Dimensionless Heat Transfer Coefficient Research Articles

Analysis of the heat transfer in subsurface porous media with considering Robin-type boundaries and arbitrary surface temperature variations

Heat occurs everywhere in the environment and has been used as a natural groundwater tracer in many hydrogeological studies. Several studies have developed various mathematical models to analyze the heat transfer in subsurface porous media. However, most of these models have two limitations: (1) the media have semi-infinite thicknesses, and (2) the surface temperature variations follow specific temporal patterns. As a result, the models are qualified for only some specific situations. To handle these geothermal problems effectively, it is essential to develop a general model. This study therefore develops a heat transfer model for simulating spatiotemporal distributions of the subsurface temperature (i.e., geotemperature) in a finite-thickness porous medium. This model comprises a heat conduction-advection equation that is subject to the condition of arbitrary surface temperature variations and a Robin-type condition for the bottom convective boundary. The solution of this model is obtained via the Laplace transform and Duhamel's principle and validated by a finite-difference solution. In a case study, we consider saturated sandy soils with the thermal properties of heat capacity cρ = 2.96×106 J/m3/ °C and thermal conductivity λ = 2.2 W/m/ °C for analyzing the geotemperature via the present solution. By way of the solution, the results show that the model can reduce to a pure-conduction model at the thermal Peclet number Pe≤10−4 and to a pure-advection model at Pe≥102. The Robin boundary condition can become the Dirichlet boundary condition at the dimensionless heat transfer coefficient Hf ≥ 103 and the Neumann boundary condition at Hf ≤ 10−2. The responses of the geotemperature to the changes in the thermal parameters are inspected in a sensitivity analysis. The present solution agrees better with the field data from the Sendai Plain in Japan than the existing solutions subject to the limitation of semi-infinite-thickness porous media on predicting geotemperature-depth profiles. As stated above, the developed solution can solve relatively comprehensive geothermal problems and greatly benefits the studies on the heat transport in subsurface porous media.

Heat transfer from a particle in laminar flows of a variable thermal conductivity fluid

We revisit the classical problem of steady-state heat transfer from a single particle in a uniform laminar flow with the assumption that the thermal conductivity of the fluid changes linearly with the temperature. We use a combination of asymptotic and scaling analyses to derive approximate expressions for the dimensionless heat transfer coefficient, i.e., the Nusselt number Nu, of arbitrarily shaped particles. The results cover the entire range of the Peclet number Pe. We find that, for a constant temperature boundary condition and fixed geometry, the Nusselt number is essentially equal to the product of two terms, one of which is only a function of Pe while the other one is nearly independent of Pe and mainly depends on the proportionality constant of the conductivity-temperature relation. We also show that, in contrast, when a uniform heat flux is imposed on the surface of the particle, Nu can be estimated as a summation of a Pe-dependent piece and one that solely varies with the proportionality constant.

Entropy generation in thermal radiative oscillatory MHD couette flow in the influence of heat source

Entropy generation and their minimization for magnetohydrodynamic oscillatory couette flow through a vertical channel, soaked with a porous medium in the existence of heat source and thermal radiation has been deliberated. In the present analysis, flow governing equations are elucidated and extricated with the help of analytical technique for the fluid velocity profile, temperature field, irreversibility distribution and Bejan number. Also, the numerical value of dimensionless shearing stress and heat transfer coefficient are obtained and presented through tables with reference to flow governing parameters. It has noticed that entropy generation can be regulated or minimized with the change in the applied magnetic field and thermal radiation, and this result is useful in several thermodynamic industries and engineering field for attaining the high performance of devices with minimum heat loss.

Thermo-Hydraulic Performance of Square Micro Pin Fins under Forced Convection

Thermal management of the new generation’s high performance electronic and mechanical devices is becoming important due to their miniaturization. Conventionally, the plate fin arrangement is widely used for removal of dissipated heat but, their effectiveness is not up to mark. Among different options, the most attractive and efficient alternative for overcoming this problem is micro pin fin heat sink. This paper presents the experimental investigation of square micro-pin fins heat sink for identifying the most suitable pin fin geometry for heat removal applications under forced convection. Twenty five square micro pin fin heat sinks were tested for three different heat load and Reynolds number. The results show that for large fin height lower thermal resistance was observed at the cost of large pressure drop. The dimensionless heat transfer coefficient increases with fin height and Reynolds number while it decreases with increasing fin spacing. The improvement in micro pin fin efficiency were observed by about 2 to 9% owing to presence of fins on the impingement surface, flow mixing, disruption of the boundary layers, and augmentation of turbulent transport.

Heat transfer enhancement of laminar impinging slot jets by nanofluids and metal foams

A study on impinging slot jets in a confined channel filled with metal foam, saturated with nanofluids, and lower wall partially heated is numerically accomplished. The partially heated wall is at an assigned temperature and buoyancy effects are taken into consideration. A two-dimensional domain is analyzed considering the local thermal non-equilibrium for the metal foam and the single-phase model is assumed to simulate the nanofluids at assigned Rayleigh number for several Peclet numbers. The governing equation solutions are accomplished using the Ansys-Fluent code and simulations are carried out for aluminum foams with nanofluids, Al2O3/water based, as working fluids. Several porosity values, from 0.90 to about 0.97, for different pore density, pore per inches (PPI), from 5, to 40 PPI, are used. The volumetric concentrations change from 0% to 5% with a particle diameter of 30 nm. The distance between the slot jet outlet section and the lower heated surface is five times the slot jet width. The presented results point out that the dimensionless convective heat transfer coefficients increase with increase in values of Peclet number, and decrease with the volumetric concentration. It is noted that the surface heat transfer coefficient shows different behavior varying porosity for assigned Peclet and Rayleigh numbers. Some correlations for the average total Nusselt number in terms of porosity and volumetric concentration are proposed in quadratic forms for assigned pore density and Peclet number.

Investigation of non‐Newtonian blood flow with power‐law model: Effects of coronary congenital heart defect on a specific age type

Nowadays, humans are suffering from chronic cardiovascular diseases, including Congenital Heart Defect (CHD). These diseases have far-reaching consequences, such as disruption of the daily life of humans by reducing their ability to perform daily routines. This problem is due to impaired cardiac pumping capability. The present numerical simulation studied the effects of CHDs on pressure drop and AWSS. Numerical calculation of non-Newtonian blood flow parameters, including power-law indices and the Reynolds number, were also investigated. To construct a 3D model of CHDs, an OSS program using DICOM and MRI was used. Besides, the vessel wall was assumed as solid. The non-Newtonian blood flow was assumed as a laminar flow with the slip boundary conditions at the vessel wall. AWSS, pressure drop, and dimensionless heat transfer coefficient are directly correlated with power-law indices, Reynolds number, and constant heat flux boundary conditions of the body. CHDs increased velocity, pressure drop, and AWSS in all steps of the simulation process.

Assessment of heat transfer performance from modified horizontal rectangular heat sink under forced convection dominating mode of mixed convection

In the current research, an experimental assessment of heat transfer performance from rectangular fins in the horizontal arrangement has been presented. The specific types of mixed convention i.e. natural (NCDMMC) as well as forced convection dominating mode (FCDMMC) are considered. The parameters encompassed for experimentation are spacing between the fins (S = 2 to 14 mm), flow of air (ReH = 1190 to 2610), input to heater (Q = 25 to 100 W), ratio of width to height of the fin (W/H = 3.0) and, ratio of length to height of the fin (L/H = 5.0) for an array of fins. The outcomes received from the present experimental work are satisfactory and authenticates the FCDMMC. It is observed that alterations in the spacing of the fin, flow velocity considerably influenced the rate of heat transfer from fins. In the case of modified fins under NCDMMC optimum values of average convective coefficient of heat transfer (ha), base convective coefficient of heat transfer (hb) are achieved at wider fin spacing (S) of 10 mm. Whereas optimum magnitudes of ha, hb obtained at compact fin spacing of 6 mm are 30.2, 288.7 W/m2-0C respectively in the case of FCDMMC. The augmentation of about 78.8% in the magnitude of ha is achieved on the compensation of little energy input (0.8 to 1.5 W) to fan as compared to ha in NCDMMC under equivalent conditions. Ineffective areas of fins have been identified with the help of flow virtualization and temperature mapping technique. The central portion of each fin is provided with perforations in the triangular format giving an improvement in the average Nusselt number (Nua) by about 41.2% with respect to the plain fins. The statistical generalized correlations for dimensionless heat transfer coefficient, air flow governing and key geometrical parameters have been developed and presented.

Analysis of thermocline thermal energy storage systems with generic initial condition algebraic model

Thermal energy storage is key in making solar-thermal power plants more economically competitive compared to conventional plants. In this work, a new algebraic solution for thermocline thermal energy storage tanks, allowing for any initial temperature profile, is developed and presented. The model, called the Algebraic IC model, is successfully validated by comparing with experimental data and numerical solution of the governing partial differential equations. Additionally, the algebraic solution is extended to incorporate heat losses from the thermocline tank walls to the environment. The algebraic solution is significantly less computationally expensive than other one-dimensional models, since algebraic, rather than differential, equations are solved. An explicit formula for optimal fluid velocity is developed and validated through a parametric study of a thermocline tank. The effect of the dimensionless heat transfer coefficient is also investigated. Finally, the operation of thermocline tanks under multiple consecutive charging and discharging cycles is studied. The tank efficiency depends on the amount of thermocline allowed to exit during each cycle, and was found to decrease initially and subsequently reach steady state in less than 10 cycles.

Experimental investigation of the performance of a falling-film drain water heat recovery system

Drain water heat recovery (DWHR) devices are utilized to reduce the energy consumption of domestic water heating by recovering waste heat from warm greywater. In this study, the thermal performance of a gravity film DWHR device type is experimentally investigated under steady operating conditions. The thermal performance is measured at different flow rates and wet surface conditions using the effectiveness – number of transfer units and the logarithmic mean temperature difference models. A thermal resistance model is developed to determine the convection heat transfer coefficient of the falling film at the fully wet surface condition. The thermal resistance model showed that the largest thermal resistance in the device is the falling film convection resistance. A new correlation is developed for the falling film dimensionless convection heat transfer coefficient in the Reynolds number range of 1000–5000. The obtained correlation has good agreement with the experimental values with a correlation coefficient of 85%. In addition, it is found that at partially wet surface condition; which is expected in actual device operation, there is a considerable reduction in the device effectiveness that could reach 28.5% of its value at the fully wet condition.

Convective heat transfer and laminar flow characteristics of flow over a circular cylinder in presence of control plates

The location and orientation effect of control plates (CP) in and around the flow separation region of a circular cylinder has been numerically investigated in the laminar flow regime at Reynolds number 100. The vortex shedding and convective heat transfer characteristics have been analysed for both upstream and downstream locations of the control plates using Ansys Fluent 18.0. The drag and lift coefficient (CD, CL), the dimensionless vortex shedding frequency (Sr) and dimensionless convective heat transfer coefficient (Nu) are reported for various CP orientation and locations. The CP positioned along the main flow direction and located near the cylinder induce more shear on the cylinder surface, stabilities the wake vortices. In addition to shear generation, the CP orientation interacts effectively with the cylinder wake. The vortex shedding suppression with reduced drag on the cylinder is identified at many locations of CP. Convective heat transfer from the cylinder is suppressed at most of the locations of CP, at very few locations the cylinder heat transfer enhanced.

Effect of Nanofluid Thermophysical Properties on the Performance Prediction of Single-Phase Natural Circulation Loops

Specifying nanofluids’ thermophysical properties correctly is crucial for correct interpretation of a system’s thermo-hydraulic performance and faster market-uptake of nanofluids. Although, experimental and theoretical studies have been conducted on nanofluids’ thermophysical properties; their order-of-magnitude change is still a matter of debate. This numerical study aims to reveal the sensitivity of single phase natural circulation loops (SPNCL), which are the passive systems widely used in solar thermal and nuclear applications, to thermophysical property inputs by evaluating the effects of measured and predicted nanofluid thermophysical properties on the SPNCL characteristics and performance for the first time. Performance and characteristics of an SPNCL working with water-based-Al2O3 nanofluid (1–3 vol.%) for heating applications is evaluated for different pipe diameters (3–6 mm). The thermal conductivity effect on SPNCL characteristics is found to be limited. However, viscosity affects the SPNCL characteristics significantly for the investigated cases. In this study, Grm ranges are 1.93 × 107–9.45 × 108 for measured thermophysical properties and 1.93 × 107–9.45 × 108 for predicted thermophysical properties. Thermo-hydraulic performance is evaluated by dimensionless heat transfer coefficients which is predicted within an error band of ±7% for both the predicted and measured thermophysical properties of the data. A Nu correlation is introduced for the investigated SPNCL model, which is useful for implementing the SPNCL into a thermal system.

Numerical investigation of the gas–solid heat transfer characteristics of packed multi-size particles

Real industrial particles generally have a wide size distribution. Therefore, the gas–solid heat transfer characteristics of packed multi-size particles should be studied. A mathematical model of gas–solid heat transfer for packed multi-size particles is established. This model includes gas–solid convection heat transfer and intraparticle and interparticle conduction. The cooling processes of packed binary- and quintuple-size particles ranging from 10 mm to 60 mm under different conditions are investigated. The EDEM software is used to obtain the porosities of different cases. Results show that the presence of small particles in the packed multi-size particles reduces porosity and increases specific surface area, thereby benefiting the gas–particle heat transfer process. The temperature of large particles is always higher than that of small particles during particle cooling. Particle–particle conduction helps in the cooling process of large particles, and the maximum heat flux ratio of interparticle conduction to gas–solid convection for large particles reaches 0.196. The volumetric heat transfer coefficient of the packed multi-size particles varies with time. The initial heat transfer coefficient is the average value weighted by mass fractions, and the limit of the final value is that of the large particle under the actual porosity. The proposed dimensionless volumetric heat transfer coefficient can be a general description of gas–solid heat transfer characteristic of various packed multi-size particles. Its time variation can be well described by an exponential correlation, and the variation rate is related to the variance of particle size in each case.

Visualization study on direct contact condensation characteristics of sonic steam jet in subcooled water flow in a restricted channel

Steam jet in subcooled water is a typical mode of direct contact condensation (DCC) where condensation occurs on the interface between steam and water. A visualization study of sonic steam jet condensation in subcooled water flow in a restricted channel has been performed for a convergent nozzle over a wide range of operating conditions. The DCC characteristics, including steam plume shapes, penetration length and average heat transfer coefficient, were discussed in detail. Method of digital image processing using MATLAB software was employed to evaluate steam plume shapes, penetration length, interface area and contours of gas volume fraction. Using a high-speed camera, five different steam plume shapes were typically observed, i.e. hemispherical, conical, contraction–expansion-contraction, ellipsoidal and divergent shapes, which are described in a three-dimensional map of plume shapes depending on steam mass flux, subcooled water temperature and Reynolds number of water flow. The measured data of dimensionless penetration length and average heat transfer coefficient are found to be in the range of 0.8–4.5 and 1.6–5.5 MW/(m2·K), respectively. By means of fitting 140 groups of measured data, the empirical correlations for dimensionless penetration length and average heat transfer coefficient as a function of dimensionless steam mass flux, condensation driving potential and Reynolds number of water flow were proposed. Both of the measured data and predictions show a good agreement with each other, which are suggested to predict the condensation characteristics of sonic steam jet in water flow in a restricted channel.

Non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium

Purpose This study aims to numerically analyze natural convection of alumina-water nanofluid in a differentially-heated square cavity partially filled with a heat-generating porous medium. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been considered for the description of the nanoparticles transport effect in the present study. Local thermal non-equilibrium approach for the porous layer with the Brinkman-extended Darcy model has been used. Design/methodology/approach Dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method. The effects of the Rayleigh number, Ostrogradsky number, Nield number and nanoparticles volume fraction on nanofluid flow, heat and mass transfer have been analyzed. Findings It has been revealed that the dimensionless heat transfer coefficient at the fluid/solid matrix interface can be a very good control parameter for the convective flow and heat transfer intensity. The present results are original and new for the study of non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium. Originality/value The results of this paper are new and original with many practical applications of nanofluids in the modern industry.

Experimental Observation of Natural Convection Heat Transfer Performance of a Rectangular Thermosyphon

This study experimentally investigates the natural convection heat transfer performance of a rectangular thermosyphon with an aspect ratio of 3.5. The experimental model is divided into a loop body, a heating section, a cooling section, and two adiabatic sections. The heating section and the cooling section are located in the vertical legs of the rectangular loop. The length of the vertical heating section and the length of the upper and lower horizontal insulation sections are 700 mm and 200 mm, respectively, and the inner diameter of the loop is 11 mm. The relevant parameters and their ranges are as follows: the input thermal power is 30–60 W (with a heat flux in the range of 60–3800 W/m2); the temperature in the cooling section is 30, 40, or 50 °C; and the potential difference between the hot and cold sections is 5, 11, or 18 for the cooling section lengths of 60, 45, and 30 cm, respectively. The results indicate that the value of the dimensionless heat transfer coefficient, the Nusselt number, is generally between 5 and 10. The heating power is the main factor affecting the natural convection intensity of the thermosyphon.

Experimental study on the condensation of sonic steam in the underwater environment

Abstract Steam jet condensation is of great importance to pressure suppression containment and automatic depressurization system in nuclear power plant. In this paper, the condensation processes of sonic steam jet in a quiescent subcooled pool are recorded and analyzed, more precise understanding are got in direct contact condensation. Experiments are conducted at atmospheric pressure, and the steam is injected into the subcooled water pool through a vertical nozzle with the inner diameter of 10 mm, water temperature in the range of 25–60 °C and mass velocity in the range of 320–1080 kg/m2s. Richardson number is calculated based on the conservation of momentum for single water jet and its values are in the range of 0.16–2.67. There is no thermal stratification observed in the water pool. Four condensation regimes are observed, including condensation oscillation, contraction, expansion-contraction and double expansion-contraction shapes. A condensation regime map is present based on steam mass velocity and water temperature. The dimensionless steam plume length increase with the increase of steam mass velocity and water temperature, and its values are in the range of 1.4–9.0. Condensation heat transfer coefficient decreases with the increase of steam mass velocity and water temperature, and its values are in the range of 1.44–3.65 MW/m2°C. New more accurate semi-empirical correlations for prediction of the dimensionless steam plume length and condensation heat transfer coefficient are proposed respectively. The discrepancy of predicted plume length is within ± 10% for present experimental results and ± 25% for previous researchers. The discrepancy of predicted condensation heat transfer coefficient is with ± 12%.

Numerical investigation on heat transfer and flow characteristics in helically coiled mini-tubes equipped with dimples

Heat transfer and flow in dimpled helically coiled mini-tubes are numerically examined. The effects of Reynolds number Re, ratio of tube diameter to coil diameter t, dimple density d and dimple size s are examined. It is shown the dimple case provides a higher Nusselt number Nu upon the smooth case. The highest and lowest dimensionless heat transfer coefficients Nu/Nu0 are 2.281 and 1.788, respectively. The Nu/Nu0 firstly rises and then declines against the increase in Re, producing a peak value. Greater Nu/Nu0 is achieved when a lower t is used. A decrease in d or s results in a higher Nu/Nu0 with Re lower than particular-Re, while an opposite trend occurs with Re higher than particular-Re. The highest and lowest evaluation parameter (Nu/Nu0)/(f/f0)1/3 are 1.830 and 1.437, respectively. A better performance from energy saving viewpoint is achieved with a lower t. Besides, great reduction in wall temperature level is achieved due to dimples. With the increase in Re, the flow pattern develops accompanied with more obvious separation and reattachment behavior. Utilization of dimples produces significant promotion in velocity level close to the boundary layer, which is principally responsible for heat transfer enhancement. The boundary velocity coefficient shows great similarity to Nu/Nu0. Tangential velocity is greatly promoted when dimples are fixed, which is believed to generate intensified secondary flow. The thickness of the low velocity layer and the high temperature region in the fluid domain are greatly reduced due to dimples. Furthermore, a lower temperature gradient level and a more uniform fluid temperature field are achieved owing to dimples. The dimple case brings about great reduction on average heat transfer entropy generation level, with enhanced effect at a lower t. An evident decrease in maximum wall temperature is identified when dimples are used. Correlations for predicting Nusselt number and friction factor are obtained.

Acoustic Streaming under Thermal Boundary Conditions of the Third Kind

A numerical study of acoustic streaming in a cylindrical cavity subjected to vibrational action with a small vibration amplitude is performed. The dependence of the streaming character on the intensity of heat exchange with the surrounding medium is studied. A change in the forms of the acoustic streaming vortices is shown for a smooth transition from adiabatic to isothermal boundary conditions, which occurs via variation in the heat transfer coefficient. The values of the dimensionless heat transfer coefficient are determined for which the acoustic streaming pattern is close to the limiting cases corresponding to adiabatic and isothermal boundary conditions. For limiting cases of thermal boundary conditions, comparison with an analytical solution is performed.

Experimental study of direct contact condensation of steam jet in water flow in a vertical pipe with square cross section

Direct contact condensation phenomenon (DCC) is widely used in applications which heat and mass transfer efficiently. In this study, several experiments are conducted to investigate the DCC of steam injected in water flow in a vertical square cross-section pipe. The characteristics of condensation, including steam plume shape and length, average heat transfer coefficient, and average Nusselt number, are studied. The dimensionless steam plume length and average heat transfer coefficient are found in the range of 0.5–5.1 and 0.716–3.131 MW/m2 K, respectively. Additionally, the influence of effective operating parameters, namely steam mass flux, water temperature, and water flow Reynolds number, on each condensation characteristic is investigated. Using a high-speed camera, three main regimes of steam plume (chugging, oscillatory, and stable jet) are observed. The distribution of these regimes versus flow effective parameters is presented in a three-dimensional condensation regime map. Finally, empirical correlations for a stable steam plume, which show a good agreement with measurements, are suggested to predict each characteristic of DCC of steam jet in water flow.

The experimental facility for investigation of MHD heat transfer in perspective coolants in nuclear energetics.

Paper presents the current results of work conducted by a joint research group of MPEI–JIHT RAS for experimental study of liquid metals heat transfer. The team of specialists of MPEI–JIHT RAS put into operation a new mercury MHD facility RK-3. The main components of this stand are: a unique electromagnet, created by specialists of the Budker Institute of Nuclear Physics (BINP), and a sealed liquid-metal circuit. The facility will be explored lifting and standpipe flow of liquid metal in a transverse magnetic field in channels of different forms. For the experiments on the study of heat transfer and hydrodynamics of flows for measuring characteristics such as temperature, speed, pulse characteristics, probe method is used. Presents the first experimental results obtained for a pipe in a transverse magnetic field. During the experiments with various flow parameters data was obtained and processed with constructing temperature fields, dimensionless wall temperature distributions and heat transfer coefficients along the perimeter of the work area. Modes with low frequency pulsations of temperature were discovered. The boundaries where low frequency temperature fluctuations occur were defined in a circular tube.