Convection-conduction Heat Transfer Research Articles

Investigation of convective-conductive heat transfer in geothermal system

Abstract Geothermal energy is one of the well-known types of renewable energies that can be considered as a promising alternative to fossil fuels in order to mitigate the CO2 emission in atmosphere. Geothermal energy has recently been used for heating and cooling systems in many countries of the world. Therefore, studying such kind of energy seems important and necessary. This paper studies the heat transfer processes in a borehole heat exchanger (BHE). The flow of fluid in a BHE has been considered with different geometries and heat transfer processes are modeled numerically and in a finite volume method through convection and conductivity. First, a single U-shaped BHE was modeled and its thermal properties were investigated and then other geometries were studied to obtain the best geometry and heat transfer efficiency. In order to increase the heat transfer in the inner part of the pipes, the fin with the given specifications was used and the modeling was carried out and the thermal parameters were compared for three BHE’s with different geometries. In the final part, optimization results are presented, and the interaction of parameters on the Nusselt number and friction coefficient have been investigated. Also, the desirability of optimization and reliability is given to the results presented in percentage terms. Comparing the results of this article with the results of previous research shows a very good agreement and therefore the applied method is reliable and accurate.

Stability of static conjugate heat transfer coupling approaches using Robin interface conditions

The combined solution of fluid convective and solid conductive heat transfer, known as conjugate heat transfer, is becoming increasingly important for engineering design applications, because it allows for more accurate and reliable predictions compared to single-domain simulations. However, predicting conjugate heat transfer requires a coupled simulation approach, where interactions between both domains are accounted for. A prevalent method uses a partitioned thermal fluid-solid coupling approach; this method, however, invokes stability complications. Recent research has focused on establishing efficient algorithms for predicting conjugate heat transfer, while in previous studies [1, 2] the authors revealed that the stability of partitioned coupling methods depends mainly on the Biot number of the problem. This work extends the stability prediction to the more general Robin–Robin interface conditions. For the fluid domain, Robin conditions are an uncommon, however, promising boundary condition, which essentially leads to three new coupling methods. Applying a perturbation method for the stability analysis, this work derives a new stability criterion for the considered interface conditions, again, solely depending on the Biot number of the problem. The obtained stability criterion is the most general criterion applicable to static partitioned coupling approach and includes the previously found results. As proof of concept, the validity of the derived criterion is demonstrated with numerical experiments on a flat plate test case.

On the Wave Heat Transfer at Times Comparable with the Relaxation Time upon Intensive Convective-Conductive Heating

The behavior of temperature fields in the vicinity of the boundary of a body at nanosecond durations comparable with relaxation time has been studied on the basis of an analytic solution to the problem of a hyperbolic equation for heat conductivity under the obtained conditions for convective-conductive heat transfer. The presence of first-order damped discontinuities in a temperature profile at a finite rate of the propagation of heat perturbations and convexity of the temperature profile in the vicinity of body boundary have been shown. The method of reduction of restoring relaxation time by experimental values of temperature field has been proposed.

Numerical Investigation of the Thermal Regime of Underground Channel Heat Pipelines Under Flooding Conditions with the Use of a Conductive-Convective Heat Transfer Model

This paper presents the results of numerical analysis of thermal regimes and heat losses of underground channel heating systems under flooding conditions with the use of a convective-conductive heat transfer model with the example of the configuration of the heat pipeline widely used in the Russian Federation — a nonpassage ferroconcrete channel (crawlway) and pipelines insulated with mineral wool and a protective covering layer. It has been shown that convective motion of water in the channel cavity of the heat pipeline under flooding conditions has no marked effect on the intensification of heat losses. It has been established that for the case under consideration, heat losses of the heat pipeline under flooding conditions increase from 0.75 to 52.39% due to the sharp increase in the effective thermal characteristics of the covering layer and the heat insulator caused by their moistening.

Effect of Prandtl number on the average exit temperature of coolant in a heat‐generating vertical parallel plate channel: A conjugate analysis

AbstractA coupled conduction–convection heat transfer analysis is carried out for a two‐dimensional rectangular, vertical parallel plate channel producing volumetric energy (uniform and nonuniform), subjected to laminar forced‐convection incompressible fluid flow under steady‐state conditions. The equations governing the thermal and flow field are solved by using finite difference method, and the resulting algebraic equations are solved by using the tridiagonal matrix algorithm method. Four coolants with their Prandtl numbers (Pr), namely, liquid sodium (Pr = 0.005), sodium‐potassium (Pr = 0.00753), lead (Pr = 0.02252), and helium (Pr = 0.666) are used for the present conjugate analysis. Effects of different thermal and fluid flow parameters such as Reynolds number (ReH) ranging from 500 to 1500, conduction–convection parameter (Ncc), and total heat generation (Qt) on average exit temperature (θae) of coolants are studied. From the obtained results, it is found that the θae of coolant strongly depends on Pr, ReH, Ncc, and Qt when the aspect ratio (Ar) is kept constant. It is also found that with a nonuniform rate of heat generation, the coolant θae is high compared to uniform heat generation rate, whereas with increasing Ncc, the θae decreases, and with increasing Qt, the θae increases irrespective of coolants.

Conductive-convective heat transfer in an inclined enclosure with vertical partition

Conductive-convective heat transfer in an inclined enclosure with vertical partition

Numerical simulations for analyzing deformation characteristics of hydrate-bearing sediments during depressurization

Natural gas hydrates have been treated as a potential energy resource for decades. Understanding geomechanical properties of hydrate-bearing porous media is an essential to protect the safety of individuals and devices during hydrate production. In this work, a numerical simulator named GrapeFloater is developed to study the deformation behavior of hydrate-bearing porous media during depressurization, and the numerical simulator couples multiple processes such as conductive-convective heat transfer, two-phase fluid flow, intrinsic kinetics of hydrate dissociation, and deformation of solid skeleton. Then, a depressurization experiment is carried out to validate the numerical simulator. A parameter sensitivity analysis is performed to discuss the deformation behavior of hydrate-bearing porous media as well as its effect on production responses. Conclusions are drawn as follows: the numerical simulator named GrapeFloater predicts the experimental results well; the modulus of hydrate-bearing porous media has an obvious effect on production responses; final deformation increases with decreasing outlet pressure; both the depressurization and the modulus decrease during hydrate dissociation contribute to the deformation of hydrate-bearing porous media. Cited as : Liu, L., Lu, X., Zhang, X., et al. Numerical simulations for analyzing deformation characteristics of hydrate-bearing sediments during depressurization. Advances in Geo-Energy Research, 2017, 1(3): 135-147, doi: 10.26804/ager.2017.03.01

Thermal performance of scrap tire blocks as roof insulator

This work shows a feasible re-use of scrap tires as thermal insulator for residential building roofs. The main focus of this study was to test the use of natural color and white-painted scrap tire blocks (STBs) as insulating material in a residential building prototype (RBP) and to compare their performance with a common insulating material (polystyrene). The STBs were prepared with a simple method using isoBond adhesive and tire particles from different suppliers. The thermal conductivity and water absorption of the materials were recorded. Moreover, several statistical parameters such as range, time lag and decrement factor were analyzed. The results showed that the STBs had higher thermal conductivity than polystyrene however, the ability to maintain the interior temperatures was nearly similar. This fact was explained by the combined convection-conduction heat transfer mechanism inside STBs. The water absorption of the STBs was relatively low in comparison with other organic insulating materials, such as palm fibers. The STBs performed better as insulating material when the outer-facing side was painted white, leading to an increase in the decrement factor (f) and the rate of heat loss as well as a decrease in the rate of heat gain. Finally, STB’s are a practical option as insulating material for residential buildings in warm climates.

Analytical model for convection-conduction heat transfer during water injection in fractured geothermal reservoirs with variable rock matrix block size

The purpose of management in geothermal reservoirs is to economically enhance the energy recovery. This paper describes a model to analyze the process of cold water injection into a fully penetrating well with a number of n equally spaced horizontal fractures in a fractured geothermal reservoir. Previous models basically focused on the numerical and semi-analytical methods or a combination of two. Here, an analytical model is presented in which the effects of thermal convection and conduction are investigated. This solution has the ability to account the following phenomena: convection transport in fractures and conduction from the matrix block to the fracture. Specified assumptions are made which allow the model to be formulated as two coupled one-dimensional partial differential equations, one for the fracture and one for the matrix block in the direction perpendicular to the fracture. The convection-conduction heat transfer between fracture and matrix is not affected by the matrix block size distribution in dual porosity models. In the present study, a heat transfer model is introduced for a radial system with matrix block size distribution to assess the heat transfer shape factor known as a matrix-fracture exchange coefficient. The results delineated that heat transfer is strongly dependable on matrix block size distribution during the early time region. To calculate the total amount of heat extracted from a geothermal reservoir, two methods were defined and also a conceptual definition for the thermal recovery efficiency was presented. Finally, the proposed model was validated by comparing the results of the analytical solution with a pre-defined numerical method in the literature.

Analyzing wellbore stability in chemically-active anisotropic formations under thermal, hydraulic, mechanical and chemical loadings

Several factors influence the stress state in subsurface rocks. In addition to pore pressure and far-field in-situ stresses, thermal and chemical gradients have substantial bearings on the in-situ stress state during and after drilling operations. Drilling inclined boreholes through laminated formations such as shaley sands presents several challenges. Due to their laminated nature, shales demonstrate high degree of elastic anisotropy, and are often chemically-reactive to drilling fluid. The majority of models utilized in the industry assume a homogeneous isotropic elastic static model that fails to give an accurate depiction of the observed borehole failure. In this work, governing equations for anisotropic porochemothermoelasticity are developed to simulate the drilling of an inclined borehole problem in a transversely isotropic rock. Using the developed constitutive and transport equations, a finite element method based numerical model is constructed to estimate the pore pressure, temperature, solute concentration and stress distribution. Nonlinear conductive-convective heat transfer and diffusive-advective solute transfer models are considered in this work to address both high and low permeability formations. Finally, the model is used to assess time-dependent wellbore stability during and after drilling. The novel pseudo-3D analysis developed in this work is advantageous for real-time operations due to its computational speed and stability.

Prospective of employing high porosity open-cell metal foams in passive cryogenic radiators for space applications

Passive cryogenic radiators work on the principle of dissipating heat to the outer space purely by radiation. High porosity open-cell metal foams are a relatively new class of extended surfaces. These possess the advantages of high surface area density and low weight, characteristics which the space industry looks for. In case of radiative heat transfer, the porous nature of metal foams permits a deeper penetration of the incident radiation. Consequently, the heat transfer area participating in radiative heat exchange increases thereby enhancing the heat transfer rate. However, effective heat conduction in between the foam struts reduces as a result of the void spaces. These two conflicting phenomenon for radiation heat transfer in metal foams have been studied in this work. Similar to the foam conduction-convection heat transfer analysis, a conduction-radiation heat transfer model has been developed for metal foams in analogy with the conventional solid fin theory. Metal foams have been theoretically represented as simple cubic structures. A comparison of the radiative heat transfer through metal foams and solid fins attached to a surface having constant temperature has been presented. Effect of changes in foam characteristic properties such as porosity and pore density have also been studied.

Soil Apparent Thermal Diffusivity Estimated by Conduction and by Conduction–Convection Heat Transfer Models

Abstract Soil heat transfer is complex, and conduction-alone models may not always perform well in estimating soil apparent thermal diffusivity. Soil apparent thermal diffusivity is related to soil temperature change propagation rates. Soil temperature data collected at the Tazhong station in China were used to examine the characteristics of soil apparent thermal diffusivity determined by three different algorithms and the sum of vertical gradient of soil apparent thermal diffusivity and apparent water flux density . The results showed that 1) soil apparent thermal diffusivity obtained with a conduction–convection algorithm had a better agreement with soil apparent thermal diffusivity obtained with a phase algorithm than with soil apparent thermal diffusivity obtained with an amplitude algorithm except for the case of = 0; 2) when > 0, , and when < 0, ; 3) for a given soil temperature phase shift, increased (decreased) with increasing logarithmic amplitude attenuation when the phase shift was larger (smaller) than the logarithmic amplitude attenuation, reached a maximum value when the phase shift equaled the logarithmic amplitude attenuation, and increased with increasing logarithmic amplitude attenuation; and 4) for a given logarithmic amplitude attenuation, decreased with increasing phase shift and increased (decreased) with increasing phase shift when the phase shift was larger (smaller) than times the logarithmic amplitude attenuation. These mathematical conclusions were also confirmed with field data.

Effect of geometrical and temperature-dependence parameters on forced convection of a nanofluid in a micro-channel heat sink

Purpose The purpose of this study is the numerical prediction of the thermal and hydraulic characteristics (Nusselt number and shear stress) of a forced convection laminar flow through a rectangular micro-channel heat sink, using constant and temperature-dependent thermo-physical properties. The effects of the solids volume fraction and the size of the micro-channel on heat transfer enhancement have also been investigated. Design/methodology/approach The authors use the flow of a water-Al2O3 nanofluid and a single-phase approach. The equations are solved using the commercial code Fluent Version 6.3. This code uses the finite volume approach to solve the equations subject to the boundary conditions, which govern three-dimensional conjugate convection-conduction heat transfer model. The physical domain was meshed using the code GAMBIT. The mesh used is non-uniform and was obtained by sweeping in the Z direction an X-Y surface meshed with QUAD/pave type cells. Findings The results clearly show that the inclusion of nanoparticles produces a considerable increase in the heat transfer. Also, the temperature-dependent models present higher values of local and average Nusselt number than in the case of constant thermo-physical properties, and an increase in the channel dimensions leads to an important increase in heat transfer. Consequently, we ensure a better cooling of the base of the micro-channel heat sink. Research limitations/implications Because of the settling of nanoparticles, the research results may not be generalized to high values of solids volume fraction. Therefore, researchers are encouraged to find other techniques of cooling when the heat loads exceed values that cannot be dissipated using nanonofluids. Practical implications The paper includes implications for the miniaturization of electronic devices such as in microprocessors or those used in robotics and automotive industries, where continually increasing power densities are requiring more innovative techniques of heat dissipation from a small area and small coolant requirements. Originality/value This paper shows the implementation of variable property nanofluid models in CFD commercial codes.

Modeling of a Bayonet Reactor for Sulfurinc Acid Decomposition in Thermo-Electrochemical Hydrogen Production Processes

Hydrogen is the most abundant element on Earth. However, being a very reactive element, it does not occur in significant quantities in a pure state. Most hydrogen is combined with other elements and is found in water, fossil fuels, biomass and similar compounds. A hydrogen economy requires primary energy sources to provide the energy to release the hydrogen from these compounds. Water-splitting processes are particularly attractive, since water is abundant around the planet, the unique products from water splitting are hydrogen and oxygen and a variety of primary energy sources can be used to produce the hydrogen. External power (e.g. nuclear power, solar power, etc.) can be used to produce hydrogen by conventional water electrolysis [1], which first requires the production of electricity. A more efficient and potentially more cost effective approach is to use external heat to power a thermochemical water splitting process, which breaks the hydrogen-oxygen bounds through a series of heat-driven chemical reactions, with recirculation of intermediate substances of different type. By this approach the external heat which drives the chemical reactions is converted into chemical energy of the hydrogen produced from water splitting. Among the various thermochemical water splitting processes, the Hybrid Sulfur (HyS) is one of the most appealing cycles. It has only fluid reactants and is comprised of only two global reaction steps: a low temperature electrochemical exothermic section, operating at temperatures on the order of 100 °C, and a high temperature thermal section operating at temperatures of about 800 °C.In the electrochemical section SO2 and H2O combine together to produce electrochemically H2 at the electrolyzer cathode and H2SO4 at the electrolyzer anode. Sulfuric acid is recycled inside the plant and decomposed, in the high temperature thermal section, into SO2, O2 and H2O. The endothermic decomposition of sulfuric acid takes place in two main reactions: H2SO4 --> SO3 + H2O (1) SO3 --> SO2 + 0.5 O2 (2)The required thermal power is provided by external source and by internal heat recovery from the SO2-O2 product of the decomposition reaction. An efficient heat transfer system to operate Reactions 1 and 2 is based on the bayonet reactor concept. This system allows: (1) efficient internal heat recovery from the decomposition products and (2) low temperature connections with the interfaced HyS equipment (e.g. tubing, valves etc). The concept has been demonstrated only as electrically heated lab scale component and most of the modeling analysis has been carried out adopting lumped parameter models [2,3,4]. In order to achieve a conceptual design of the component for larger scale hydrogen production the assessment of the reaction yield and the gradients of temperature and concentration inside the component is of primary importance. A detailed transport model has been developed at University of South Carolina, in conjunction with the Savannah River National Laboratory, within the DOE-EERE Solar Thermochemical Hydrogen (STCH) program. The model is comprised of mass, energy and momentum balance equations, as well as SO3 reaction decomposition kinetics. The model not only evaluates the performance of the internal recovery heat transfer process, but also analyzes the heat exchange with external fluid. A baseline configuration has been established with helium as the baseline heat transfer fluid, leveraging experience from nuclear applications [3,4]. The sulfuric acid mixture flows at 14 bar, while helium flows outside the reactor tubing at 40 bar. The Figure shows temperature profile for the Reaction (2). A 2D radial section of a single tube (length = 2 m) is shown in the Figure, with SO3 mixture flowing in the internal tube and helium flowing in the external annular region. Results demonstrate the effective heat transfer between helium and the reacting mixture, reaching final temperatures on the order of 750 °C. Suitable heat transfer coefficient correlations have also been established based on the results obtained, accounting for convective heat transfer processes (both helium and reacting mixture side) and conductive heat transfer (internal tube walls).

Cooling Li-ion batteries of racing solar car by using multiple phase change materials

A numerical study of the unsteady phase change convection-conduction heat transfer of an ion-lithium battery with volumetric heat generation used in solar vehicles is presented. The cooling process is investigated for a total of seven arrays of phase change material (PCM): capric acid (PCM 1), eicosane (PCM 2), decahydrated sodium carbonate (PCM 3) and octadecane (PCM 4) located in one or three layers around the battery. The results show that heat conduction predominates in the battery with a PCM and the liquid phase fraction of the PCM indicates that the melting initiates after 7min, reaching totally liquid state after 14.25min. From the different configurations of PCM around the battery, the configuration “B” (multiple PCM: PCM 1 (5mm)+PCM 3 (2.9mm)+PCM 2 (4.3mm)) and the configuration with a single layer of PCM 3 (14.3mm) respectively reduce the maximum temperature of the battery about 20.9 and 23.2K compared with the temperature reached by the battery without PCM. This result occurs because of the Decahydrated Sodium Carbonate PCM, since it has the highest latent heat and has a low melting point.

A single domain formulation on conjugate heat transfer in parallel plate microchannel with electrical double layer

In this study, the conjugate conduction-convection heat transfer in the thermally developing region of a parallel plate microchannel with the constant heat flux at the walls is investigated. The flow is forced to move by applying the pressure difference and is assumed to be fully developed. Moreover, the effects of electrical double layer (EDL) with low zeta potential on the fluid flow and on the temperature field are taken into account. To do so, an analytical/numerical method is proposed to solve the energy equation in a single domain formulation. The energy equation is split and a series solution based on the variational calculus is employed to determine the temperature field. The effects of various parameters such as Peclet number, non-dimensional wall thickness, thermal conductivity ratio, and the zeta potential are studied in details. The obtained results show that the increasing of zeta potential decreases the heat transfer rate. Moreover, the Nusselt number has a non-monotonic behavior when the wall thickness varies.

Nonlocal unique solvability of a steady-state problem of complex heat transfer

A boundary value problem of radiative–conductive–convective heat transfer in a threedimensional domain is proved to be uniquely solvable. An iterative algorithm is proposed for finding its solution.

A new heat balance equation for sap flow calculation during continuous linear heating in tree sapwood

This article introduces a new “linear heat balance (LHB) method” that is based on exact (physically correct) equation analytically derived from fundamental conduction–convection heat transfer equation. Therefore, the aim of this paper is to derive and analyze a new heat balance equation for sap flow calculation from measured temperature differences around continuously heated needle. The formula is derived from the steady-state conduction and convection heat transfer equation with linear source of heat power. This paper deals with the theoretical (analytical and numerical) and experimental analysis of heat and water transfer in the conductive xylem (sapwood) of trees. The analysis and verification of the new formula is based on numerical simulation (using finite element method) and the new LHB method is demonstrated on experimentally measured data. This new approach is important not only because of more exact sap flow calculation but also for information about thermal conductivity that can be used for water content estimation.

Unified approach for conjugate heat-transfer analysis of high speed air flow through a water-cooled nozzle

ABSTRACTThis article presents a unified approach to solve steady-state conjugate heat-transfer problem including simultaneously gas, liquid and solid regions in just one 3D domain, distinguished by their particular properties. This approach reduces approximation errors and the time to solve the problem, which characterise iterative methods based on separated domains. The formulation employs RANS equations, realisablek-ε turbulence model and near-wall treatment model. A commercial CFD code solves the pressure-based segregated algorithm combined with spatial discretisation of second order upwind. The problem consists of a convergent-divergent metallic nozzle that contains cooling channels divided in two segments along the wall. The nozzle wall insulates the high-speed hot air flow, dealt as perfect gas, from the two low-speed cold water flows, dealt as compressed liquid, both influenced by transport properties dependent of the local temperature. The verification process uses three meshes with increasing resolutions to demonstrate the independence of the results. The validation process compares the simulation results with experimental data obtained in high-enthalpy wind tunnel, demonstrating good compliance between them. Results for the bulk temperature rise of the water in the second cooling segment of the nozzle showed good agreement with available experimental data. Numerical simulations also provided wall temperature and heat flux for the gas and liquid sides. Besides, distribution of temperature, pressure, density and Mach number were plotted along the nozzle centerline showing a little disturbance downstream the throat. This phenomenon has been better visualised by means of 2D maps of those variables. The analysis of results indicates that the unified approach herein presented can make easier the task of simulating the conjugate convection-conduction heat-transfer in a class of problems related to regeneratively cooled thrust chambers.

Conjugate natural convection in a cavity with a conductive partition and filled with different nanofluids on different sides of the partition

In this study, conjugate natural convection–conduction heat transfer in an inclined partitioned cavity filled with different nanofluids (Al2O3–water and CuO–water) on different sides of the partition is numerically investigated by using finite element method. The left and right vertical walls of the square enclosure are maintained at constant hot and cold temperatures while other wall enclosures are assumed adiabatic. Different combinations of solid nanoparticle volume fractions are imposed in the left and right half cavities. Numerical simulations are performed for different values of Grashof numbers (between 103 and 106), inclination angles of the cavity (between 0o and 275o), partition locations (between 0.15 and 0.75), thermal conductivity ratio (between 0.01 and 10) and solid volume fraction of the nanofluids of the two cavities (between 0 and 0.04). The averaged heat transfer enhances with Grashof number and solid particle volume fraction. It is also observed that adding nanoparticles with low thermal conductivity on the right cavity is effective for the heat transfer enhancement as compared to adding nanoparticles with high thermal conductivity. As the thermal conductivity ratio of the partition increases, the averaged heat transfer rate enhances and the highest value of the thermal conductivity ratio of 10, 14.11% of averaged heat transfer enhancement is obtained when both cavities are filled with nanofluids at the highest value of nanoparticle volume fractions.