Heat transfer in a reaction–diffusion system with a moving heat source

A general formulation is presented for a moving boundary problem in which heat is generated at the boundary due to an exothermic reaction involving a species which diffuses into a dispersed phase from an external medium of finite volume. The speed of the moving boundary is prescribed based on the solution of the mass diffusion problem and an analysis is presented of the thermal dynamics of the system. The set of equations describing heat transport leads to a Green’s function type problem with time dependent boundary conditions and the Galerkin finite element method is employed to develop a numerical solution. Transformations are introduced to freeze the moving boundary and partition the domain for ease of computation, and an iterative scheme is defined to satisfy the heat flux jump boundary condition and match the temperature field across the moving boundary. The numerical results are used to set the limits of applicability of an analytical perturbation solution. Essential aspects of thermal dynamics in the system are described and parametric regions resulting in a local temperature hot spot are delineated. Computed contour plots describing thermal evolution are presented for different combinations of parameter values. These may be of utility in the prediction of thermal development, for control and avoidance of hot spot formation, and in physical parameter estimation.     

Hydromagnetic natural cooling of a triangular heat source in a triangular cavity with water–CuO nanofluid

This paper presents a numerical analysis of natural cooling of a right triangular heat source by a water–CuO nanofluid in a right triangular cavity that is under the influence of a horizontal magnetic field. A computational domain is defined and a numerical scheme based on the control volume formulation using the SIMPLE algorithm is developed. The convection–diffusion terms are discretised using a power-law scheme. The effects of the Rayleigh number, the solid volume fraction, the Hartmann number and the heat source position in the cavity on the heat transfer performance of the cavity are examined. The thermal performance of the cavity is enhanced as the Rayleigh number increases, the Hartmann number decreases and the distance of the heat source with the cold walls decreases. An optimum solid volume fraction is found that maximises the heat transfer at high Rayleigh numbers.     

CO2 payback–time assessment of a regional-scale heating and cooling system using a ground source heat–pump in a high energy–consumption area in Tokyo

We present an assessment of installing a regional heating and cooling system in the Nishi(West)-Shinjuku area of Tokyo, Japan. In this assessment, we estimate the CO₂ payback–time, when air source heat–pumps (ASHP) are replaced with a ground–source heat–pump (GSHP) system. We calculate CO₂ emissions from transportation of the cooling tower, materials for the underground heat exchanger, and the digging loads and transportation loads incurred when the GSHP system is installed to replace the air source cooling system. The total CO₂ emission from the installation of the GSHP system was estimated to be 67,701t-CO₂, with 87% of the CO₂ emissions resulting from the digging process. CO₂ emissions from the operation of the GSHP system were estimated from the total energy-efficiency of the system and the heating and cooling demand in Nishi-Shinjuku area. Using the GSHP system, 33,935t-CO₂ would be emitted per year. We estimate that using the GSHP system would result in a reduction of 54% of the CO₂ emissions, or 39,519t-CO₂ per year. From these results, the CO₂ payback–time for replacing the conventional ASHP in the 1 km² studied region with the GSHP system is assessed to be 1.7 years.     

Rayleigh–Bénard convection in a Boussinesq–Stokes ferromagnetic fluid under sinusoidal and non-sinusoidal internal heat modulation

Internal heat modulation has several applications in nuclear reactor design and safety, as well as meteorology. In this paper, the influence of internal heat modulation on Rayleigh–Bénard convection in a Boussinesq–Stokes ferromagnetic fluid is explored using linear and nonlinear analyses. The impact of the square, sine, triangular, and sawtooth wave type of internal heat modulation on the onset of convection and heat transport is considered. Using a Venezian method, linear stability analysis is performed to derive the correction Rayleigh number and the critical Rayleigh number for all four waveforms. A nonautonomous Lorenz model is derived and solved for the amplitude to obtain the Nusselt number, which quantifies the heat transport. The impact of the nondimensional parameter on the convective onset and heat transfer under heat source/sink modulation is analyzed. The study shows that all four types of internal heat modulation destabilize the system. It is also found that the presence of a heat source/sink modulation affects the impact of all four types of internal heat modulation on heat transport.     

Development and comparison of two-bed silica gel–water adsorption chillers driven by low-grade heat source

A novel silica gel–water adsorption chiller (driven by hot water of 60–90 °C) with three vacuum chambers has been built in Shanghai Jiao Tong University (SJTU). This chiller was an improvement of an earlier deigned chiller and it integrated two single-bed systems (basic system) with only one vacuum valve. The performance of the chiller was tested and compared with the former adsorption chiller. The results show that the cooling power and COP of the chiller are 8.70 kW and 0.39 for the heat source temperature of 82.5 °C, cooling water temperature of 30.4 °C and chilled water outlet temperature of 12 °C. For a higher chilled water outlet temperature of about 16 °C, the COP increases to 0.43 while the cooling power is about 11.0 kW. Compared with that of the former chiller, the COP of this chiller increases by 20%.     

Effect of rotation and internal heat generation on Darcy–Brinkman convection in Oldroyd-B liquid

Convection in an Oldroyd-B liquid saturated highly permeable porous medium is studied via both linear and nonlinear theories. Estimating a convection threshold is the objective of linear-stability analysis whereas convection amplitudes and heat transfer are elucidated by performing nonlinear-stability analysis. The eigenvalue problem is solved by the Galerkin method of weighted residuals. The oscillatory mode becomes dominant over the stationary mode. This is because of the race among diffusivity, viscoelasticity, internal-heat generation, and rotation. The increasing permeability, internal heat generation coefficient, and stress-relaxation parameter are liable to subcritical motions while the rotation, viscosities ratio, heat capacities ratio, and strain retardation parameter are responsible for the system attaining a supercritical state. The Runge–Kutta–Gill method presents the mechanism to evaluate the amount of heat transfer. The increasing Rayleigh number, internal Rayleigh number, Darcy number, Deborah number, Prandtl number, and the heat capacities ratio enhance the heat transfer. This offers a convenient mechanism for regulating convection. The results obtained in the present paper are expected to play a decisive role in some of the real-life applications such as oil-reservoir modeling, crude oil extraction, crystal growth, medicine industries, geothermal-energy utilization, and so on.     

A performance comparison between a horizontal source and a vertical source heat pump systems for a greenhouse heating in the mild climate Elaziğ, Turkey

The investigation presented in this article is aimed at demonstrating the technical and design feasibility of using ground-source heat pump systems in the mild climate applications for greenhouse heating, where heating requirements are dominant. An experimental comparison between a horizontal ground-source heat pump system and a vertical ground-source heat pump system was shown by focusing on the heating performance. For this purpose, an experimental set-up was constructed. The heating system mainly consists of two different ground heat exchangers, a heat pump, measuring units and a heating space of a model-sized glass greenhouse with 30 m² located in the greenhouse location.The heating coefficient of performances of the two ground-source heat pumps (COP_HP,H–V) and the overall system (COP_sys,H–V) were obtained to be in the range of 3.1–3.6 for HGSHP and 3.2–3.8 for VGSHP and 2.7–3.3 for HGSHP and 2.9–3.5 for VGSHP, respectively. Although significant savings are possible with these heating systems, a substantial investment in equipment and facilities may be required. The experimental results were obtained from November to April in heating seasons of 2007–2008. The results showed that the utilization of the ground-source heat pump is suitable for greenhouse heating in this district.     

Effect of heat source on Rayleigh–Bénard convection in rotating viscoelastic liquids

The influence of heat sources on instability in rotating viscoelastic liquids is studied. Linear stability analysis is done using normal modes. Computations are done for 10 boundary combinations and the results reveal that convection manifests via the oscillatory mode in this case. The critical values of the oscillatory and stationary instability have been studied. The results indicate individual stabilizing influences of rotation and strain retardation along with heat source in the case of free isothermal boundary conditions. It has quite unpredictable influences on the system stability in all the other boundary conditions for the chosen parameters. By suitable limiting processes, results pertaining to Oldroyd liquid B will lead to those of Maxwell, Newtonian, and Rivlin–Ericksen liquids. The problem finds applications in a working media consisting of viscoelastic liquids with nonisothermal systems.     

Entropy generation in a hollow cylinder with temperature dependent thermal conductivity and internal heat generation with convective–radiative surface cooling

This article investigates entropy generation in an asymmetrically cooled hollow cylinder with temperature dependent thermal conductivity and internal heat generation. The inside surface of the cylinder is cooled by convection on its inside surface while the outside surface experiences simultaneous convective–radiative cooling. The thermal conductivity of the cylinder as well as the internal heat generation within the cylinder are linear functions of temperature, introducing two nonlinearities in the one-dimensional steady state heat conduction equation. A third nonlinearity arises due to radiative heat loss from the outside surface of the cylinder. The nonlinear system is solved analytically using the differential transformation method (DTM) to obtain the temperature distribution which is then used to compute local and total entropy generation rates in the cylinder. The accuracy of DTM is verified by comparing its predictions with the analytical solution for the case of constant thermal conductivity and constant internal heat generation. The local and total entropy generations depend on six dimensionless parameters: heat generation parameter Q, thermal conductivity parameter β, conduction–convection parameters Nc₁ and Nc₂, conduction–radiation parameter Nr, convection sink temperature δ and radiation sink temperature η.     

Charge–discharge properties of surface-modified carbon by resin coating in Li-ion battery

The effect of an epoxy resin coating on the electrochemical performance of Li-ion batteries is investigated. Mesocarbon microbeads (MCMB), which constitute a promising carbon anode material for rechargeable Li-ion batteries is used as a starting carbon material. The surface coating of the MCMB is carried out by refluxing in a dilute H₂SO₄ solution and mixing in the epoxy resin-dissolved tetrahydrofuran (THF) solution. After heat treatment at 1000–1300 °C, the resin coating layer on the MCMB is converted to an amorphous phase which is identified by means of a high resolution transmission electron microscope (HRTEM) and a electron energy loss spectroscopy (EELS) analyses. The Brunauer–Emmett–Teller (BET) surface area of MCMB is increased by the formation of the amorphous epoxy resin coating layer. The electrochemical performance of the MCMB, such as the charge–discharge capacity and cycleability, is enhanced by the surface modification through epoxy resin coating. The reasons for the improvement of electrochemical performance are discussed in terms of the results from HRTEM observation, EELS analysis, and cyclicvoltammetry     

Three-dimensional thermal stresses Green’s functions for an unbounded parallelepiped under an inner point heat source

The aim of this study is to derive new constructive formulas and analytical expressions for Green’s functions (GFs) to 3D generalized boundary value problem (BVP) for an unbounded parallelepiped under a point heat source. These results were obtained using the developed harmonic integral representation method. On the base of derived constructive formulas it is possible to obtain analytical expressions for thermal stresses GFs to 16 BVPs for unbounded parallelepiped. An example of such kind is presented for a spatial BVP, GFs of which are presented in the form of the sum of elementary functions and double infinite series, containing products between exponential and trigonometric functions. An integration formula for thermal stresses, caused by the thermal data, distributed on the boundary strips at homogeneous locally mixed mechanical boundary conditions was also derived. The main di?culty to obtain these results was calculating an integral of the product between two GFs for Poisson’s equation. This integral taken on the base of the earlier established statement that main thermoelastic displacement Green’s functions (MTDGFs) satisfy the boundary conditions: (a) homogeneous mechanical conditions with respect to points of findings MTDGFs and (b) homogeneous thermal conditions with respect to points of the application of the heat source.     

Comparative study of sinusoidal and non-sinusoidal two-frequency internal heat modulation in a Rayleigh-Bénard system

A linear stability analysis is assented to investigate the effect of two-frequency internal heat modulation at the onset of convection in a Newtonian liquid. The correction Rayleigh number and wave number for small amplitudes is calculated using the Venezian approach. Under two-frequency internal heat modulation, the motion is found to be subcritical. To quantify heat transfer in the system, the three-mode Lorenz model is solved numerically. Various combinations of sinusoidal and non-sinusoidal waveforms influence the onset of convection and heat transfer in the system due to two-frequency internal heat modulation. The parameters' influence on heat transfer is seen to be dependent on the presence of a heat source or sink.     

Investigation of a multiple piezoelectric–magnetic fan system embedded in a heat sink

Previous studies have investigated the thermal performance of embedding a single piezoelectric fan in a heat sink. Based on this work, a multiple piezoelectric–magnetic fan system (“MPMF”) has been successfully developed that exhibits lower fan power consumption, optimum fan pitch and an optimum fan gap between the fan tips and the heat sink. In this study, the cooling performance and heat convection improvement for the MPMF system embedded in a heat sink are evaluated at different fan tip locations. The results indicate that the fan tip location of the MPMF system at x/S_l = 0.5 and y/S_h = 0 is an optimum configuration, improving the thermal resistance by 53.2% over natural convection condition for the fan input power of 0.1 W. The MPMF system breaks the thermal boundary layer and causes fluctuations inside the fins of the heat sink to enhance the overall heat transfer coefficient. Moreover, the relationship between the convection improvement and the Reynolds number for the MPMF system has been investigated and transformed into a correlation line for nine different fan tip locations to provide a means of predicting the cooling performance for the MPMF system embedded in a heat sink.     

Fabrication and characterization of a YSZ/YDC composite electrolyte by a sol–gel coating method

The compatibility of a composite electrolyte composed of a yttria stabilized zirconia (YSZ) film and a yttria-doped ceria (YDC) substrate in a solid oxide fuel cell (SOFC) that can be operated under 800 °C was evaluated. The YSZ film coated on a YDC substrate was derived from a polymeric YSZ sol using a sol–gel spin coating method followed by heat-treatment at 1400 °C for 2 h. The SEM and XRD analysis indicated that there were no cracks, pinholes, or byproducts. The composite electrolyte comprising a YSZ film of 2 μm thickness and a YDC substrate of 1.6 mm thickness was used in a single cell performance test. A 0.5 V higher value of open circuit voltage (OCV) was found for the composite electrolyte single cell compared with an uncoated YDC single cell between 700 and 1050 °C and confirmed that the YSZ film was an electron blocking layer. The maximum power density of the composite electrolyte single cell at 800 °C, 122 mW/cm² at 285 mA/cm², is comparable with that of a YSZ single cell with the same thickness at 1000 °C, namely 144 mW/cm² at 330 mA/cm². The hypothetical oxygen partial pressure at the interface between the YSZ film and the YDC substrate for the composite electrolyte with the same thickness ratio at 800 °C is 5.58×10⁻¹⁸ atm which is two orders of magnitude higher than the equilibrium oxygen partial pressure of Ce₂O₃/CeO₂, 2.5×10⁻²⁰ atm, at the same temperature.     

Radiative heat transfer in a participating medium with specular–diffuse surfaces

The results obtained by ray-tracing method can be regarded as benchmarks for its good accuracy. However, up to now, this method can be only used to solve radiative transfer within medium confined between two specular surfaces or two diffuse surfaces. This article proposes a hybrid ray-tracing method to solve the radiative transfer inside a plane-parallel absorbing–emitting–scattering medium with one specular surface and another diffuse surface (S–D surfaces). By the hybrid ray-tracing method, radiative transfer coefficients (RTCs) for S–D surfaces are deduced. Both surfaces of the medium under consideration are considered to be semitransparent or opaque. This paper examines the effects of scattering albedo, opaque surface emissivity and anisotropically scattering on steady-state heat flux and transient temperature fields. From the results it is found that the effects of anisotropic scattering is more for a bigger optical thickness medium; and keeping other optical parameters unchanged, anisotropic scattering affects transient temperature distributions so much in a small refractive index medium.     

Flow and heat transfer in a micro-cylindrical gas–liquid Couette flow

Analytic solutions for the gas and liquid velocity and temperature distribution are determined for steady state one-dimensional microchannel cylindrical Couette flow between a shaft and a concentric cylinder. The solution is based on the continuum model and takes into consideration the velocity slip and temperature jump in the gaseous phase defined by the Knudsen number range of 0.001 < Kn < 0.1. The two fluids are assumed immiscible. The gas layer is adjacent to the shaft which rotates with angular velocity ω_s and is thermally insulated. The outer cylinder rotates with angular velocity ω_o and is maintained at uniform temperature. The governing parameters are identified and the effects of the Knudsen number and accommodation coefficients on the velocity and temperature profiles, reduction in the overall temperature rise due to the gas layer, the Nusselt number and shear reduction are examined. It was found that the required torque to rotate the liquid in the annular space is significantly reduced by introducing a thin gas layer adjacent to the shaft. Also, reduction in shaft temperature is enhanced through a combination of high energy accommodation coefficient and low momentum accommodation coefficients. Results also indicate that the gas layer becomes more effective in reducing the shaft temperature when the housing angular velocity is much larger than the shaft angular velocity.     

Effects of heat absorption and thermal radiation on heat transfer in a fluid–particle flow past a surface in the presence of a gravity field

A continuum two-phase fluid–particle model accounting for fluid-phase heat generation or absorption and thermal radiation is developed and applied to the problem of heat transfer in a particulate suspension flow over a horizontal heated surface in the presence of a gravity field. Analytical solutions for the temperature distributions and the wall heat fluxes for both phases are obtained. Two cases of wall thermal conditions corresponding to stationary and periodic temperature distributions are considered. Numerical evaluations of the analytical solutions are performed and the results are reported graphically to elucidate special features of the solutions. The effects of heat absorption and thermal radiation are illustrated through representative results for the temperature distributions and heat fluxes of both phases for various fluid–particle suspensions. It is found that heat absorption increases the total heat transfer rate for various particulate volume fraction levels while thermal radiation decreases it.     

Determining parameters of heat exchangers for heat recovery in a Cu–Cl thermochemical hydrogen production cycle

A heat exchanger is a device built for efficient heat transfer from one medium to another. Shell and tube heat exchangers are separated wall heat exchangers and are commonly used in the nuclear and process industry. The CuCl cycle is used to thermally crack water in to H₂ and O₂. The present study presents the heat exchanger thermal design using analysis of variance for heat recovery from oxygen at 500 °C, coming from the molten salt reactor. Polynomial regressions in terms of the amount of chlorine in the oxygen, the mass flow rate on the tube side, and the shell's outlet temperature are estimated for various exchanger parameters and the results are compared with the bell Delaware method. Based on energy and exergy analysis, this study also discusses the best possible path for the recovered heat from oxygen. Optimal heat exchanger parameters are estimated by Design-Expert^® Stat-Ease for most effective heat recovery.     

Unsteady fluid mechanics and heat transfer study in a double-tube air–combustor heat exchanger with porous medium

Fluid mechanics and heat transfer are studied in a double-tube heat exchanger that uses the combustion gases from natural gas in a porous medium located in a cylindrical tube to warm up air that flows through a cylindrical annular space. The mathematical model is constructed based on the equations of continuity, linear momentum, energy and chemical species. Unsteady fluid mechanics and heat transfer by forced gas convection in the porous media, with combustion in the inner tube, coupled to the forced convection of air in the annular cylindrical space are predicted by use of finite volumes method. Numerical simulations are made for four values of the annular air flow Reynolds number in the range 100 ? Re ? 2000, keeping constant the excess air ψ = 4.88, the porosity ε = 0.4, and the air–fuel mixture inlet speed Uo = 0.43 m/s. The results obtained allow the characterization of the velocity and temperature distributions in the inner tube and in the annular space, and at the same time to describe the displacement of the moving combustion zone and the annular porous media heat exchanger thermal efficiency. It is concluded that the temperature increase is directly related to the outer Reynolds number.