Effect Of Different Flow Patterns Research Articles

The dynamic evolution of powder flow and wall normal stress in different flow pattern silos

Major safety accidents involving silos in industrial processes are closely associated with abnormal wall stresses. The effects of different flow patterns and particle velocity distribution on wall stresses are investigated during silo discharge. The existence of particle velocity retardation layer near the wall boundary in the mass flow was observed by tracer particles and high-speed camera. The silo discharge undergoes a transformation from funnel flow to mass flow at a hopper half angle of 30°. As the outlet diameter increases, the time point of the flow pattern transformation becomes more and more later. The evolution of particle velocity in the central of the funnel flow is related to the outlet velocity wave propagation and the V-shaped surface expansion. The relationship between stress fluctuations and velocity characteristics is established. The flow channel simultaneously expands upwards as the velocity wave propagates and generates a periodic fan-shaped velocity wave at the top. The formation of stress concentration zone at the bin/hopper transition was observed.

The effect of non-uniform inlet boundary conditions on the performance of the multiphase pump

Multiphase pump is an important equipment for oil and gas transportation. The gas-liquid distribution pattern at the inlet of a multiphase pump is crucial to its performance. We propose through an experiment that slug flow and annular flow are the main forms of gas-liquid distribution at the inlet of multiphase pumps. The effects of different flow patterns on the performance of multiphase pumps were investigated through numerical simulations and experimental tests. The results show that the multiphase pump is best adapted to the homogeneous bubble model, followed by the elastic flow and poorly by the annular flow. The energy conversion characteristic of annular flow is poor, and the higher the GVF is, the more obvious this characteristic is. The pressure distribution in the outlet region of the guide vane of the slug flow model is the most inhomogeneous, thus creating a larger vortex scale. The decrease in pressurization of the annular flow is most obvious with increasing GVF. At 30 % GVF, it decreased by 43 kPa compared to the uniform bubble flow model. The different flow patterns have a large effect on the impeller performance, but the distribution of the gas-liquid two-phase at the guide vane outlet tends to stabilize. The significance of this study is to further understand the performance of the first stage impeller of multiphase pumps under special working conditions, and then provide reference for the overall design of multistage pumps to broaden the scope of multiphase pump applications.

Improved ventilation efficiency due to continuous gas flow compared to decelerating gas flow in mechanical ventilation: results of a porcine trial.

In pressure-controlled ventilation (PCV), a decelerating gas flow pattern occurs during inspiration and expiration. In contrast, flow-controlled ventilation (FCV) guarantees a continuous gas flow throughout the entire ventilation cycle where the inspiration and expiration phases are simply performed by a change of gas flow direction. The aim of this trial was to highlight the effects of different flow patterns on respiratory variables and gas exchange. Anesthetized pigs were ventilated with either FCV or PCV for 1 h and thereafter for 30 min each in a crossover comparison. Both ventilation modes were set with a peak pressure of 15 cmH2O, positive end-expiratory pressure of 5 cmH2O, a respiratory rate of 20/min, and a fraction of inspired oxygen at 0.3. All respiratory variables were collected every 15 min. Tidal volume and respiratory minute volume were significantly lower in FCV (n = 5) compared with PCV (n = 5) animals [4.6 vs. 6.6, MD -2.0 (95% CI -2.6 to -1.4) mL/kg; P < 0.001 and 7.3 vs. 9.5, MD -2.2 (95% CI -3.3 to -1.0) L/min; P = 0.006]. Notwithstanding these differences, CO2-removal as well as oxygenation was not inferior in FCV compared with PCV. Mechanical ventilation with identical ventilator settings resulted in lower tidal volumes and consecutive minute volume in FCV compared with PCV. This finding can be explained physically by the continuous gas flow pattern in FCV that necessitates a lower alveolar pressure amplitude. Interestingly, gas exchange was comparable in both groups, which is suggestive of improved ventilation efficiency at a continuous gas flow pattern.NEW & NOTEWORTHY This study examined the effects of a continuous (flow-controlled ventilation, FCV) vs. decelerating (pressure-controlled ventilation, PCV) gas flow pattern during mechanical ventilation. It was shown that FCV necessitates a lower alveolar pressure amplitude leading to reduced applied tidal volumes and consequently minute volume. Notwithstanding these differences, CO2-removal as well as oxygenation was not inferior in FCV compared with PCV, which is suggestive of improved gas exchange efficiency at a continuous gas flow pattern.

Flow pattern-dependent mitochondrial dynamics regulates the metabolic profile and inflammatory state of endothelial cells.

Endothelial mitochondria play a pivotal role in maintaining endothelial cell (EC) homeostasis through constantly altering their size, shape, and intracellular localization. Studies show that the disruption of the basal mitochondrial network in EC, forming excess fragmented mitochondria, implicates cardiovascular disease. However, cellular consequences underlying the morphological changes in the endothelial mitochondria under distinctively different, but physiologically occurring, flow patterns (i.e., unidirectional flow [UF] versus disturbed flow [DF]) are largely unknown. The purpose of this study was to investigate the effect of different flow patterns on mitochondrial morphology and its implications in EC phenotypes. We show that mitochondrial fragmentation is increased at DF-exposed vessel regions, where elongated mitochondria are predominant in the endothelium of UF-exposed regions. DF increased dynamin-related protein 1 (Drp1), mitochondrial reactive oxygen species (mtROS), hypoxia-inducible factor 1, glycolysis, and EC activation. Inhibition of Drp1 significantly attenuated these phenotypes. Carotid artery ligation and microfluidics experiments further validate that the significant induction of mitochondrial fragmentation was associated with EC activation in a Drp1-dependent manner. Contrarily, UF in vitro or voluntary exercise in vivo significantly decreased mitochondrial fragmentation and enhanced fatty acid uptake and OXPHOS. Our data suggest that flow patterns profoundly change mitochondrial fusion/fission events, and this change contributes to the determination of proinflammatory and metabolic states of ECs.

Effect of thermal stratified flow on algal blooms in a tributary bay of the Three Gorges reservoir

After the impoundment of Three Gorges Reservoir (TGR), its tributaries have been frequented by algal blooms, especially the Xiangxi River (XXR). Stratified flow induced by temperature difference often occurs, which likely influences the water exchange and algae transport process between the tributary and TGR. To investigate the variation of flow field and algae concentration in XXR, a 2-dimensional hydrodynamic and water quality model is developed. The simulation results show good agreement with field observed data, reproducing the water exchange and algal bloom process. Notwithstanding the hydrodynamic environment of XXR is complicated, the thermal stratified flows are generalized into six typical patterns in this paper. Subsequently, algae transport processes under the influence of different thermal stratified flow patterns are examined. Thermal stratified flows from upstream and TGR intrude into the bay tributary through different layers with different combinations, resulting in water exchange of XXR is the major cause of algae transport difference. We show that when the mainstream intrusive flow and upstream inflow separately intrude into the XXR through the surface and bottom layer, hydrodynamic environments are favorable to algae transport, with the final chlorophyll-a (Chl-a) concentrations of entire XXR lower than algal bloom threshold value. The worst scenarios occur when the mainstream flow intrudes through middle or bottom layer while the upstream inflow enter through bottom layer, with the final algal bloom coverage rate (Ralg) of 82.3% and 78.1%, respectively. In terms of superimposed effect of different flow patterns, when the sequentially thermal stratified flows have different effect on algae transport direction, algae will concentrate in the reach rather than discharged which increase the risk of multiple algal blooms. These findings represent an important step towards understanding the multiple outbreaks of algal bloom in XXR during the spring and provide a new perspective for the research of algal bloom governance.

Effects of Different Temperatures on the Softening of Red-Bed Sandstone in Turbulent Flow

The rates of chemical reactions are highly dependent on temperature, meaning that the actual geological rock mass is affected by different temperatures. Only when the temperature effect is considered can the mechanism of the influence of temperature on the interaction between water and rock be further understood. It was found that the condition of turbulent flow is more likely to promote the softening of red-bed sandstone than the conditions of laminar flow and static water in an experimental study on the softening effects of different flow patterns on red-bed sandstone. Therefore, based on a multi-functional self-circulating open channel hydraulic test system, this paper designs and completes equal volume saturated tests of red-bed sandstone at low temperature (1 °C), medium temperature (23 °C), and high temperature (45 °C) under the turbulent conditions of three equal temperature gradients. The chemical action of the circulating solution in water flow at different temperatures, the propagation of micro-cracks in rock and the changes in mechanical indexes are discussed. The influence laws and mechanisms of the different temperatures on the softening of red-bed sandstone in turbulent flow are revealed. The results show that low-temperature flow can inhibit the softening of red-bed sandstone in the range of 1–45 °C. With the increase in water flow temperature, the development degrees of micro-structures and the mechanical damage of the corresponding rock become more notable. That is, temperature affects the physical and chemical water-rock interactions and then changes the internal structure of rock, thus affecting the softening and failure processes of red-bed sandstone. The study provides a theoretical basis for the further investigation of the softening laws and mechanisms of other red layered soft rocks by temperature under turbulent conditions.

Influence Mechanism of Different Flow Patterns on the Softening of Red-Bed Soft Rock

As a typical representative of red beds, the softening and disintegration of red sandstone when it encounters water is an important cause of initiated engineering disasters. However, research on the softening of this kind of rock has mainly focused on the still water–rock interaction. There is still a lack of quantitative analysis and a mechanistic explanation for the basic experimental study of dynamic water–rock interactions. Therefore, based on the independently developed multifunctional open channel hydraulic test equipment, the still water was used as the reference by designing the saturation test of red sandstone under two typical flow patterns—laminar flow and turbulent flow—and combined with a three-dimensional numerical simulation; specifically, the chemical, physical and mechanical effects of different flow patterns on the softening of red sandstone are discussed, and the mechanism of the influence of different flow patterns on the softening of red sandstone was further revealed. The results show that under different flow patterns, as the flow of water increased, the alkalinity of the circulating solution became stronger, the speed of stabilization of the ion concentration became faster, the development of the microscopic structure of the corresponding rock became higher and the decrease in mechanical strength became greater. The flow state affects the processes of rock softening and breaking by acting on the rock from the three aspects of chemistry, physics and mechanics. The study makes up for the deficiency of the quantitative analysis index of rock softening under dynamic water conditions and further improves the influence mechanism of different flow patterns on soft rock softening in red beds under dynamic water conditions. This research also provides a specific method for the protection of estuarine and coastal bank slopes with rich red-bed soft rock dissection under different flow patterns.

Hemodynamics-Based Strategy of Using Retinoic Acid Receptor and Retinoid X Receptor Agonists to Induce MicroRNA-10a and Inhibit Atherosclerotic Lesion.

The protocols in this chapter describe methods for identifying the functional roles of retinoic acid receptor (RAR) and retinoid X receptor (RXR) signaling in atherosclerosis and developing RARα/RXRα-specific agonists as hemodynamics-based therapeutic components for atherosclerosis treatment. In vitro cell culture flow system is used to elucidate the effects of different flow patterns and shear stresses, i.e., atherogenic oscillatory shear stress (OS) vs. atheroprotective pulsatile shear stress (PS), on RAR/RXR signaling and inflammatory responses in vascular endothelial cells (ECs). Western blotting, nuclear and cytoplasmic protein extraction, immunoprecipitation, and in situ proximity ligation assay are used to examine the expression, location, and association of RARs (i.e., RARα, RARβ, and RARγ) and RXRs (i.e., RXRα, RXRβ, and RXRγ) in ECs in response to OS vs. PS. Chromatin immunoprecipitation is used to examine the binding activity of RARα/RA-responsive elements (RARE). RT-microRNA (miR) quantitative real-time PCR and RT-PCR are used to detect the expressions of miR-10a and pro-inflammatory molecules, respectively. Specific siRNAs of RARα and RXRα, precursor miR-10a (PreR-10a), and antagomiR-10a (AMR-10a) are used to elucidate the regulatory roles of RARα, RXRα, and miR-10a in pro-inflammatory signaling in ECs. RARα/RXRα-specific agonists are used to induce miR-10a expression and inhibit OS-induced pro-inflammatory signaling in ECs in vitro. Apolipoprotein E-deficient (ApoE-/-) mice are used as an atherosclerotic animal model. Administration of ApoE-/- mice with RARα/RXRα-specific agonists results in inhibitions in atherosclerotic lesion formation. Co-administration of ApoE-/- mice with RARα/RXRα agonists and AMR-10a is performed to identify the role of miR-10a in RARα/RXRα agonists-mediated inhibition in atherosclerotic lesions. Oil Red O staining and H&E staining are used to examine the levels of atherosclerotic lesions in the vessel wall. In situ miR hybridization and immunohistochemical staining are used to detect the expression of miR-10a and pro-inflammatory molecules and the infiltration of inflammatory cells in the vessel wall. RARα/RXRα-specific agonists are used to mimic the atheroprotective effects of PS to induce endothelial miR-10a and hence repress OS-induced pro-inflammatory signaling and atherosclerotic lesion formation in vivo. The results indicate that RAR/RXR-specific agonists have great potential to be developed as hemodynamics-based therapeutic components for atherosclerosis treatment.

The Influence of Fluid Mixed State on Microorganisms: A Test Case with &lt;i&gt;Bacillus &lt;/i&gt;&lt;i&gt;subtilis&lt;/i&gt;

Flow pattern and mode have a far influence on the efficiency of biological treatment systems. In order to investigate the effects of different flow patterns on the growth of Bacillus subtilis, a self-developed fluid mixing device was designed to produce different liquid fluidization. It was found that the greater Re, the more conducive to the growth of bacteria, which evidenced by the logarithmic phase shorter and reached stationary phase bacteria concentration increased; when the Reynolds number is low, growth curve of Bacillus subtilis appeared Growth - stationary - growth and cell precipitation phenomenon, both phenomena gradually disappeared when Re increases. Besides, it can consume dissolved oxygen after inoculation with Bacillus subtilis, which keeping the dissolved oxygen in the medium at a lower level (0~1mg/L)

Effects of different flow patterns and end-inspiratory pause on oxygenation and ventilation in newborn piglets: an experimental study.

BackgroundHistorically, the elective ventilatory flow pattern for neonates has been decelerating flow (DF). Decelerating flow waveform has been suggested to improve gas exchange in the neonate when compared with square flow (SF) waveform by improving the ventilation perfusion. However, the superiority of DF compared with SF has not yet been demonstrated during ventilation in small infants. The aim of this study was to compare SF vs. DF, with or without end-inspiratory pause (EIP), in terms of oxygenation and ventilation in an experimental model of newborn piglets.MethodsThe lungs of 12 newborn Landrace/LargeWhite crossbred piglets were ventilated with SF, DF, SF-EIP and DF-EIP. Tidal volume (VT), inspiratory to expiratory ratio (I/E), respiratory rate (RR), and FiO2 were keep constant during the study. In order to assure an open lung during the study while preventing alveolar collapse, a positive end-expiratory pressure (PEEP) of 6 cmH2O was applied after a single recruitment maneuver. Gas exchange, lung mechanics and hemodynamics were measured.ResultsThe inspiratory flow waveform had no effect on arterial oxygenation pressure (PaO2) (276 vs. 278 mmHg, p = 0.77), alveolar dead space to alveolar tidal volume (VDalv/VTalv) (0.21 vs. 0.19 ml, p = 0.33), mean airway pressure (Pawm) (13.1 vs. 14.0 cmH2O, p = 0.69) and compliance (Crs) (3.5 vs. 3.5 ml cmH2O−1, p = 0.73) when comparing SF and DF. A short EIP (10%) did not produce changes in the results.ConclusionThe present study showed that there are no differences between SF, DF, SF-EIP and DF-EIP in oxygenation, ventilation, lung mechanics, or hemodynamics in this experimental model of newborn piglets with healthy lungs.

Shear stress, SIRT1, and vascular homeostasis

Shear stress imposed by blood flow is crucial for maintaining vascular homeostasis. We examined the role of shear stress in regulating SIRT1, an NAD(+)-dependent deacetylase, and its functional relevance in vitro and in vivo. The application of laminar flow increased SIRT1 level and activity, mitochondrial biogenesis, and expression of SIRT1-regulated genes in cultured endothelial cells (ECs). When the effects of different flow patterns were compared in vitro, SIRT1 level was significantly higher in ECs exposed to physiologically relevant pulsatile flow than pathophysiologically relevant oscillatory flow. These results are in concert with the finding that SIRT1 level was higher in the mouse thoracic aorta exposed to atheroprotective flow than in the aortic arch under atheroprone flow. Because laminar shear stress activates AMP-activated protein kinase (AMPK), with subsequent phosphorylation of endothelial nitric oxide synthase (eNOS) at Ser-633 and Ser-1177, we studied the interplay of AMPK and SIRT1 on eNOS. Laminar flow increased SIRT1-eNOS association and eNOS deacetylation. By using the AMPK inhibitor and eNOS Ser-633 and -1177 mutants, we demonstrated that AMPK phosphorylation of eNOS is needed to prime SIRT1-induced deacetylation of eNOS to enhance NO production. To verify this finding in vivo, we compared the acetylation status of eNOS in thoracic aortas from AMPKalpha2(-/-) mice and their AMPKalpha2(+/+) littermates. Our finding that AMPKalpha2(-/-) mice had a higher eNOS acetylation indicates that AMPK phosphorylation of eNOS is required for the SIRT1 deacetylation of eNOS. These results suggest that atheroprotective flow, via AMPK and SIRT1, increases NO bioavailability in endothelium.

Mechanical Stimulation of HUVEC: Different Flow Patterns have Differential Effects on TF Expression

Human umbilical vein endothelial cells (HUVECs) are known to respond differentially to various mechanical stimuli, and these different responses maybe involved in atherogenesis. Here we investigated the differential effects of different flow patterns, such as laminar flow (LF) and orbital shear stress (OSS), on the expression of tissue factor (TF). HUVECs were seeded on fibronectin coated glass slides and selectively in the periphery of gelatin coated culture dishes. When HUVECs on slides reached confluence, they were exposed to two, four, or six hours of LF (14 dynes/cm2). HUVECs in culture dishes were exposed to the same time course of low OSS (4 dynes/cm2) or high OSS (11 dynes/cm2). OSS was generated by placing dishes on an orbital shaker. TF mRNA levels were quantified with reverse transcription polymerase chain reaction (RT-PCR), with b-actin as the reference gene. Fold changes are expressed as the mean ± SE. Statistical significance between treated groups and controls was evaluated using the Mann-Whitney test. Analysis of variance (ANOVA) and Tamhane's post-hoc analysis were employed for between group analysis and P < .05 was considered significant. Fold changes as compared with controls are summarized in the Table and Fig (P values are in brackets). LF resulted in significant increases in TF expression throughout the six-hour time course when compared with static controls. However no significant differences were noted between the two, four, and six-hour LF groups. Both HOSS and LOSS reduced TF mRNA levels with significance attained at four and six hours respectively. No significant differences were observed between the different OSS groups.TableTF expression fold changes compared with controlsN = 6HOSSLOSSLF2 hrs1.17 ± 0.15 (.80)1.34 ± 0.37 (.21)10.44 ± 6.63 (.002)4 hrs0.67 ± 0.05 (<.001)0.64 ± 0.1 (.08)9.34 ± 3.8 (.002)6 hrs0.73 ± 0.15 (.07)0.69 ± 0.18 (.03)5.00 ± 1.32 (.056)HOSS, High orbital sheer stress; LF, laminar flow; LOSS, low orbital sheer stress; TF, tissue factor. Open table in a new tab HOSS, High orbital sheer stress; LF, laminar flow; LOSS, low orbital sheer stress; TF, tissue factor. LF induced a significant increase of TF mRNA levels. Interestingly both high and low levels of OSS seemed to decrease TF expression after two hours. These data demonstrate that different flow patterns have differential effects on the expression of TF in HUVEC, indicating the involvement of different intracellular signaling pathways. Current efforts are focused on the interaction of flow patterns with chemical stimulation, as a means of elucidating the intracellular signal conduction pathway.

The Effect of Different Flow Patterns on Anode Fluid Behaviors of Micro Direct Methanol Fuel Cells

Based on the visualization technology, we investigated experimentally the effect of different flow patterns on anode fluid behaviors of the μDMFC (Micro Direct Methanol Fuel Cell) with a transparent material under the same condition. Stainless steel mesh was utilized as the current collector which was distinct from the carbon cloth or carbon paper. Four dissimilar flow patterns were developed and tested. The observation of the effect of different flow patterns revealed that movements of dilute methanol solutions and CO2 gas bubbles in the dot and parallel flow fields represented more difficult, which could result in a decline of the μDMFC performance. The study also showed that a channel blocking in the single-serpentine flow field would be extremely terrible which could lead to a fuels leaking of the μDMFC, meanwhile the liquid-gas flow was more fluent and stable in a double-serpentine flow field. Therefore, due to its advantages, a double-serpentine flow pattern is more suitable for the μDMFC application compared with the other flow patterns.

A finite element method to solve a population dynamics stage-structured model of intertidal barnacles

Many marine organisms are fixed or highly sedentary as adults but the adult population may be strongly dependent on the oceanic transport of planktonic larvae. In order to assess interactions between oceanographic and biological processes that determine the population dynamics of marine organisms with a sessile adult phase restricted to the coastline and a planktonic larval phase, we present a stage-structured finite element model for the barnacle Balanus glandula that inhabits the rocky intertidal zone of central California, USA. The larval dispersal depends on knowing the flow pattern. To this end, we develop a numerical procedure to couple physical and biological models in a very simple way when the velocity flow field is known on some discrete values in the domain of interest and at a given time. We investigate the effects of different flow patterns and velocity speeds on the abundance and the distribution of this organism.

Effects of Flow Patterns on the Localization and Expression of VE-Cadherin at Vascular Endothelial Cell Junctions: In vivo and in vitro Investigations

Atherosclerosis occurs preferentially at vascular curvature and branch sites where the vessel walls are exposed to fluctuating shear stress and have high endothelial permeability. Endothelial permeability is modulated by intercellular adhesion molecules such as VE-cadherin. This study was designed to elucidate the effects of different flow patterns on the localization and expression of VE-cadherin in endothelial cells (ECs) both in vivo and in vitro. VE-cadherin staining at EC borders was much stronger in the descending thoracic aorta and abdominal aorta, where the pulsatile flow has a strong net forward component than in the aortic arch and the poststenotic dilatation site beyond an experimental constriction, where the flow near the wall is complex and reciprocating with little net flow. With the use of flow chambers the effects of pulsatile flow (12 ± 4 dyn/cm² at 1 Hz) and reciprocating flow (0.5 ± 4 dyn/cm² at 1 Hz) on VE-cadherin organization in endothelial monolayers were studied in vitro. VE-cadherin staining was continuous along cell borders in static controls. Following 6 h of either pulsatile or reciprocating flow, the VE-cadherin staining at cell borders became intermittent. When the pulsatile flow was extended to 24, 48 or 72 h the staining around the cell borders became continuous again, but the staining was still intermittent when the reciprocating flow was similarly extended. Exposure to pulsatile or reciprocating flow for 6 and 24 h neither change the expression level of VE-cadherin nor its distribution between membrane and cytosol fractions as determined by Western blot and compared with static controls. These findings suggest that the cell junction remodeling induced by different flow patterns may result from a redistribution of VE-cadherin within the cell membrane. Both the in vivo and in vitro data indicate that pulsatile and reciprocating flow patterns have different effects on cell junction remodeling. The lack of junction reorganization in regions of reciprocating flow in vivo and in vitro may provide a mechanistic basis for the high permeability and the preferential localization of atherosclerosis in regions of the arterial stress with complex flow patterns and fluctuating shear stress.

Similarities between the effect of different flow patterns on diffusion with chemical reaction near an interface

Theoretical models of mass transfer across an interface generally ignore the effect of velocity variation. For mass transfer accompanied by psuedo nth order reaction, it is shown that, at sufficiently high values of reaction rate constant, the rate of mass transfer will be independent of the velocity variation. Thus, in scale-up studies, it is often unnecessary to match flow conditions in laboratory and large-scale equipment, so that laboratory apparatus may safely be chosen on the grounds of simplicity and convenience.

The effect of gas flow patterns on radiative transfer in cylindrical furnaces

The prediction of performance of industrial furnaces is conventionally estimated by making gross assumptions as to the effect of temperature variations in the gas. The zone method of allowing for the effect, on radiative transfer, of the temperature variation in furnace enclosures has been applied to the problem of interaction between radiation and other modes of heat transfer. The effect of different flow patterns on the gas temperature-field and wall-flux distribution in a cylindrical furnace has been examined by use of the following flow models : plug flow ; parabolic velocity profiles ; ducted-jet flow (axial feed) with recirculation rates of 0, 1, and 11 times the flue-gas flow rate. A sixteenfold range of diameters and firing densities was studied. The reduced efficiencies were correlated, for a fixed surface temperature and for each of the flow models, in terms of a reduced firing rate. The wide range of heat flux distribution patterns found in the study emphasizes the need to include allowance for gas temperature variation in any furnace analysis in which the heat flux pattern is important.