Uniform Wall Temperature Conditions Research Articles

Two Models on the Unsteady Heat and Fluid Flow Induced by Stretching or Shrinking Sheets and Novel Time-Dependent Solutions

Abstract This study sheds light on unsteady heat and fluid flow problems over stretching and shrinking surfaces, enriching our understanding of these complex phenomena. We derive two mathematical models using a rigorous approach. The first model aligns with the model commonly employed by researchers in this field, but its steady-state solution remains trivial. The second model, introduced in this work, demonstrably captures the physically relevant steady-state solutions well-studied in the literature. Notably, we introduce new similarity solutions for the temperature field specifically within the first model. We further demonstrate that a uniform wall temperature condition leads to the optimal heat transfer rate. While similarity solutions can be derived for specific cases with the second model, nonsimilar solutions may be necessary for more general scenarios. We discuss the implications of our analysis for stagnation-point flow and non-Newtonian viscoelastic fluid flow problems, illuminating future research directions in the open literature.

Experimental study of turbulent air natural convection in open-ended vertical parallel plates under asymmetric heating conditions

In this study, we investigated the turbulent air natural convection phenomena between open-ended vertical parallel plates under asymmetric heating conditions. The rectangular air channel consisted of two insulating walls and two heated walls: one of the vertical walls is heated to maintain uniform wall temperature conditions at various temperatures from 50 to 500 °C, and the other wall is indirectly heated by thermal radiation from the directly heated wall. We measured both wall temperature distributions in the vertical direction and the air temperature profiles with the horizontal direction at certain heights.The results showed that when both walls are heated asymmetrically, reverse flow was absent at the outlet of the channel, as confirmed by a simple visualization method. In addition, we confirmed the practical result of a deviation between the mean air temperature and the measured air temperature at the center of the channel. From the results of the wall temperature distributions and the air temperature profiles, we suggest a reasonable flow behavior, which is the generation of two different recirculation flow patterns that are not affected by changes in the thermal boundary. In addition, we compared the ratio between the convective and radiative heat rates on the directly heated wall. Based on the experimental results, we analyzed the natural convection heat transfer between vertical parallel plates and we proposed two correlations. The heat transfer correlation agreed well with the correlation for turbulent natural convection on a single infinite vertical plate. The correlating equation related to the induced flow rate was presented as a modified Rayleigh number to estimate the flow rate.

Comparison of urban airflow between solar-induced thermal wall and uniform wall temperature boundary conditions by coupling CitySim and CFD

Previous studies investigated the urban wind airflow under the isothermal condition, solar-induced thermal wall and uniform wall temperature boundary conditions. The differences in spatially-averaged airflow properties among those three boundary conditions have not been investigated yet. This study investigated different scenarios to identify: (1) whether the solar-induced non-uniform wall temperatures could be replaced by the uniform wall temperatures (average of all wall temperatures from solar-induced scenario) in the analysis of urban wind airflow and (2) the wind conditions that the wall thermal boundary conditions might be neglected. In this study, urban energy model, CitySim, was employed to calculate the solar-induced walls’ temperatures of an idealized 5 × 5 building array, which were set as thermal boundary conditions in computational fluid dynamic (CFD) simulations. The simulation results were compared to those obtained from cases with uniform wall temperatures and isothermal conditions. The results showed that excluding wall thermal boundary conditions underestimated the spatially-averaged flow properties when reference wind speed (Uref) was lower than 2.0 m s−1 under the designed scenarios and noticeable difference of airflow pattern was observed between isothermal and non-isothermal conditions. The solar-induced wall temperature condition might be replaced by uniform wall temperature condition with Uref of 3.0 m s−1 under parallel wind condition, and with Uref of 5.0 m s−1 under oblique wind conditions. Meanwhile, the airflow structures of the street canyons inside the three-dimensional building array differed significantly from the previous results obtained from isolated street canyon model.

Effect of Helical Surface Disc Turbulators on Heat Transfer and Friction Factor Characteristics in the Annuli of a Double‐Pipe Heat Exchanger

AbstractThe heat transfer and pressure drop characteristics in annuli of a double‐pipe heat exchanger (DPHE) using helical surface disc turbulators (HSDTs) are experimentally investigated. The effect of a helical surface disc turbulator is studied for three pitch ratios, three diameter ratios, and varying Reynolds numbers. Water flows in the inner tube and air through the annulus. The tests are conducted for air with uniform wall temperature condition. The heat exchanger with the least pitch ratio and least diameter ratio was found to exhibit the highest Nusselt number and pressure drop. The thermal performance factor turned out to be greater than unity for all cases. Correlations were developed for Nusselt number, friction factor, and thermal performance.

Exact and statistical computations of radiated flow of nano and Casson fluids under heat and mass flux conditions

Abstract The statistical and exact analysis of the unsteady radiative flow of Nano and Casson fluids past a vertical plate with Dufour effect is carried out. The heat transport phenomenon is studied under uniform heat flux (UHF) and uniform wall temperature (UWT) conditions. The exact solution to the problem is found using the Laplace transform method (LTM). The effects of various parameters on velocity, temperature and concentration profiles are examined via graphs. The heat transfer rate and skin friction are analyzed through statistical tools like probable error and regression. The Dufour effect enhances the velocity and temperature profiles. It is also observed that the velocity profile is slightly greater in the case of UWT than the UHF case for both nanofluid and Casson fluid. From the regression analysis, it is established that the Dufour number and nanoparticle volume fraction have a negative impact whereas the radiative heat parameter has a positive impact on the rate of heat transfer. Highlights The statistical analysis of the unsteady radiated flow on a vertical plate with Dufour effect is performed. The uniform heat flux (UHF) and uniform wall temperature (UWT) conditions are accounted. The Nusselt number and friction factor are analysed through statistical tools. The velocity profile is greater for UWT case than the UHF case.

Heat transfer augmentation in double pipe water to air counter flow heat exchanger with helical surface disc turbulators

Present investigation reports the effect of helical surface disc turbulators (HSDTs) on heat transfer and pressure drop characteristics in double pipe heat exchanger (DPHE). HSDTs has been utilized in the annulus region. Tests are conducted by insertion of HSDTs with various operating parameters including three different diameter ratios (DR = do/Di = 0.42, 0.475 and 0.54), three different helix angles (ɸ = 20°, 30° and 40°) and varied range of Reynolds Number (3500–10500). Water, used as hot fluid, flows in the inner tube, while air, used as cold fluid, flows through the annulus. The tests are conducted for air for uniform wall temperature condition. The heat exchanger with least diameter ratio and increased helix angle is found to exhibit the highest Nusselt number and friction factor. Results indicate that maximum enhancement is obtained for smallest diameter ratio (DR = 0.42) and helix angle (ɸ = 40°). The thermal performance factor is found to be greater than unity for each configuration studied with DPHE using HSDTs. Correlations have been developed Nusselt number, friction factor and thermal performance factor for Reynolds number varying between 3500–10,500.

Heating intensity and radiative effects on turbulent buoyancy-driven airflow in open square cavities with a heated immersed body

The influence of the radiative heat transfer and the effects of air variable properties on the natural convection flows within a vented square cavity with a heated inner body are numerically investigated. Two-dimensional, unsteady, laminar, transitional and turbulent simulations are obtained, for both uniform wall temperature and uniform heat flux heating conditions. The average Nusselt number and the dimensionless mass-flow rate are obtained for a wide range of the Rayleigh number varying from 104 to 1012. The results obtained for different heating intensities are analyzed and compared. The influence of considering surface radiative effects on the differences reached for the Nusselt number and the mass-flow rate obtained with several heating intensities is studied for the isothermal heating condition. For isoflux heating, the obtained results show that the effects of thermal radiation on the appearance of the burnout phenomenon are particularly relevant under given circumstances. The conditions under which the flow becomes unstable, giving rise to a transient, mainly oscillating solution, are determined. The relevant changes produced in the flow patterns into the cavity, are also explained.

Numerical study of the laminar flow and heat transfer characteristics in a tube inserting a twisted tape having parallelogram winglet vortex generators

The usage of wings or/and winglets vortex generators (VGs) could provide excellent heat transfer performance with a minimal increase in pressure loss comparing with other VGs in a wide range of Reynolds number. For classical twisted tape, the contact area between twisted tape and working fluid is large, which would result in high friction drag. Motivated by this fact, a newly designed twisted tape having parallelogram winglet VGs (PWVGs) is proposed to enhance heat transfer. This twisted tape with winglet VGs is formed by cutting at the edge of the straight tape with parallelogram shape to produce a parallelogram winglet as twisting around its longitudinal axis. The laminar fluid flow and conjugate heat transfer characteristics in a circular tube inserting the twisted tape with PWVGs were analyzed using numerical method under uniform wall temperature condition, and four different attack angle α (α=27.64°, 21.44°, 17.44° and 14.67°) and four different axial spacing St (St=0.83D, 1.0D, 1.25D and 1.67D). The results show that (1) the newly designed twisted tape has two ways to generate secondary flow, including secondary flow generated by the twisted base tape and extra secondary flow generated by PWVGs; (2) the combination of twisted base tape and PWVGs has evident effects on the local flow and heat transfer characteristics; (3) compared with the reference empty tube, the twisted tape with PWVGs can effectively enhance heat transfer under identical pumping power condition, for studied case of α=17.44°, St/D=1.25 and Re ranging from 50 to 600, the average Nusselt number and friction factor are increased by 76.4–190.9% and 179.9–289.1%, respectively, and the corresponding thermal performance factor ranges from 1.25 to 1.85; and (4) as Re ranges from 50 to 600, the helical angle α of PWVGs is a very important parameter in design of the modified twisted tape, and when α is large and St is small the heat transfer performance of the twisted tape with PWVGs is better.

Laminar Forced Flow and Heat Transfer in Cross-Corrugated Triangular Ducts

The fluid flow and heat transfer characteristics in a cross-corrugated triangular channel are studied under laminar forced flow and uniform wall temperature conditions. Both the local and the periodic mean values of friction factor and wall Nusselt numbers in the hydro and thermally developing entrance region are investigated. It is found that at higher Reynolds numbers, recirculations in the lower wall valleys are a dominant factor for flow and heat transfer, while at lower Reynolds numbers, parallel flows in the upper wall corrugation are the predominant factor. Compared with a parallel flat plates duct, the Nusselt numbers in a cross-corrugated triangular duct can be enhanced, and can be even higher at higher Reynolds numbers. The growth of steady recirculations and the concomitant periodic disruption and thinning of the boundary layer promote enhanced transport of heat as well as momentum. Effects of heat transfer enhancement are more obvious under higher Reynolds numbers. Two correlations are proposed to predict the periodic mean values of Nusselt numbers and friction factors for Reynolds numbers from 10 to 2000.

The effect of symmetrical perforated holes on the turbulent heat transfer in the static mixer with modified Kenics segments

The numerical simulation on forced convective heat transfer of water in the modified Kenics static mixer (MKSM) was investigated by the three-dimensional turbulent and steady incompressible flow of computational fluid dynamics (CFD). The conservation equations were solved by using finite volume method (FVM) and the SIMPLEC algorithm scheme in ANSYS Fluent 16.1. The simulation results of Nusselt number and the friction factor in MKSM have a good agreement with the literature results. The effects of Reynolds number, perforated diameter, perforated spacing, and segment number on the heat transfer are evaluated in the range of Re=2000–20,000 under uniform heat tube wall temperature conditions. The Nusselt number increases gradually with increasing Re. Furthermore, both the values and deviations of Nusselt number for different perforated diameter accord with an antisymmetrical tendency at the critical Re=11,000. It could be seen that the Nusselt number and the friction factor are not sensitive to the increasing perforated spacing within a given perforated diameter. In view of thermal performance factor, the geometrical diameter and spacing of two symmetrical perforated holes are optimized. The MKSM with d/W=0.3 and s/W=0.6 have the best performance with the consideration of both heat transfer rate and friction loss compared to the others. Thermal performance factor decreases gradually with increasing Re which indicated that the modified Kenics segments are more effective for heat transfer in lower Re. The local and global synergies between secondary flow and temperature fields have been investigated through field synergy principle.

Radiative effects on turbulent buoyancy-driven airflow in open square cavities

The effects of the radiative effects and the air variable properties (density, viscosity and thermal conductivity) on the buoyancy-driven flows established in open square cavities are investigated. Two-dimensional, laminar, transitional and turbulent simulations are obtained, considering both uniform wall temperature and uniform heat flux heating conditions. In transitional and turbulent cases, the low-Reynolds k−ω turbulence model is employed. The average Nusselt number and the dimensionless mass-flow rate have been obtained for a wide range of the Rayleigh number varying from 103 to 1016. The results obtained taking into account the variable thermophysical properties of air are compared to those calculated assuming constant properties and the Boussinesq approximation. In addition, the influence of considering surface radiative effects on the differences reached for the Nusselt number and the mass flow rate obtained with several intensities of heating is studied; specifically, the effects of thermal radiation on the appearance of the burnout phenomenon is analyzed. The changes produced in the flow patterns into the cavity when the radiative heat transfer and the effects of variation of properties are relevant, are also shown.

The effects of element direction and intersection angle of adjacent Q-type inserts on the laminar flow and heat transfer

Three dimensional numerical studies were performed for laminar heat transfer and fluid flow characteristics of circular tubes equipped with two Q types of RL- and RR-series inserts. The simulation results of axial velocity distribution in Q-type static mixer (QSM) have a good agreement with the experimental results from the literature using water as working fluid. The effects of Reynolds number, element direction and intersection angle of adjacent Q-type inserts on the heat transfer are evaluated in the range of Re = 20–100 under uniform heat tube wall temperature conditions. The friction factor decreases with the increase of Re, and the deviations of friction factor in RL-QSM with different intersection angles are within 1% when the sum of two angles is equal to 180°. The product of friction factor and Re in QSM linearly increases with an increase in Re, and it is 3.5–10.7 times higher than predicted by empirical theory for tubes without inserts. Taking the effect of hydraulic diameter into account, a modified performance evaluation plot is generated. The ratios of heat transfer rate in QSM to that in smooth tube are larger than 1 and the maxima approach 3.4 under the identical pumping power constraint. The heat transfer augmentation is attained by the swirl flow formation induced by the Q-type inserts and tube wall. Based on the numerical results, synergies between velocity field and temperature field have been investigated through field synergy principle.

Heat Transfer and Pressure Drop Characteristics of Nanofluid Flows Inside Corrugated Tubes

An experimental investigation is carried out to study the heat transfer and pressure drop characteristics of multiwalled carbon nanotubes (MWCNTs)/heat transfer oil nanofluid flows inside horizontal corrugated tubes under uniform wall temperature condition. To provide the applied nanafluids, MWCNTs are dispersed in heat transfer oil with mass concentrations of 0.05, 0.1, and 0.2 wt%. The Reynolds number varies between 100 and 4,000. Three tubes with hydraulic diameters of 11.9, 13.2, and 15.5 mm are applied as the test section in the experimental setup. Tubes are corrugated four times on the cross section; that is, there are four different helices around the tube. Depths of the corrugations are chosen as 0.9, 1.1, and 1.3 mm, and pitch of corrugation is 14 mm. The acquired data confirm the increase of heat transfer rate as a result of utilizing nanofluids in comparison with the base fluid flow. However, corrugating the tubes decreases the heat transfer rate at low Reynolds numbers. The highest increase in heat transfer rate is observed for the Reynolds numbers for which the smooth tube is in the transition regime and the corrugated tube reaches the turbulent flow, that is, Reynolds number in the range of 1,000 to 3,000. Rough correlations are proposed to predict the Nusselt number and friction factor.

Numerical Study on Temperature Variation in Adsorption Bed under Solar Insolation

The internal temperature change of an adsorbent bed, which is subjected to the solar insolation, has been numerically simulated. As the intensity of the solar radiation changes with the sun movement, the temperature distribution in the bed evolves continually. Based on the configuration of the evacuated tube bed, a two-dimensional model of heat transfer has been established and numerically solved. To identify the effect of the internal cooling mode, three kinds of thermal boundary condition have been applied to the cooling tunnel. The numerical results reveal that the uniform wall temperature condition presents the best cooling effect, while the natural air convection presents the worst effect. In addition, the temperature change of the bed with the bed diameter has been examined, incorporating with the effect of cooling channel size. For the cooling condition of the natural air convection, the sun-facing side of the bed not only warms up the most rapidly, but also shows the highest temperature. In contrast, the temperature rising of the sun-shading side is much less. The temperature difference between the sun-facing side and the sun-shading side can reach 70℃. The non-uniform distribution of the temperature of the bed will hinder the adsorption cooling performance.

Semi-analytical solution for fully developed forced convection in metal-foam filled tube with uniform wall temperature

Fully developed flow and heat transfer in metal-foam filled tube with uniform wall temperature (UWT) is semi-analytically investigated based on the Brinkman-Darcy model and the two-equation model, in which the inertia term, axial conduction, and thermal dispersion are ignored. A two-dimensional numerical simulation that adopts the full governing equations is also conducted to analyze the effects of neglected terms on flow and thermal transport performance by comparing with the semi-analytical solution. The effects of the relevant parameters and thermal boundary conditions including UWT and uniform heat flux (UHF) on the heat transfer characteristics are discussed based on the semi-analytical solution. The results show that the inertia term has a significant effect on the prediction of pressure drop, but has a relatively mild effect on Nusselt number. The axial conduction has significant effect on the Nusselt number at lower Reynolds number, and the effects of thermal dispersion can be neglected when the thermal conductivity ratio between fluid and solid is remarkably smaller for air/metal foam as example (kf/ks<3×10−3). The predicted Nusselt number of the semi-analytical solution is about 8% to 15% lower than that of the numerical solution with full model in the range of 4×10−5<kf/ks<3×10−3. Moreover, the temperature profile of solid is more sensitive to pore density and porosity than that of fluid under UWT condition. The Nusselt number under UWT is about 7% to 25% lower than that under UHF, and the difference is mainly determined by interfacial convection rather than solid conduction.

Convective heat transfer of MWCNT / HT-B Oil nanofluid inside micro-fin helical tubes under uniform wall temperature condition

Experiments are performed to investigate the single-phase flow heat transfer augmentation of MWCNT/HT-B Oil in both smooth and micro-fin helical tubes with constant wall temperature. The tests in laminar regime were carried out in helical tubes with three curvature ratios of 2R/d=22.1, 26.3 and 30.4. Flow Reynolds number varied from 170 to 1800 resulting in laminar flow regime. The effect of some parameters such as the nanoparticles concentration, the dimensionless curvature radius (2R/d) and the Reynolds number on heat transfer was investigated for the laminar flow regime. The weight fraction of nanoparticles in base fluid was less than 0.4%. Within the applied range of Reynolds number, results indicated that for smooth helical tube the addition of nanoparticles to the base fluid enhanced heat transfer remarkably. However, compared to the smooth helical tube, the average heat transfer augmentation ratio for finned tube was small and about 17%. Also, by increasing the weight fraction of nanoparticles in micro-fin helical tubes, no substantial changes were observed in the rate of heat transfer enhancement.

Heat Transfer and Pressure Drop Studies Through a Square Duct Fitted With Increasing and Decreasing Order of Twisted Tape

Experimental investigation of heat transfer and friction factor characteristics of a square duct fitted with an increasing and decreasing order of twist ratio set have been studied under a nearly uniform wall temperature condition for laminar flow using water as test liquid. The Reynolds number was varied from 100 to 2100. Cold water flows through the inner square duct, and hot water passes through the circular annulus, in countercurrent fashion. There is not much change in the magnitude of heat transfer coefficient enhancement with increasing twist ratio and with decreasing twist ratio set, as the intensity of swirl generated at the inlet or at the outlet in the order of increasing twist ratio or decreasing twist ratio is the same in both the cases. The experimental results show that Nusselt numbers were found to be 1.33–4.27 and 0.9–3.46 times the plain square duct forced convection values based on constant flow rate and constant pumping power criteria, for increasing and decreasing order of twist ratio sets, respectively.

Laminar Heat Transfer Augmentation through A Square Duct and Circular Tube Fitted with Twisted Tapes

Experimental studies on friction factor and heat transfer characteristics for the laminar flow of ethylene glycol in a square duct fitted with twisted tapes of different twist ratios under nearly uniform wall temperature conditions are reported in this article. The Nusselt numbers were found to be 5.44–7.49 and 2.46–4.87 times that of plain square duct forced convection values based on constant flow rate and constant pumping power criteria, respectively, for y = 2.66. The augmented friction factor and Nusselt number for a square duct is about 1.9 and 2.10 times higher than that for an augmented circular tube.

Experimental heat transfer and friction factor studies through a square duct fitted with helical screw tapes

AbstractExperimental investigations of friction factor and heat transfer characteristics through a square duct fitted with helical screw tapes of various twist ratios have been studied under nearly uniform wall temperature conditions. The experimental results reveal that the use of helical screw tapes leads to a considerable increase in heat transfer and friction loss over those of a plain square duct. The Nusselt number increases with the rise of Reynolds number and the reduction of twist ratio. The Performance evaluation criteria have been presented and maximum performance ratio was observed for minimum twist ratio.

An experimental investigation on heat transfer characteristics of multi-walled CNT-heat transfer oil nanofluid flow inside flattened tubes under uniform wall temperature condition

An experimental investigation on heat transfer characteristics of MWCNT-heat transfer oil nanofluid flow inside horizontal flattened tubes has been carried out under uniform wall temperature condition. Nanoparticle weight fractions were 0%, 0.1%, 0.2%, and 0.4%. The copper tubes of 14.5mm I.D. were flattened and used as the test section of oblong shape with inside heights of 13.4mm, 11.7mm, 10.6mm, and 8.6mm. The nanofluid flowing inside the tube was heated inside a steam chamber to keep the temperature of the tube wall constant. The required data were acquired for laminar hydrodynamically fully developed regime. The effects of different parameters such as volumetric flow rate, nanoparticle weight fraction, and hydraulic diameter on the heat transfer behavior of the tested systems have been investigated experimentally. For a given flattened tube at a constant nanoparticle weight fraction, increasing volumetric flow rate results in heat transfer enhancement. In addition, as the tube profile becomes more flattened and the hydraulic diameter decreases, the heat transfer coefficient goes up at constant volumetric flow rate. Utilizing nanofluids instead of the base fluid, the heat transfer rate enhances remarkably. The higher the nanoparticles weight fraction, the more the rate of heat transfer enhancement. Finally, the results show that the amount of increase in heat transfer coefficient caused by employing nanofluid instead of the base fluid is comparable to what caused by flattening the tube.