Computational Fluid Dynamics Investigation Research Articles

A Computational Fluid Dynamic Investigation of a Data Centre Employing Rear Door Heat Exchangers

As the global demand for data services expands, cooling in data centres continues to evolve towards more efficient and cost-effective systems. Incorporating active rear door heat exchangers has become a popular and reliable method that increases the capability of data centres to operate at higher power densities. This study conducts a thermal analysis of a data centre employing active rear door heat exchangers with the use of computational fluid dynamic (CFD) techniques. The data centre under investigation contains seventy-seven cooled racks with three additional uncooled racks operating in the centre of the hall. The main purpose of this study is to understand how the uncooled racks affect the temperature distribution in the data centre. This study presents a modelling technique which uses temperature and velocity field measurements to facilitate the modelling of rear door heat exchangers. Computer server modelling server was carried out at varying inlet temperature and load. Server simulation results have been utilized with field measurements to create four data centre scenarios. Scenarios were created to show how inlet temperature and load affect the temperature distribution in the data centre. Data centre scenarios have been used to validate and compare with field measurements performed. It was found that heat dissipation in the server was directly related to the server’s velocity profile. From the data centre scenarios created it was found that when higher loaded racks are isolated amongst lower loaded racks the distribution of heat is less significant than if the higher loaded racks were situated in clusters of three or more. It was also found that higher loaded racks could be positioned strategically to diminish the effect of the untreated air produced by the uncooled racks in the data centre. The findings from this paper help to understand the thermal behaviour in data centres and suggests areas to consider when reviewing pre-existing data centre designs.

Computational fluid dynamics investigation of a misaligned-phase parallel external gear pump

To clarify the flow characteristics of the misaligned-phase parallel external gear pump with different phases and rotational speeds, the flow pulsation and cavitation of the misaligned-phase parallel external gear pump under different working conditions were systematically studied by combining theoretical analysis with tridimensional numerical simulation. The flow pulsation characteristics of the misaligned-phase parallel external gear pump are analyzed. Compared with the same-phase gear pump, the flow pulsation of the misaligned-phase parallel external gear pump was reduced. When the phase angle is [Formula: see text], the pressure and flow pulsations of the parallel gear pump are minimum, the flow pulsation is less than 1/4 of the same-phase gear pump. The relationship between cavitation and phase angle of the misaligned-phase parallel external gear pump is verified. When the rotational speed is different, with the increase in the rotational speed, the amplitude of the pressure fluctuation increases, and the effect of pressure pulsation overlapping and counteracting each other in the misaligned phase is more ideal. The flow does not fluctuate with the rotational speed and is only related to the phase angle, the cavitation is aggravated with the increase in the rotational speed.

Numerical investigation into water entry problems of a flat plate with air pockets

Computational Fluid Dynamics (CFD) investigations into water entry problems of a rigid flat plate with air pockets were systematically conducted. The Volume of Fluid (VOF) model was utilised to capture localised slamming phenomena that occur during, and post-impact events. The model's geometry was modified to include a pocket on the slamming impact surface to investigate the effect of air entrapment on the magnitude and distribution of slamming forces and pressures. A parametric study was conducted on the geometric parameters of the modelled pocket by altering its area, depth, and volume to examine the response of slamming force and pressure loading under several impact velocities. The numerical results of slamming forces and pressures were in good agreement with experimental drop test measurements (with relative error of -6% and 7% for the magnitude of slamming force and pressure, respectively). The numerical results proved that the peak pressure is proportional to the magnitude of impact velocity squared (pmax∝v2).

Computational fluid dynamic simulation of hull reservoir wave energy device

Abstract This paper presents a Computational Fluid Dynamics (CFD) analysis of a wave energy device called the Hull Reservoir Wave Energy Converter (HRWEC). The device consists of a floating hull and a flap connected to the shaft of power take-off system (PTO), which is integral to the hull structure. It is unique due to its ability to convert wave energy by utilizing the pitch motion of the hull and rotating flap due to the internal water movement in the hull. Due to the complexity of the internal fluid dynamics, a CFD-based analysis was considered most appropriate. The CFD investigation of the dynamics of the device was done under regular wave conditions by using the ANSYS-AQWA and ANSYS FLUENT. Relative pitch angle variation, the hydrodynamic coefficients, which determine the degree of power extraction, were obtained from simulated results. A simulation was designed exhibiting complete system dynamics for different configurations varying on internal water height. Excellent convergence was observed, and an optimum configuration was identified. It is expected to validate the simulation results through experiments in the foreseeable future.

Computational fluid dynamics investigations of aerodynamic control surfaces of a vertical landing configuration

The European project RETALT (Retro Propulsion Assisted Landing Technologies), funded by the Horizon 2020 framework program (Grant agreement No 821890), has as main objective to investigate critical technologies for the assisted descent and landing of re-usable first stages. Among these technologies, one can find aerodynamics, aerothermodynamics, flight dynamics, guidance navigation and control (GNC), Structures, mechanisms, thrust vector control (TVC) and thermal protection systems (TPS). The present paper focuses in particularly on the aerodynamics technology applied to a vertical landing launcher configuration, called RETALT1, including retro-propulsion. During the landing phase of the first stage of the launcher, the main devices for control and trim of the vehicle (besides the retro-propulsion) are the aerodynamic control surfaces (ACS). Three types of aerodynamic control surfaces are investigated by means of numerical computations, using the NSMB (Navier Stokes Multi Block) CFD code. The control surfaces considered are the deployable interstage segments (also named petals), grid fins and planar fins. Aerodynamic coefficients as well as forces acting on the control surfaces are extracted from the CFD computations to assess the efficiency of each type of devices and to populate the Aerodynamic Database (AEDB) for flight dynamic analysis.

CFD Investigation on The Jet-Engine Inspired Wind Turbine

The Malaysian Government has set a more ambitious target to achieve higher penetration of Renewable Energy (RE) in the Malaysian energy mix which was 31% by 2025. Compared to the penetration of solar and wind power specifically in the European region, whose sharing was more than 50% of total generation, Malaysia currently only has 2% of its energy coming from RE generation sources, which mostly was provided by solar photovoltaic. In Malaysia’s energy sources point of view, wind RE-based power generation system was foreseen a promising potential provided the technology was suitably designed for low wind conditions. Therefore, the potentiality of the Jet-Engine inspired Wind Turbine operating under low-speed wind environment by mean of Computational Fluid Dynamics (CFD) numerical approach were explored in This study. The main objectives were to develop a reliable numerical model for accessing the capability of the Jet-Engine inspired Wind Turbine and to regulate its performance with influence of curly shroud on the induced flow. The conventional shrouded Wind Turbine has been modified which consist of a stator and a rotor blade covered by curly-shaped shroud adapting the concept of Jet-Engine. A constant wind speed of 5 m/s which was the average wind speed in Malaysia, and tip speed ratio (TSR) varies from 2 to 6 were specified in the simulation. The investigation discovered that the curly-shaped shroud gave an impact to the performance of the Wind Turbine as it can be reviewed from the comparison of the power coefficient on the Jet-Engine inspired Wind Turbine with shroud and without shroud. It was found that the shrouded Wind Turbine improved the power coefficient by 8.6% which was from 0.35 to 0.38. The effect of the curly shroud was also analysed by obtained the velocity and pressure contour from the ANSYS Fluent, where there was a swirl formation at the shroud as the air mixed at different angle, which causes the pressure drop and inlet velocity increased.

Functional analysis of the airways after pulmonary lobectomy through computational fluid dynamics

Pulmonary lobectomy, which consists of the partial or complete resection of a lung lobe, is the gold standard intervention for lung cancer removal. The removal of functional tissue during the surgery and the re-adaptation of the remaining thoracic structures decrease the patient's post-operative pulmonary function. Residual functionality is evaluated through pulmonary function tests, which account for the number of resected segments without considering local structural alterations and provide an average at-the-mouth estimation. Computational Fluid Dynamics (CFD) has been demonstrated to provide patient-specific, quantitative, and local information about airways airflow dynamics. A CFD investigation was performed on image-based airway trees reconstructed before and after the surgery for twelve patients who underwent lobectomy at different lobes. The geometrical alterations and the variations in fluid dynamics parameters and in lobar ventilation between the pre and post-operative conditions were evaluated. The post-operative function was estimated and compared with current clinical algorithms and with actual clinical data. The post-operative configuration revealed a high intersubject variability: regardless of the lobectomy site, an increment of global velocity, wall pressure, and wall shear stress was observed. Local flow disturbances also emerged at, and downstream of, the resection site. The analysis of lobar ventilation showed severe variations in the volume flow rate distribution, highlighting the compensatory effects in the contralateral lung with an increment of inflow. The estimation of post-operative function through CFD was comparable with the current clinical algorithm and the actual spirometric measurements. The results confirmed that CFD could provide additional information to support the current clinical approaches both in the operability assessment and in the prescription of personalized respiratory rehabilitation.

Electroosmotic modulated unsteady squeezing flow with temperature-dependent thermal conductivity, electric and magnetic field effects

Modern lubrication systems are increasingly deploying smart (functional) materials. These respond to various external stimuli including electrical and magnetic fields, acoustics, light etc. Motivated by such developments, in the present article unsteady electro-magnetohydrodynamics squeezing flow and heat transfer in a smart ionic viscous fluid intercalated between parallel plates with zeta potential effects is examined. The proposed mathematical model of problem is formulated as a system of partial differential equations (continuity, momenta and energy). Viscous dissipation and variable thermal conductivity effects are included. Axial electrical distribution is also addressed. The governing equations are converted into ordinary differential equations via similarity transformations and then solved numerically with MATLAB software. The transport phenomena are scrutinized for both when the plates move apart or when they approach each other. Also, the impact of different parameters such squeezing number, variable thermal conductivity parameter, Prandtl number, Hartmann number, Eckert number, zeta potential parameter, electric field parameter and electroosmosis parameter on the axial velocity and fluid temperature are analysed. For varied intensities of applied plate motion, the electro-viscous effects derived from electric double-capacity flow field distortions are thoroughly studied. It has been shown that the results from the current model differ significantly from those achieved by using a standard Poisson–Boltzmann equation model. Axial velocity acceleration is induced with negative squeeze number (plates approaching, S < 0) in comparison to that of positive squeeze number (plates separating, S > 0). Velocity enhances with increasing electroosmosis parameter and zeta potential parameter. With rising values of zeta potential and electroosmosis parameter, there is a decrease in temperatures for U e > 0 for both approaching i.e. squeezing plates (S < 0) and separating (S > 0) cases. The simulations provide novel insights into smart squeezing lubrication with thermal effects and also a solid benchmark for further computational fluid dynamics investigations.

Effect of inflow conditions on transonic turbine airfoil limit loading

To better understand airfoil limit loading and the effect inflow conditions have on local efficiency, a computational fluid dynamic investigation was performed for four different transonic turbine airfoils under sub-critical, critical, and supercritical conditions. A computational baseline was established using data previously collected at the Pratt and Whitney Canada High-Speed Wind Tunnel at Carleton University near design conditions using the Reynolds-Averaged Naiver-Stokes shear stress transport k − ω turbulence model with γ transition. The effects of inflow conditions on aerodynamic performance were examined by varying incidence by ± 20°, mainstream turbulence intensity from 5 to 20% and mainstream turbulent length scale from 1 to 100% of the airfoil pitch. Quantitative data of mass-flow averaged Mach numbers, mass-flow averaged flow angles, surface isentropic Mach number distributions and mass-flow averaged total pressure loss coefficients were collected and are presented alongside flow visualizations of numerical Schlieren images to allow for a detailed description of the entire flow domain. Similar to previous experimental work the limit loading pressure ratio and the mass-flow averaged outlet flow angle were strongly correlated with the airfoil outlet metal angle. The influence of inflow conditions was minimal on the exit flow profile with the exception of the mass-flow averaged total pressure loss coefficients. Results show incidence variation to change the total pressure loss coefficient depending on the airfoil, whereas, turbulence intensity and turbulent length scale predicted a drastic increase in loss with increased turbulence level for all airfoils considered.

Human in silico trials for parametric computational fluid dynamics investigation of cerebrospinal fluid drug delivery: impact of injection location, injection protocol, and physiology

BackgroundIntrathecal drug delivery has a significant role in pain management and central nervous system (CNS) disease therapeutics. A fluid-physics based tool to assist clinicians in choosing specific drug doses to the spine or brain may help improve treatment schedules.MethodsThis study applied computational fluid dynamics (CFD) and in vitro model verification to assess intrathecal drug delivery in an anatomically idealized model of the human CSF system with key anatomic features of the CNS. Key parameters analyzed included the role of (a) injection location including lumbar puncture (LP), cisterna magna (CM) and intracerebroventricular (ICV), (b) LP injection rate, injection volume, and flush volume, (c) physiologic factors including cardiac-induced and deep respiration-induced CSF stroke volume increase. Simulations were conducted for 3-h post-injection and used to quantify spatial–temporal tracer concentration, regional area under the curve (AUC), time to maximum concentration (Tmax), and maximum concentration (Cmax), for each case.ResultsCM and ICV increased AUC to brain regions by ~ 2 logs compared to all other simulations. A 3X increase in bolus volume and addition of a 5 mL flush both increased intracranial AUC to the brain up to 2X compared to a baseline 5 mL LP injection. In contrast, a 5X increase in bolus rate (25 mL/min) did not improve tracer exposure to the brain. An increase in cardiac and respiratory CSF movement improved tracer spread to the brain, basal cistern, and cerebellum up to ~ 2 logs compared to the baseline LP injection.ConclusionThe computational modeling approach provides ability to conduct in silico trials representative of CSF injection protocols. Taken together, the findings indicate a strong potential for delivery protocols to be optimized to reach a target region(s) of the spine and/or brain with a needed therapeutic dose. Parametric modification of bolus rate/volume and flush volume was found to have impact on tracer distribution; albeit to a smaller degree than injection location, with CM and ICV injections resulting in greater therapeutic dose to brain regions compared to LP. CSF stroke volume and frequency both played an important role and may potentially have a greater impact than the modest changes in LP injection protocols analyzed such as bolus rate, volume, and flush.

Semi-Automatic Reconstruction of Patient-Specific Stented Coronaries based on Data Assimilation and Computer Aided Design.

The interplay between geometry and hemodynamics is a significant factor in the development of cardiovascular diseases. This is particularly true for stented coronary arteries. To elucidate this factor, an accurate patient-specific analysis requires the reconstruction of the geometry following the stent deployment for a computational fluid dynamics (CFD) investigation. The image-based reconstruction is troublesome for the different possible positions of the stent struts in the lumen and the coronary wall. However, the accurate inclusion of the stent footprint in the hemodynamic analysis is critical for detecting abnormal stress conditions and flow disturbances, particularly for thick struts like in bioresorbable scaffolds. Here, we present a novel reconstruction methodology that relies on Data Assimilation and Computer Aided Design. The combination of the geometrical model of the undeployed stent and image-based data assimilated by a variational approach allows the highly automated reconstruction of the skeleton of the stent. A novel approach based on computational mechanics defines the map between the intravascular frame of reference (called L-view) and the 3D geometry retrieved from angiographies. Finally, the volumetric expansion of the stent skeleton needs to be self-intersection free for the successive CFD studies; this is obtained by using implicit representations based on the definition of Nef-polyhedra. We assessed our approach on a vessel phantom, with less than 10% difference (properly measured) vs. a customized manual (and longer) procedure previously published, yet with a significant higher level of automation and a shorter turnaround time. Computational hemodynamics results were even closer. We tested the approach on two patient-specific cases as well. The method presented here has a high level of automation and excellent accuracy performances, so it can be used for larger studies involving patient-specific geometries.

Performance analysis of a solar heat collector through experimental and CFD investigation

In order to attain maximum efficiency in a solar drying system, continuous effort is made to the key component of solar dryer – solar heat collector (SHC). This research aimed to evaluate the thermal performance of SHC with different flow configuration in the air passage, namely single-pass (S-SHC) and multiple-pass (M-SHC), under natural convection (average air velocity = 0.2 m/s). In order to study the flow and heat transfer characteristics across the SHC, performance analysis was carried out by Computational Fluid Dynamic (CFD) simulation and later validated by experimental results. From the simulation model, the collector outlet temperature and efficiency of M-SHC at maximum solar radiation were 67.4 °C and 10.04%, respectively with percentage error of 8.6% and 17.79% to the experimental results. The presence of recirculation region indicated extended drying air residence time in the M-SHC, resulting in high temperature growth from 8.8% to 12.1% across the air passage compared to S-SHC. In addition, heat transfer enhancement in M-SHC was achieved by compensating radiation heat loss observed in S-SHC through the modification of airflow configuration. Both experimental and theoretical analysis in this study showed that the proposed enhancement significantly improved the performance of SHC having air passage made from recycled aluminium cans.

CFD analysis for heat transfer comparison in circular, rectangular and elliptical tube heat exchangers filled with PCM

A two-dimensional computational fluid dynamics (CFD) investigation of the melting of phase change material (PCM) and heat transfer characteristics of a heat exchanger of shell and tube type having circular, rectangular and elliptical tubes are analyzed in this study. Gallium in the rectangular shell of heat exchange is considered as the working fluid in this present study. A fixed temperature boundary condition is applied at the circumference of the tubes and a standard k-epsilon turbulence model is used for the simulation. The variation in the shape of the tubes at a fixed temperature of 60 °C has been utilized for the analysis and the effect of the shape of these tubes on melting of PCM in terms of liquid proportion and melting time has been analyzed. The melting duration of PCM is 745 s for a configuration with circular tubes, 650 s for a configuration with rectangular tubes, and 740 s for a configuration with elliptical tubes and the duration by the PCM to reach 60 °C for a configuration with circular tubes is 800 s, for a configuration with rectangular tubes is 725 s, and for a configuration with elliptical tubes is 770 s. Hence it is indicated by the results that the lowest melting time of PCM can be obtained by the heat exchanger having rectangular tubes followed by elliptical tubes and circular tubes at a temperature of 60 °C.

Computational Fluid Dynamics Investigations of Flow, Heat Transfer, and Oxidation in Heat Recovery Steam Generator

Computational Fluid Dynamics Investigations of Flow, Heat Transfer, and Oxidation in Heat Recovery Steam Generator

CFD investigation into resistance characteristics of a pusher-barge system in calm water

Prediction of ship’s total resistance of a pusher-barge system has become enormous complexity involving nonlinear-hydrodynamic flows behaviour along their hull forms. Both of empirical and simplified numerical solutions may still lead into inaccurate results due to presence of nonlinear characteristics of the pressure and viscous resistances. The use of a more sophisticated method would obviously necessitate to solve the above problem. This paper presents a Computational Fluid Dynamics (CFD) approach to predict the total ship’s resistance of a pusher-barge system at various barge’s configurations. To achieve such objective, four different configurations of the barge models incorporated with various Froude numbers have been taken into account in the computational simulation. In general, the results revealed that the increase of Froude number (Fr = 0.182 to 0.312) was proportional to the magnitude of RT, RP and RV. Regardless of the various Froude number, the pusher-barge system with a 13BP configuration provides the highest resistance compared to the 12BP and 11BP. In addition, the arrangement of barges in the longitudinal (12BP) and lateral (21BP) configurations produced a significant effect with increases in RT, RP and RV values of 110%, 167.5% and 77.6%, respectively. The possible reason for this is that the increase of the total wetted surface area for 21BP has produced to a proportionally higher amount of the pressure and viscous resistance. Overall study, the numerical results were presented and analysed based on few aspects involved the total resistance and resistance coefficient in terms of pressure and viscous resistance of the pusher-barge system. This analysis provides very valuable information on choosing the most reliable arrangement of pusher-barge system. This analysis provides very valuable information on choosing the most reliable arrangement of pusher-barge system

Numerical Investigation of Oil Gas Separation with the Use of VOF CFD

In this research paper, a numerical study regarding gas-oil separation is presented. Employing the geometry of a classic separator used by the NRDI for Gas Turbines COMOTI and a Computer-Aided Design (CAD) software, the computational domain was defined. To perform the Computational Fluid Dynamics (CFD) investigation, the mesh was created with the ANSYS Meshing tool, and the ANSYS CFX was employed as a solver. The computational domain was split into 5 subdomains, 3 were fluid and 2 were defined as porous media. The volume porosity, loss model, and permeability were set up. In terms of turbulence flow, the standard k–ε model was adopted. The results of the numerical calculations in terms of oil volume fraction and streamline profiles were used to analyze the separator configuration. The results show that the numerical investigation with the VOF (Volume of Fluid Method) - CFD model is capable of analyzing the performance of a two-phase separator equipped with two demisters-porous media.

CFD Investigation on Hydrodynamic Resistance of a Novel Subsea Shuttle Tanker

The Subsea Shuttle Tanker (SST) was proposed by Equinor as an alternative to subsea pipelines and surface tankers for the transportation of liquid carbon dioxide (CO2) from existing offshore/land facilities to marginal subsea fields. In contrast to highly weather-dependent surface tanker operations, the SST can operate in any condition underwater. Low resistance is paramount to achieving maximum range. In this paper, the resistance of the SST at an operating forward speed of 6 knots (3.09 m/s) and subject to an incoming current velocity of 1 m/s is computed using Computational Fluid Dynamics (CFD). The Delayed Detached Eddy Simulation (DDES) method is used. This method combines features of Reynolds-Averaged Navier–Stokes Simulation (RANS) in the attached boundary layer parts at the near-wall regions, and Large Eddy Simulation (LES) at the unsteady, separated regions near to the propeller. The force required to overcome forward resistance is calculated to be 222 kN and agrees well with experimental measurements available in the open literature. The corresponding power consumption is calculated to be 927 kW, highlighting the high efficiency of the SST. The method presented in this paper is general and can be used for resistance optimization studies of any underwater vessel.

Experiment and computational fluid dynamics investigation of biochar elutriation in fluidized bed

AbstractIn fluidized bed biomass fast pyrolysis, the biomass is converted to biochar and elutriated. The elutriation rate is a key parameter in reactor designs and operations. This research presents a video‐based continuous measurement of biochar elutriation rate in a fluidized bed with sands and biomass as bed materials. The fluidized bed is simulated with the computational fluid dynamics—coarse‐grained discrete element method (CFD‐CGDEM) in MFiX. The fluidization behavior of nonspherical sands can be more accurately captured when a rolling friction model is used. The predicted elutriation rate is close to the experimental measurement when the particle size distributions are considered and the filtered drag with a shape correction is used. These results validated the accuracy of the MFiX‐based CFD framework for the prediction of biochar elutriations in the fluidized bed biomass fast pyrolysis reactor.

CFD investigation of a natural ventilation wind tower system with solid tube banks heat recovery for mild-cold climate

Passive strategies are increasingly being employed in buildings to minimize their total energy consumption and emissions. Wind tower, a natural ventilation device, can capture the wind flow from higher locations and supply the air into the buildings' indoor space without consuming electric power. However, its use in mild-cold climate is limited due to excessive heat loss and thermal discomfort, in particular, during winter. Limited research has been conducted to explore the pre-heating of the supply air in the wind tower to address the issue and potentially increase its adoption in mild-cold climates. Therefore, a novel wind tower ventilation system integrated with solid tube banks heat recovery (HR) is proposed in this research. By combining with a passive heat recovery device, a wind tower can be operated under winter conditions to improve indoor ventilation while reducing the building heating energy consumption. A three-dimensional computational fluid dynamics (CFD) model was developed to investigate the effects of the longitudinal pitch (SL) and the transverse pitch (ST) of the HR device on the ventilation and thermal performance. The overall performance of the wind tower was evaluated under different outdoor wind speeds. The results show that the heat recovery can be improved by reducing SL and ST, raising the supply fresh air temperature by up to 6.4 °C. Furthermore, the proposed wind tower can provide sufficient ventilation for a typical classroom occupied by 15 people when the external wind speed exceeds 3 m/s.

Conjugate Effect on the Thermal Characteristics of Air Impinging Jet

A computational fluid dynamics (CFD) investigation to determine the conjugate heat transfer (CHT) effect on the stagnation and local thermal characteristics due to an impinging process has been carried out in this study using STAR-CCM+ - Siemens PLM commercial code. The transient Navier-Stokes’s equations are numerically solved using a finite volume approach with k-ω SST eddy viscosity as the turbulence model. A fully developed circular air jet with different Reynolds numbers, impinging vertically onto a heated flat disc with different metals, thicknesses, and boundary heat fluxes are employed in the current study to examine the thermal characteristics and provide an enhanced picture for the convection mechanism that used in jet cooling technology. It is found that the thermal characteristics are influenced by the thermal conductivity and thickness of the target upon using air as a cooling jet. The CHT process enhances the local convective heat transfer at the fluid-solid interface due to the variation in transverse and axial conductive heat transfer inside the metal up to a certain redial extent from the stagnation region compared to the process with no CHT. The extent of the radial enhancement depends on the thermal conductivity of the metal. For a given thermal conductivity, the CHT process acts to increase the temperature and convective heat flux of the stagnation region as the metal thickness increases.