Transient thermocapillary flow in rectangular tanks with phase change

A numerical and experimental study is performed on transient natural convection in an insulated rectangular tank. The liquid is suddenly heated by a line source or cooled by a line sink being placed at the center of the free surface to initiate a thermocapillary force. Evaporation or condensation takes place on the free surface. A finite-difference technique is employed to numerically integrate the unsteady vorticity and heat transport equations. Numerical results are obtained to determine the effects of dimensionless governing parameters on the transfer phenomena. In an evaporative system with low Marangoni number (Ma), three distinct convective mechanisms are identified: surface tension-driven, buoyancy-driven and mixed types. The differences in the flow behavior are disclosed between condensation, evaporation and no phase change. Theory is in qualitative agreement with evaporation experiments in high Ma systems.     

Convective Heat Transfer in a Vertical Rectangular Duct Filled with a Nanofluid

An analysis is performed to study natural convective heat transfer in a vertical rectangular duct filled with a nanofluid. One of the vertical walls of the duct is cooled by a constant temperature, while the other wall is heated by a constant temperature. The other two sides of the duct are thermally insulated. The transport equations for a Newtonian fluid are solved numerically with a finite volume method of second‐order accuracy. The influence of pertinent parameters such as Grashof number, Brinkman number, aspect ratio and solid volume fraction on the heat transfer characteristics of natural convection is studied. Results for the volumetric flow rate and skin friction for Copper and Diamond nanoparticles are also drawn. The Nusselt number for various types of nanoparticle such as silver, copper, diamond and titanium oxide are also tabulated. The results indicate that inclusion of nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximizes the heat transfer rate.     

Experimental and Numerical Investigation on Forced Convection in Circular Tubes With Nanofluids

In this paper an experimental and numerical study to investigate the convective heat transfer characteristics of fully developed turbulent flow of a water–Al₂O₃ nanofluid in a circular tube is presented. The numerical simulations are accomplished on the experimental test section configuration. In the analysis, the fluid flow and the thermal field are assumed axial-symmetric, two-dimensional, and steady state. The single-phase model is employed to model the nanofluid mixture and the k-? model is used to describe the turbulent fluid flow. Experimental and numerical results are carried out for different volumetric flow rates and nanoparticles concentration values. Heat transfer convective coefficients as a function of flow rates and Reynolds numbers are presented. The results indicate that the heat transfer coefficients increase for all nanofluids concentrations compared to pure water at increasing volumetric flow rate. Heat transfer coefficient increases are observed at assigned volumetric flow rate for nanofluid mixture with higher concentrations, whereas Nusselt numbers present lower values than the ones for pure water.     

FLUID FLOW AND HEAT TRANSFER IN MULTIPLY-FOLDED,CONTINUOUS FLOW PASSAGES INCLUDING CONJUGATE THERMAL INTERACTION BETWEEN THE FLUID AND BOUNDING WALLS

A numerical simulation has been performed for the fluid flow and heat transfer in a flow passage consisting of a series of 180° bends connected by straight sections. The basic passage cross-section geometry is that of a flat rectangular duct. The simulation problem encompassed three-dimensional flows of both fluid and heat and involved the conjugate interaction of thermal phenomena in the fluid and in its bounding wall. The implementation of the numerical model was performed using FLUENT 5.0. Several results of practical interest were deduced from the simulation. With regard to the motivating application, the heating of biofluids prior to their introduction into the human body, local hotspots were found to occur whose presence could be injurious to living cells. The heating of the flowing fluid (a liquid to properly model the biofluid application) was found to be highly nonuniform at low values of the volumetric flowrate of the fluid despite the fact that the bounding walls of the flow passage were uniformly heated. Local-averaged heat transfer coefficients were evaluated at numerous locations along the length of the flow passage. Except for the regions of the bends of the passage, the local-averaged heat transfer coefficient was nearly constant and closely coincided with the fully developed heat transfer coefficient for flow in a flat rectangular duct.     

Study of trans-critical CO2 natural convective flow with unsteady heat input and its implications on system control

Natural convective flow of supercritical fluid has become hot topic both in scientific research and engineering applications. Natural circulation thermosyphon using supercritical/trans-critical CO₂ can be a potential substitute for effective transportation of heat and mass without valves/pumping devices. This paper presents numerical investigations into the effect of unsteady heat input on the trans-critical CO₂ thermosyphon, including sudden/quick increase of heat input, gradual/slow increase of heat input and sudden decrease of heat input. Those unsteady input situations are often seen in real applications and have become the core problem of efficiency and safety improvement. In the present study, two-dimensional rectangular natural circulation loop model is set up and numerically investigated. New heat transport model aiming at trans-critical thermosyphon heat input and system stability laws is proposed with supercritical/trans-critical turbulence model incorporated. It is found that when compared with supercritical CO₂ condition, trans-critical CO₂ thermosyphon has quite different behaviors. Natural convective thermosyphon stability is found to be of routinely dependent for different heat input change mode. Stability factors of natural convective trans-critical CO₂ flow and its implications on real system control are also discussed in this paper.     

Buoyancy driven flow in a hot water tank due to standby heat loss

Results of experimental and numerical investigations of thermal behavior in a vertical cylindrical hot water tank due to standby heat loss of the tank are presented. The effect of standby heat loss on temperature distribution in the tank is investigated experimentally on a slim 150 l tank with a height to diameter ratio of 5. A tank with uniform temperatures and with thermal stratification is studied. A detailed computational fluid dynamics (CFD) model of the tank is developed to calculate the natural convection flow in the tank. The distribution of the heat loss coefficient for the different parts of the tank is measured by experiments and used as input to the CFD model. Water temperatures at different levels of the tank are measured and compared to CFD calculated temperatures. The investigations focus on validation of the CFD model and on understanding of the CFD calculations.The results show that the CFD model predicts satisfactorily water temperatures at different levels of the tank during cooling by standby heat loss. It is elucidated how the downward buoyancy driven flow along the tank wall is established by the heat loss from the tank sides and how the natural convection flow is influenced by water temperatures in the tank. When the temperature gradient in the tank is smaller than 2 K/m, there is a downward fluid velocity of 0.003–0.015 m/s. With the presence of thermal stratification the buoyancy driven flow is significantly reduced. The dependence of the velocity magnitude of the downward flow on temperature gradient is not influenced by the tank volume and is only slightly influenced by the tank height to tank diameter ratio. Based on results of the CFD calculations, an equation is determined to calculate the magnitude of the buoyancy driven flow along the tank wall for a given temperature gradient in the tank.     

Convective Heat Transfer of an Air Bubble in Water With Variable Thermophysical Properties

A numerical study of convective heat transfer of an air bubble in water with variable thermophysical properties is considered. Two-dimensional simulations of multifluid flows with heat transfer include the Navier–Stokes, energy, and volume of fluid (VOF) advection equations. The solver computes the flow field and temperature by solving the systems of Navier–Stokes equations and the energy equation using the finite–volume method with the SIMPLE algorithm and tracks the position of interface between two fluids with different fluid properties by the VOF method with piecewise linear interface construction technique. Empirical correlations in terms of temperature for thermophysical properties are considered in the simulations. The convective heat transfer model is assessed with a benchmark problem of cooling of water and compared with previous literature data showing good agreement. Finally, a numerical study of the effect of the bubble diameter in the range from 2 mm to 3 mm on heat transfer is performed.     

Analysis of the flow and heat transfer characteristics for assisting incompressible laminar flow past an open cavity

A numerical study has been carried out to analyze the effects of mixed convective assisting flow past three-dimensional open cavity over a wide range of Reynolds (100–1000) and Richardson (0.001–10) numbers. The vertical walls in the inflow and outflow sides are isothermal while all other walls are adiabatic. The cavity is assumed to be cubic in geometry and the flow is laminar. A direct numerical simulation is undertaken to investigate the flow structure, the heat transfer characteristics and the complex interaction between the induced stream flow at ambient temperature and the buoyancy-induced flow from the heated wall. It is found that the flow becomes stable at moderate Grashof number and exhibits a three-dimensional structure, while for high Richardson number the mixed convection effects come into play and push the recirculating zone further upstream and the flow may becomes unstable.     

Experimental study of natural convection in fluid-superposed porous layers heated locally from below

An experimental study of natural convection in fluid-superposed porous layers heated locally from below is reported. Measurements are made in a rectangular chamber with 3 mm DIA glass beads as the porous layer and distilled water as the saturating fluid. The effects of the heater-to-cavity length ratio and the porous layer-to-cavity height ratio on the overall heat transfer coefficients are reported. Average heat transfer coefficients over the heated surface increase with a decrease in porous layer-to-cavity height ratio, but no clear effect of heater-to-cavity length ratio is seen. Temperature profiles in the domain reveal a plume like flow with a single pair of circulating cells and evidence of convective motion inside the porous layer.     

Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity

In this paper, thermal characteristics of natural convection in a rectangular cavity heated from below with water-based nanofluids containing alumina (Al₂O₃ nanofluids) are theoretically investigated with Jang and Choi’s model for predicting the effective thermal conductivity of nanofluids and various models for the effective viscosity. To validate theoretical results, we compare theoretical results with experimental results presented by Putra et al. It is shown that the experimental results are put between a theoretical line derived from Jang and Choi’s model and Einstein’s model and a theoretical line from Jang and Choi’s model and Pak and Cho’s correlation. In addition, the effects of the volume fraction, the size of nanoparticles, and the average temperature of nanofluids on natural convective instability and heat transfer characteristics of water-based Al₂O₃ nanofluids in a rectangular cavity heated from below are theoretically presented. Based on the results, this paper shows that water-based Al₂O₃ nanofluids is more stable than base fluid in a rectangular cavity heated from below as the volume fraction of nanoparticles increases, the size of nanoparticles decreases, or the average temperature of nanofluids increases. Finally, we theoretically show that the ratio of heat transfer coefficient of nanofluids to that of base fluid is decreased as the size of nanoparticles increases, or the average temperature of nanofluids is decreased.     

Upflow turbulent mixed convection heat transfer in vertical pipes

The present work deals with the results of an experimental investigation on heat transfer in water cooled vertical pipes, for thermal–hydraulic conditions ranging from forced convective flow to mixed convective flow. The flow of water in the pipe is upwards.Experimental data confirm the reduction in the heat transfer rate for mixed convection in upward heat flow, mainly due to the laminarization effect in the near-wall region (buoyancy effect) . They are in a very good agreement with numerical methods, such as the k–-model.A new method for the calculation of the heat transfer coefficient in upward mixed convection heated flow is proposed. It is based on the well-known superposition method (heated downflow) modified accounting for the phenomenology of the upward heated flow in comparison with downflow heated conditions.     

Computational modeling of heat transfer in magneto-non-Newtonian material in a circular tube with viscous and Joule heating

Numerous industrial and engineering systems, like, heat exchangers, chemical action reactors, geothermic systems, geological setups, and many others, involve convective heat transfer through a porous medium. The diffusion rate, drag force, and mechanical phenomenon are dealt with in the Darcy–Forchheimer model, and hence this model is vital to study the fluid flow and heat transport analysis. Therefore, numerical simulation of the Darcy–Forchheimer dynamics of a Casson material in a circular tube subjected to the energy losses due to the viscous heating and Joule dissipation mechanisms is performed. The novelty of the present investigation is to scrutinize the convective heat transport characteristics in a circular tube saturated with Darcy–Forchheimer porous matrix by utilizing the non-Newtonian Casson fluid. The flow occurs due to the elongation of the surface of a tube with a uniform heat-based source/sink. The similarity solution of the nonlinear problem was obtained using dimensionless similarity variables. The effects of operating parameters related to the flow phenomena are analyzed. Further, the friction factor and Nusselt number are also analyzed in detail. The present flow model ensures no flow reversal and acts as a coolant of the heated cylindrical surface; the existence of the magnetic field, as well as an inertial coefficient, acts as the momentum-breaking forces, whereas Casson fluidity builds it. The Joule heating phenomenon enhances the magnitude of temperature. The thermal field of the Casson fluid is higher at the surface of the circular pipe due to convective thermal conditions.     

Forced Convective Heat Transfer in a Plate Channel Filled with Solid Particles

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Numerical method for interfacial heat transfer in an oil-water displacement flow

A numerical study of interfacial heat transfer is performed in an oil-water displacement flow. The process of oil-water displacement is one of the key technologies for the underwater tank in offshore oil exploitation. There is a need to investigate the interfacial heat transfer between oil and water as the wax precipitation and solidification of high pour point crude oil at low temperature will particularly affect the flow of oil. Before the numerical simulation is performed, it is necessary to find out the optimal numerical method. For the volume of fluid method, the property parameters in the temperature equation are mixture ones weighted by each fluid. When the unsteady term, convective term, and diffusion term are considered, there are three property parameters that are the coefficient of each term. For each coefficient, whether an algebraic scheme or a harmonic scheme could be used. When the three coefficients are considered together, there would be eight combinations of weighting form. A numerical method is developed by exploring an optimal combination of the weighting form. The results are demonstrated with an analytical solution. It is found that the combination of three harmonic schemes will significantly improve the error. The maximum and total error from this combination are reduced by 62% and 79% compared to the second-best one and by 86% and 93% compared to the worst one. Meanwhile, the clock time only increases by 1.6% and 0.4%. The combinations of three harmonic schemes will result in the largest order of accuracy which is as large as 1.60. The harmonic scheme should be used for the property parameter of all the three terms in the vertical oil-water flow.     

Numerical studies on heat and fluid flow of nanofluid in a partially heated vertical annulus

A numerical investigation on natural convective heat transfer of nanofluid (Al₂O₃+water) inside a partially heated vertical annulus of high aspect ratio (352) has been carried out. The computational fluid dynamics solver Ansys Fluent is used for simulation and results are presented for various volume fraction of nanoparticles (0‐0.04) at different heat flux values (3‐12 kW/m²). Two well‐known correlations for evaluating thermal conductivity and viscosity have been used. Thus different combinations of the available correlations have been set to form four models (I, II, III, and IV). Therefore, a detailed analysis has been executed to identify effects of thermophysical properties on heat transfer and fluid flow of nanofluids using different models. The results show enhancement in heat transfer coefficient with volume fraction of nanoparticles. Highest enhancement achieved is found to be 14.17% based on model III, while the minimum is around 7.27% based on model II. Dispersion of nanoparticles in base fluid declines the Nusselt number and Reynolds number with different rates depending on various models. A generalized correlation is proposed for Nusselt number of nanofluids in the annulus in terms of volume fraction of nanoparticles, Rayleigh number, Reynolds number, and Prandtl number.     

Experimental and Numerical Study of Turbulent Fluid Flow and Heat Transfer of Al2O3/Water Nanofluid in a Spiral-Coil Tube

Enhancement of heat transfer by nanofluids is reported by a large number of researchers. In this study, numerical and experimental investigation of heat transfer and flow characteristics of Al₂O₃/water nanofluid flowing in a spiral-coil tube is performed for various flow conditions. The spiral-coil tube is immersed horizontally in a hot water bath maintained at 60°C. Experiments are conducted in a turbulent flow regime using distilled water and nanofluid with 0.5%, 1%, and 1.5% particle volume concentrations. Also, a computational fluid dynamics methodology is used to simulate heat transfer and flow characteristics corresponding to the experimental measurements and for further flow conditions. Simulation results are compared with the experimental measurements, and 85% agreement between the results is observed. The results showed that convective heat transfer coefficient of nanofluid is enhanced up to 61% compared with that of the base fluid. Based on the experimental measurements, a new correlation is developed to predict convection heat transfer from nanofluids in spiral-coil tubes.     

Numerical simulation of natural convection heat transfer from a heated square cylinder in a square cavity filled with micropolar fluid

A numerical investigation has been performed to visualize the magnetohydrodynamic natural convective heat transfer from a heated square cylinder situated within a square enclosure subjected to nonuniform temperature distributions on the left wall. The flow inside the enclosure is unsteady, incompressible, and laminar and the working fluid is micropolar fluid with constant Prandtl number (Pr = 7). The governing equations of the flow problem are the conservation of mass, energy, and linear momentum, as well as the angular momentum equations. Governing equations formulated in dimensionless velocity and pressure form has been solved by Marker and Cell method with second-order accuracy finite difference scheme. Comprehensive verification of the utilized numerical method and mathematical model has shown a good agreement with numerical data of other authors. The results are discussed in terms of the distribution of streamlines and isotherms and surface-averaged Nusselt number, for combinations of Rayleigh number, Ra (10³–10⁶), Vortex viscosity parameter, K (0–5), and Ha parameter (0–50). It has been shown that an increase in the vortex viscosity parameter leads to attenuation of the convective flow and heat transfer inside the cavity.     

Numerical analysis of convective flow and thermal stratification in a cryogenic storage tank

In this study, the liquid–vapor mixture model was used for a numerical study of natural convective flow in a cryogenic tank with a capacity of 4.9?m³ under various conditions of heat flux and filling level to understand the early stages of convective flow phenomena and the consequent thermal stratification of cryogenic liquid. Two cryogens—liquefied natural gas (LNG) and liquefied nitrogen (LN₂)—were compared to observe their effects. LN₂ exhibited faster vaporization owing to its lower heat of vaporization. It was observed that higher heat flux and lower filling level led to faster vaporization and relatively vigorous heat transfer, showing early thermal stratification.     

Numerical analysis of heat transfer due to slot jets impingement onto two cylinders with different diameters

A numerical investigation has been performed two-dimensional slot impingement onto two heated cylinders with different diameters turbulent flow conditions. Height of slot jet is taken as constant for all cases. The study is performed to see the effects of effective parameters on heat and fluid flow as jet Reynolds number (11,000 ≤ Re ≤ 20,000), diameter ratio of cylinders (0.5 ≤ D₁/D₂ ≤ 1.5) and ratio of distance between cylinders to slot jet high (L/S). Streamlines, isotherms, local and mean Nusselt numbers and Cd coefficient were obtained. These results were compared with earlier experimental and numerical works and good agreement was obtained. It is found that diameter ratios of cylinders can be a control element for heat and fluid flow.