Mathematical Model Of Heat Transfer Research Articles

A Third-Order Two-Stage Numerical Scheme for Fractional Stokes Problems: A Comparative Computational Study

Abstract A third-order numerical scheme is proposed for solving fractional partial differential equations (PDEs). The first explicit stage can converge fast, and the second implicit stage is responsible for enlarging the stability region. The fourth-order compact scheme is employed to discretize spatial derivative terms. The stability of the scheme is given for the standard fractional parabolic equation, whereas convergence of the proposed scheme is given for the system of fractional parabolic equations. Mathematical models for heat and mass transfer of Stokes first and second problems using Dufour and Soret effects are given in a set of linear and nonlinear PDEs. Later on, these governing equations are converted into dimensionless PDEs. It is shown that the proposed scheme effectively solves the fractional forms of dimensionless models numerically, and a comparison is also conducted with existing schemes. If readers want it, a computational code for the discrete model system suggested in this paper may be made accessible to them for their convenience.

Mathematical model for heat transfer during laser material processing

The article presents development of a new heat transfer model for calculating temperature distribution in porous and non-porous materials during laser cutting. The novelty of this model lies in incorporating melting and vaporization progression of porous media during laser interaction. The modelling has been implemented through a transient finite difference scheme and the results have been validated against experimental data of cutting various materials by laser including rock and metals.

Numerical Simulation Study of Gas-Solid Heat Transfer and Decomposition Processes of Limestone Calcined with Blast Furnace Gas in a Parallel Flow Regenerative Lime Kiln.

Quicklime is an essential reducing agent in the steel smelting process and its calcination from limestone is accompanied by considerable energy consumption. As a relatively economical lime kiln, the Parallel Flow Regenerative (PFR) lime kiln is used as the main equipment for the production of quicklime by various steel industries. PFR lime kilns generally use natural gas as the fuel gas. Although natural gas has a high calorific value and is effective in calcination, with the increasing price of natural gas and the pressure saves energy and protect the environment, it makes sense of exploring the use of cleaner energy sources or other sub-products as fuel gas. The use of blast furnace gas (BFG) as a low calorific value fuel gas produced in the steel smelting process has been of interest. This paper therefore develops a set of mathematical models for gas-solid heat transfer and limestone decomposition based on a Porous Medium Model (PMM) and a Shrinking Core Model (SCM) to numerically simulate a PFR lime kiln using BFG in order to investigate the feasibility of calcining limestone with low calorific fuel gas and to provide a valuable reference for future development of such processes and the kiln structure improvement.

Mathematical modeling of MHD flow and radiative heat transfer past a moving porous rotating disk with Hall effect

PurposeThe present study aims to investigate the effect of radiation on the unsteady magnetohydrodynamic (MHD) flow of a viscous, electrically conducting Newtonian fluid over rotating disk moving upward/downward immersed in a porous medium, considering the Hall effect. The study is motivated by the various applications in the context of solar power technology, electric power generation, Hall accelerators, MHDs generators and other industrial areas when the fluid flow is subjected to the previously mentioned effects such as MHD, Hall effect and thermal radiation.Design/methodology/approachSuitable similarity transformations are employed to reduce the governing nonlinear partial differential equations into the nonlinear ordinary ones. The solutions of the reduced system are numerically obtained using the boundary value problem (BVP) Midrich scheme in Maple. The results are presented graphically for vertical disk movement, magnetic parameter, Hall current, Darcy parameter, thermal radiation and Schmidt number. Skin frictions, mass and heat transfer rates are numerically tabulated.FindingsIt is revealed that the vertical motion of the disk significantly boosts the radial and annular flows. Moreover, the Hall parameter has contrasting effects on velocity profiles for the range of magnetic field but temperature field is oblivious of this behavior. It is observed that heat and mass transfer considerably enhance along vertical disk movement. Also magnetic field, temperature ratio and radiation parameter significantly enhance the temperature field, while reaction rate parameter and Schmidt number decrease the concentration profile. The current model is calibrated in its reduced form to an already published literature with good correlation to ensure the numerical scheme's validity.Originality/valueThis work is original within the best efforts of the authors.

Thermal analysis characterisation of solar-powered ship using Oldroyd hybrid nanofluids in parabolic trough solar collector: An optimal thermal application

Abstract The mathematical modeling of hybrid nanofluid flow and heat transfer with entropy generation toward parabolic trough surface collector (PTSC) inside the solar-powered ship (SPS) is performed. The mathematical model used non-Newtonian Oldroyd-B model amidst a constant inclined magnetic field influence is being considered. The mathematical model is then reduced by adopting appropriate similarity transformation into a higher-order nonlinear differential equations system. The reduced model is computed using the well-known technique called the Keller Box scheme. Physical parameters effectiveness, for instance, thermal radiation, viscous dissipation, hybrid nanoparticles, and Joule heating, is displayed in graphs. The silver-ethylene glycol (Ag-EG) characteristic performance outperformed the silver-magnetite-ethylene glycol (Ag-Fe3O4/EG). The maximum efficiency of Ag-EG is about 26.3%, while the minimum is at least 5.6%.

Optimisation of wasted air utilisation in thermal loss reduction in double-glazed windows of commercial buildings in cold regions

Ventilating of multi pane-glazed windows using wasted air of buildings is an effective technique to minimize heat loss through windows and save heating energy in cold regions. In low-scaled occupancy buildings with high WWR ratio, buildings supply a low flow rate of wasted air to windows ventilation systems, resulting in a declination in its thermal performance. Therefore, this study introduces methods of managing the utilisation of wasted air in windows ventilation to optimise the energy saving. Two methods have been implemented experimentally on a small-scaled room. The first method is a time-based division of air pump operation, an air pump ventilates multiple windows, one window at a time repetitively. The second method shares the available wasted air to multiple windows. The experimental results and mathematical heat transfer model have been employed to evaluate thermal performance of the system in different methods. The first method showed a best energy saving with a duty cycle of 50% for the air pump, and on/off operation every 10 s. An energy saving of 42.6% has been realized compared to the traditional double-glazed windows, and the heat transfer coefficient was declined from 3.82 to 2.8 W/m2 K. The second method showed an optimum thermal performance when the available flow rate of wasted air was shared with three double-glazed windows. An energy saving of 83.1% was achieved compared to the traditional double-glazed windows, and the heat transfer coefficient dropped from 3.82 to 2.36 W/m2 K.

Mathematical model of convective heat transfer for peristaltic flow of Rabinowitsch fluid in a wavy rectangular duct with entropy generation

This research article unfolds a novel mathematical model that interprets the ‘peristaltic flow of Heated Rabinowitsch fluid’ inside a wavy rectangular duct. The fluid flow characteristics are thoroughly examined for Pseudo-plastic in addition to Dilatant nature, (i.e. α > 0 for pseudo-plastic nature and α < 0 for dilatant nature respectively). Peristaltic flow inside a wavy rectangular duct is widely being studied due to immense number of biomedical and engineering applications. We have derived the dimensionless nonlinear partial differential equations in coupled form after applying certain relevant dimensionless quantities, the lubrication technique of low Reynolds number and long wavelength estimations (i.e., ). The dimensionless energy equation is solved by dividing it into two additional equations and after employing suitable procedures, an exact temperature profile solution is computed. The present study has been developed by using hit and trial method to solve the single partial differential equation having two dependent variables in form of extra stress tensors. The solution of temperature profile provides a detailed solution method to exactly solve such complex partial differential equations. For both dilatant and Pseudo-plastic fluids, effective physical parameters are used to depict velocity distribution, pressure gradient and pressure rise, convection and entropy phenomena. When compared with Pseudo-plastic fluid, the Dilatant nature of fluid has a high convection rate. Finally, the phenomenon of entrapment is examined through streamlines that provide a flow visualization inside the wavy sinusoidal duct. Peristaltic pumps are being used for transportation of many fluids like toxic chemicals in nuclear industry, food processing, heart-lung machines, roller and finger pumps and transportation of slurries etc. These usage of these pumps leads to an upgraded mechanical efficiency and lower cost for transportation purposes.

On some classes of stationary inverse problems of determining the heat transfer coefficient for mathematical models of heat and mass transfer

In the article we consider well-posedness in Sobolev spaces of stationary inverse problems of recovering the heat transfer coefficient at the interface which is included in the transmission condition of the imperfect contact type. The existence and uniqueness theorem are exhibited. The method is constructive and the approach allows to develop numerical methods for solving the problem. The proof relies on a priori estimates obtained and the fixed-point theorem.

Numerical Simulation and Economic Evaluation of Wellbore Self-Circulation for Heat Extraction Using Cluster Horizontal Wells

The heat extraction capacity of the self-circulation wellbore is usually small because of the limited heat exchange area. In the paper, the cluster horizontal well group technology was proposed to enhance the heat extraction capacity and decrease the unit cost. Based on the mathematical model of heat transfer, a numerical simulation model of wellbore self-circulation for heat extraction using cluster horizontal wells was established to study the influence of main factors on heat extraction capacity. The economic analysis of heat extraction and power generation was carried out according to the model of the levelized cost of energy. The results show that the enhancement of heat extraction capacity is limited after the injection rate exceeds 432 m3/d (1.59 MW/well). The inflection point of the injection rate can be determined as the design basis for injection-production parameters. When the thermal conductivity of formation increases from 2 to 3.5 W/(m·K), the heat extraction rate will increase 1.45 times, indicating that the sandstone reservoirs with good thermal conductivity can be preferred as the heat extraction site. It is recommended that the well spacing of cluster wells is larger than 50 m to avoid the phenomenon of thermal short circuit between wells, and the thermal conductivity of the tubing should be less than 0.035 W/(m·K) to reduce the heat loss of heat-carrying fluid in the tubing. Compared with a single well, a cluster horizontal well group can reduce the unit cost of heat extraction and power generation by 24.3% and 25.5%, respectively. The economy can also be improved by optimizing heat-carrying fluids and retrofitting existing wells.

Mathematical Model and Numerical Simulation of Coalbed Methane Migration Considering the Adsorption Expansion Effect

The influence of gas adsorption and desorption on the volumetric strain of coal was measured by a self-designed, fluid–solid coupling triaxial coal adsorption deformation experimental system. The experimental results show that coal deformation has a threshold value with an increase in gas content. Before the gas content reaches the threshold value, coal deformation is not obvious. When the gas content reaches the threshold value, the deformation will increase sharply. At the same time, coal volume strain changes with coal gas content in accordance with exponential law ε = ε0(eϒc-1). Based on the experimental results, considering the coupling effects of heat transfer, water seepage, coal and rock mass deformation, and coalbed methane desorption and seepage, a mathematical model of heat transfer–deformation–seepage coupling coalbed methane migration was established, and a numerical simulation study was carried out on the heat injection-enhanced coalbed methane mining project. The results show that (1) With continuous heat injection, the gas in the coal seam is rapidly desorbed, and the adsorbed gas content forms an elliptical funnel that extends from the extraction hole to the deep part of the coal body and takes the fracturing crack as the center to the upper and lower boundaries of the coal seam. At day 30, the adsorbed gas content in the whole drainage area has decreased to 0.1 m3/t within 2m from the fracture zone. (2) On the basis of considering the gas adsorption expansion effect, the strain of the coal body decreases from roof to floor. With the increase in the heat injection time, the strain value will also increase, and the strain increase will decrease. When the heat injection is 30 days, the maximum strain at the roof is 0.015. The research results have important guiding significance for predicting coal rock deformation and determining gas extraction efficiency in the process of heat injection-enhanced coalbed methane extraction.

Optimization of multilayer clothing assemblies for thermal comfort in cold climate

This paper presents a theoretical study on the optimization of key material parameters of multilayer clothing assemblies for thermal comfort in cold climate. A mathematical model of heat and moisture transfer through a multilayer clothing assembly is established. The existence and uniqueness of the solution of the model are verified by using the fixed point theorem. The model predicts the optimum thicknesses and porosities of the two internal layers of the clothing assembly, with which the thermal comfort index will fall within the required intervals with the greatest probability. This study is significant for the optimum design of multilayer clothing assembly for thermal comfort.

The blood heat exchanger in intra-arterial selective cooling infusion for acute ischemic stroke: A computational fluid-thermodynamics performance, experimental assessment and evaluation on the brain temperature

Intra-arterial selective cooling infusion with the autologous blood (IA-SCAI) is a promising therapeutic hypothermia induction method for conferring neuroprotection to acute ischemic stroke (AIS) patients. The blood heat exchanger (BHE) plays a crucial role in IA-SCAI's cooling capacity. However, there are no BHEs currently available that are specifically designed for the IA-SCAI, which requires a low blood flow to be compatible with cerebral hemodynamics. In an effort to develop a BHE for AIS patients, a prototype of a commercial BHE, Medtronic MYOtherm XP®, was mathematically modeled; specifically, computational fluid dynamics (CFD) was used to analyze its hemo- and thermo-dynamic characteristics under low blood flow including temperature distribution, velocity field and shear stress.Our numerical model predicted the hemolysis index to be 0.0041%–0.0581% inside the BHE with blood flows rates of 10 ml min−1–50 ml min−1. The in vitro heat transfer experiment showed that the BHE efficiently cooled the simulated blood from the initial 37 °C–5.8 °C within 150 s by using cold water (200 ml·min-1, 0 °C). The cooled simulated blood was able to cool the simulated blood in the middle cerebral artery of an artificial circulating system from 37 °C to 16.8 °C–33.7 °C depending on the blood perfusion rate (10–50 ml/min). A biological heat transfer mathematical model showed that brain tissue could be cooled by 2 °C within the initial 1min of infusion. This study verified the feasibility of using a commercial BHE for IA-SCAI and provided insights into its cooling capacity for therapeutic hypothermia.

Mathematical model of the process of forming the working flow of a thermodynamic abrasive jet tool for surface treatment

A mathematical model of heat transfer during steam cleaning of surfaces with an abrasive jet tool is developed, taking into account its design features and heat flow power. Keywords: thermo-steam-jet tool, vaporization, heat transfer, transformation ratio, water consumption. kravchenko-in71@yandex.ru

The effect of internal leakage of air streams on effectiveness of the fixed-bed regenerator for fast switching cycle of its operation: mathematical model and numerical simulations

The paper describes an original mathematical model of heat and mass transfer for a fixed bed regenerator used to determine the effect of internal airflow leakage on heat exchanger efficiency. First, the build and operating principles of a fixed-bed heat exchanger were discussed. The presence of internal leakage was shown along with a proposed solution for its elimination. Then, a mathematical model based on a modified ε-NTU method for numerical simulation and analysis of coupled heat and mass transfer in a fixed-bed heat exchanger was presented. The model was supplemented with an additional detailed submodel designed to determine frost surface temperature and frost growth analysis. Initial numerical simulations of the operation of the model were performed for low outdoor air temperature conditions. Different zones of heat and mass transfer within the regenerator matrix were distinguished. The presence of accumulated frost area and its influence on the course of heat and mass transfer processes was revealed. In addition, the presence of a relative humidity limit curve associated with a mass balance deficiency conditioning the occurrence of frost accumulation was established.

Mathematical and Computer Modeling of Convective Heat Transfer in Fuel Cartridges of Fuel Elements with Different Shapes and Packing of Rods

The paper consists of three sections and is of an informational and generalizing nature, indicating promising areas for further research. The first section "R-functions method in mathematical modeling of convective heat transfer in fuel cartridges with fuel elements" is devoted to the use of new constructive tools of the R-functions method for mathematical and computer modeling of fuel elements packings with different types of symmetry, as well as the study of convective heat transfer in fuel elements grids and the effect of the type of packing on the distribution of velocity and temperature. An octahedral cartridge with 37 fuel elements packed according to three patterns (cyclic, checkerboard and in-line) is considered. It is noted that when constructing the equations of a cartridge with bundles of fuel elements using the new method, the number of R-operations and, accordingly, the calculation time are significantly reduced. An analysis of the obtained results allows to conclude that the maximum temperature is obtained with cyclic packing. The scheme of the reactor, the cartridges of which are hexagonal casings, with 91 fuel elements placed in each of them both with checkerboard and cyclic packing, is also considered. In the second section "Thermal-hydraulic calculation of fuel elements cartridges in case of violation of the rods packing symmetry", a hexagonal fuel cartridge with 169 fuel elements and checkerboard packing is considered. An increase in temperature is analyzed in case of violation of the packing symmetry while maintaining the parallelism of the rods, as well as in case of a curvature of one of them. The third section "R-functions, fuel element with polyzonal finning of the shell and heat transfer during fluid motion" is focused on the construction of equations for various finning surfaces of fuel elements and the study of hydrodynamic and temperature fields in case of polyzonal finning of the shell. At the same time, using the apparatus of tensor analysis, a transition to a curvilinear non-orthogonal (helical) coordinate system was made. It is noted that mathematical modeling and the associated computer experiment are indispensable in cases where a full-scale experiment is impossible or difficult to conduct for one reason or another. In addition, working with mathematical model of the process and the computational experiment make it possible to investigate the properties and behavior of the process in various situations relatively quickly and without significant expenses. The reliability of the methods, results and conclusions is confirmed by comparison with the information given in the references, the results of the analysis of the numerical convergence of solutions and the calculation of the residual.

MATHEMATICAL MODELING OF THE FOREST FIRE IMPACT ON THE BRANCH OF A CONIFEROUS TREE

It is necessary to develop quantitative methods to assess the formation of thermal burns in the morphological parts of coniferous trees. The purpose of the study is mathematical modeling of heat transfer in the layered structure of a coniferous tree branch under the influence of a forest fire front. The heat propagation in the «branch — needles — flame zone» system is described by a system of non-stationary differential equations of heat conduction with the corresponding initial and boundary conditions. As an object of research, a digital model of a branch of a coniferous tree for various species, namely, pine, larch and fir, was used. Temperature distributions are obtained for different variants of the branch structure and conditions of the impact of the forest fire front. Conclusions are made about the need for further modernization of the mathematical model. The developed model is the basis for creating software tools for specialized geographic information systems.

Gradient power modified ohmic heating curing to prepare hybrid carbon fibers/high performance concrete under deep-freeze low temperature

The on-site fabrication of high-performance concrete (HPC) under ultra-low temperature environment is challenging the research community. This work presents a gradient power modified ohmic heating (OH) curing to stimulate the strength formation of conductive carbon fiber/carbon nanofiber reinforced high performance concrete (HCF-HPC) at ultra-low temperature. Specifically, the gradient power loading strategy with three-step power (3SP) OH curing method was experimentally and numerically designed. Heat transfer mathematical model based on the principle to suppress thermal expansion has been established to regulate the curing temperature of each curing step from around 30℃ to 70℃ for the samples subjected to OH curing with increasing curing steps. The results showed that the compressive strength of the 3SP OH cured HCF-HPC samples reaches up to 103.3 MPa, which is comparable with that of the sample cured by high-temperature steam curing (107.5 MPa). Moreover, multiscale analyses have been conducted to verify the positive effect of 3SP OH curing on pore structure, hydration products and hydration degree of HCF-HPC samples.

Dynamic coupling of a heat transfer model and whole building simulation for a novel cadmium telluride-based vacuum photovoltaic glazing

In recent years, building-integrated photovoltaic (BIPV) windows have drawn attention from both the building industry and academic society. As a multifunctional application of photovoltaic technologies, semi-transparent BIPV panels can generate renewable energy in situ and play the role of typical windows. Unlike those PV windows made by crystalline silicon solar cells, the semi-transparent cadmium telluride (CdTe) photovoltaic (STPV) windows can admit natural daylight with a certain degree of transmittance without any shading. Therefore, it can provide better visual comfort to occupants. However, typical BIPV windows are not suitable for cold regions due to inadequate thermal insulation. To improve the thermal performance of the BIPV glazing, a novel CdTe-based vacuum PV glazing (VPV) is developed with a highly integrated three-layer structure. To fully understand the dynamic heat transfer process and thermal behaviour, this study developed a mathematical heat transfer model for the CdTe-based VPV. The dynamic heat transfer model was validated with laboratory tests. To investigate the whole year performance of the VPV, a dynamic coupling approach is proposed to integrate the transit heat transfer model with a whole building simulation model conducted by EnergyPlus to obtain more accurate simulation results. Comparing the simulation results of the decoupled and coupled methods, it was found that EnergyPlus tends to slightly underestimate the cooling energy consumption and overestimate the heating energy consumption to a considerable level. Therefore, the dynamic coupling approach is more reliable than the EnergyPlus model, especially in the heating-dominated regions.

Solar chimney power plant combined with membrane distillation (SCPPMD), Part II: techno-economic characteristics

In this paper, the techno-economic characteristics of the solar chimney power plant combined with membrane distillation (SCPPMD) under typical operating conditions are further evaluated, based on the mathematical model of heat and mass transfer and performance analysis established in Part I and the economic evaluation model based on cash flow calculations. The sensitivity of some economic parameters and the effect of operating parameters and air gap spacing on system economy are discussed. The results show that the net present value is always positive during the service period. The total net income and total net present value are 16.79 and 2.72 million yuan respectively. The system economy is sensitive to inflation rate, loan interest rate, water price and electricity price, but not to operation and maintenance costs and personal income tax rates. The decrease of inlet seawater temperature and the increase of seawater thickness both lead to an increase in total water yield and a decrease in power generation. The increase in water yield compensates for the economic loss caused by the reduction in power generation, so the system profitability is improved. The reduction of air gap spacing causes a significant increase in total water yield and power generation. But too small an air gap has high requirements for membrane components in large-size system, inconvenient for construction, operation and maintenance.

Interrupted plate porous media design for ionic liquid-type liquid piston hydrogen compressor and analysis of the effect on compression efficiency

Hydrogen is regarded as an important energy source in the future. A hydrogen compressor is the key equipment in hydrogen-fueled vehicles. The high compression speed leads to the low efficiency for its adiabatic conditions, and the heat transfer condition of the compressor is an important solution. In this study, the porous media installed in the compression cylinder with ionic liquid is proposed to improve the heat transfer conditions and compression efficiency. A mathematical model of heat transfer and fluid resistance in the compression process was constructed. Multiple computational fluid dynamics simulations were applied to summarize the relationship among the Nusselt number, fluid flow resistance, and Reynolds number. Meanwhile, the main influencing factors affecting the convective heat transfer strength of porous media were obtained by analyzing the flow field conditions of fluid basin units in porous media inserts. Then, the relevant mechanism of enhanced heat transfer was proposed. Results show that: all different fluids conform to the quadratic relationship despite the order of magnitude differences in flow resistance. In addition, the Nusselt number is related to the Reynolds number as a power exponential function, and the value of Nusselt number increases as Reynolds number increases. The main heat dissipation surface of porous media is the side of the interrupted plate. Furthermore, the thinner the velocity boundary layer near the wall, the stronger the heat transfer capacity. For a specific compressor at 120 rpm, the porous media designed in this study can reduce the temperature at the end of compression by 14.33 K, saving 11.76% of the unnecessary energy consumption caused by heat dissipation problems.