MRD) of −4.90%, 7.18%, 11.42%, −8.63% −4.45%, and mean absolute relative deviations (MARD) of 11.61%, 21.57%, 23.60%, 18.97%, and 12.53%, respectively. Numrich's correlation demonstrated the closest congruence. Based on these results, the research proposes a new coupled heat transfer model, effectively simulating the interaction between external cooling water and steam condensation. This model simplifies the process by pre-defining coolant temperature changes per unit length, thereby reducing the need for extensive iterative calculations and eliminating assumptions about wall temperature. It accurately predicts the wall temperature, local condensing temperature, and coolant temperature in a vertical condenser. These experimental methods and models offer valuable insights for optimizing vertical condenser design and analysis. The study underscores the significance of combining simulation models with experimental measurements to enhance the understanding of heat transfer in complex systems. The findings promise to advance research in film condensation heat transfer and assist in condenser design and optimization.

Effects of electromagnetic compound field on the macroscopic morphology of laser cladding

To enhance the controllability of the molten pool morphology, a directional Lorentz force is produced within the molten pool by synchronously coupling a steady electric field and magnetic field during the laser cladding process. A 2D numerical model of the molten pool considering solid–liquid phase change, heat transfer, fluid flow, deformed geometry and electromagnetic induction is established. The experimental and simulation results demonstrate that the magnetic or electrostatic field has negligible effects on the molten pool shape. The compound electromagnetic field (simply as a compound field) that generates a downward Lorentz force significantly impacts the molten pool height, and wetting angle. As revealed by the observation of the molten pool forming process, it is found that the downward Lorentz force disrupts the force balance of the molten pool, which leads to the outward expansion of the fluid due to an increased pressure difference. As a consequence, the height of the molten pool decreases. Meanwhile, the employment of a magnetic field results in a significant increase in the viscous resistance at the solidification interface. The fluid is accumulated at the bottom of the molten pool, which increases the wetting angle. Additionally, since this approach can produce a steady volume force similar to gravity, it can be used in a weightless environment, such as in a space station, thus significantly improving the process stability.

Experimental investigation of liquid jet impingement heat transfer at superhydrophobic surfaces

This paper presents an experimental exploration of thermal transport due to a water jet impinging on post patterned superhydrophobic surfaces and provides the first experimental data for this problem. The surface is heated to temperatures much lower than the saturation value. Results are obtained for a smooth hydrophobic surface and superhydrophobic surfaces with varying microfeature pitch (w = 8, 16, and 24 µm) and cavity fraction (Fc = 0.56 and 0.85) and are compared to results derived from a previously published analytical model. The jet Reynolds number varied from 1.1 × 104 to 1.7 × 104 and the nominal surface heat flux varied from 2.5 × 104 to 4.9 × 104 W/m2. Results obtained for all superhydrophobic surfaces show a significant decrease in the local and average Nusselt numbers (up to 30 % reduction) compared to impingement on a smooth surface. Further, the reduction is a strong function of the surface post and cavity geometric parameters. The effective temperature jump length is determined for all scenarios considered, representing the first experimental measurements of temperature jump length for heat transfer at superhydrophobic surfaces. Functional relationships showing how the average Nusselt number and the non-dimensional temperature jump length depend on the superhydrophobic surface parameters are also presented.

Development of a heat transfer model for the film boiling regime in a fouling layer

Fouling accumulation on fuel claddings and steam generators of pressurized water reactors can significantly affect boiling heat transfer. The present study proposes a heat transfer model for the film boiling regime in a fouling layer. The proposed model assumes that heat transfer in the fouling layer occurs in three modes: boiling, liquid convective heat transfer within the fouling and at the coolant-foulng interface. The thickness of the steam film within the fouling is determined by the pressure balance method. The prediction error of the present model for wall superheat is about 20%. The sensitivity analysis results show that the pore size significantly influences heat transfer, and the wall superheat can vary by up to 200K within the maximum pore diameter range of the fouling layer. However, chimney tilt angle has a negligible effect on heat transfer since the pressure drop in the steam chimney accounts for only a small proportion.