Solution Of Heat Flow Research Articles

Numerical Study on the Optimal Thermally Affected Region of a Buried Oil Pipeline.

Crude oil pipeline transportation is usually a closed process under a certain depth of burial, and the condition of oil in the pipeline changes with the continuous decline of temperature during the transportation process. The safety and energy consumption of pipeline transportation are closely related to the accurate prediction of oil temperature. It is a popular technique to use the thermally affected region to overcome the problem of an unclosed calculation domain caused by the semi-infinite soil around the pipeline. However, there is no clear and unified guidance on the thermally affected region at present, and improper region size may lead to a loss of the accuracy of the pipeline system. Therefore, our study answers two questions about the optimal form of the thermally affected region and its economic scope of application. The coupled solution of heat transfer and flow in a tridimensional numerical model is carried out, and the thermodynamic influences of the geometric shape and range of the thermally affected region on the buried pipeline system are investigated. The results show that the rectangular region is more suitable for the modeling of buried oil pipelines, and a region with 16 m width and 9 m height is recommended for the conventional case.

Effect of fracture geometry, topology and connectivity on energy recovery from enhanced geothermal systems

A combination of hydraulic fracturing and horizontal wells is now being used to tap geothermal energy from naturally fractured reservoirs. Fully grid-based numerical models are currently used to simulate heat recovery from enhanced geothermal systems (EGS). Such models require a fine unstructured mesh and are computationally expensive. In this paper we present a computationally efficient model that allows us to accurately simulate fracture propagation, fluid flow, and heat transfer in networks of natural fractures that may be created in naturally fractured geothermal reservoirs.The integrated simulator is developed by combining the displacement discontinuity method (DDM) for fracture propagation in naturally fractured reservoirs with a general Green's function solution for fluid and heat flow from the matrix to the fracture. This eliminates the need to discretize the matrix domain resulting in a very computationally efficient solution. A discrete fracture network (DFN) approach is used to represent the pre-existing natural fractures.The model is first validated against an analytical solution for fluid flow and heat transfer in a rock matrix with a single fracture. The computation time with and without discretizing the rock matrix shows a 100-fold reduction in computation cost with very little loss in accuracy. Parametric studies are conducted to investigate the effect of the distribution of natural fracture density, length, and orientation. The results show that the efficiency of tapping geothermal energy is impacted by geometrical and topological complexities of the fracture network and in particular the connectivity of backbone fractures. It is, therefore, important to optimize (not maximize) the connectivity and complexity of the backbone fracture network. The computationally efficient model presented here provides a practical tool for optimizing operational parameters for efficient geothermal production.

New strategy for the numerical solution of multi-dimensional diffusion equations

PurposeThe purpose of this paper is to introduce an innovative strategy for the approximate solution of the heat flow problems in two- and three-dimensional spaces. This new strategy is very easy to implement and handles the restrictive variable that may ruin the physical nature of the problem.Design/methodology/approachThis study combines Sawi transform (ST) and the homotopy perturbation method (HPM) to formulate the idea of Sawi homotopy perturbation transform method (SHPTM). First, this study implements ST to handle the recurrence relation and then incorporates HPM to derive the series solutions of this recurrence relation. ST has the advantage in that it does not require any assumptions or hypothesis for the evaluation of series solutions.FindingsThis strategy finds the results very accurate and close to the precise solution. The graphical observations and the surface solution demonstrate that SHPTM is a reliable and powerful scheme for finding the approximate solution of heat flow problems.Originality/valueThe study presents an original work. This study develops SHPTM for the approximate solution of two- and three-dimensional heat flow problems. The obtained results and graphical representation demonstrate that SHPTM is a very authentic and reliable approach.

Steady-State Solution of MHD Heat and Mass Transfer Fluid Flow over a Semi-Infinite Vertical Plate in a Rotating System Dipped in a Porous Medium with Hall Current, Thermal Radiation, Heat Generation/Absorption and Joule Heating

The steady-state solution of unsteady MHD radiating fluid flow concerning heat and mass transfer in a rotating system dipped in a medium of porosity with Hall current along a semi-infinite vertical plate have been inquired numerically. By using appropriate usual conversions, the governing equations for the present study are converted into the form of dimensionless non-linear partial differential equations (PDEs). The explicit finite difference method (FDM) is imposed to solve the acquired coupled non-linear PDEs. MATLAB R2020a has been employed as a numerical simulation tool. For assuring accuracy and for obtaining convergence solutions the stability and convergence criteria of the present model have been fabricated. The stability analysis imposes circumscriptions on several elements as 0.50≤M≤10, 0.01≤βh≤5, K≤326.50, 0.185≤Pr≤7.56, 0.00≤R*≤80, Sc≥0.18 and Q0≤326.50. The mesh sensitivity experiment for finer mesh space and time validation experiment for steady-state solutions are comprised of acquired solutions. The consequences of the present findings are compared with several previously published research works for claiming validation. The present study accentuates the effects of those parameters, which are relevant to the dimensionless model equations. Finally, the obtained results are placed in graphs and sorted into tables.

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.

A probabilistic representation for heat flow of harmonic map on manifolds with time-dependent Riemannian metric

In this paper we will give a probabilistic representation for the heat flow of harmonic map with time-dependent Riemannian metric via a forward–backward stochastic differential equation on Riemannian manifolds. Moreover, we can provide an alternative stochastic method for the proof of existence of a unique local solution for heat flow of harmonic map with time-dependent Riemannian metric.

Dynamics of thermoelastic half-plane by action of periodic loads and heat flows at its boundary

The problem of the dynamics of a thermoelastic half-space under periodic surface forces and heat flows is solved using the model of coupled thermoelasticity. The Green’s tensor for one boundary value problem is constructed utilizing Fourier transformation. Analytical solutions for arbitrary surface forces and heat flow using the theory of generalized functions are constructed. To solve this boundary value problem, generalized function theory, tensor and differential algebra, the operator method, and integral transformations were used. The solutions obtained make it possible to investigate the thermal stress–strain state of an array with natural and artificial thermal sources and mass power forces acting at its surface.

Impact of differing heat flow solutions on hydrocarbon generation predictions: A case study from West Siberian Basin

Knowledge of the thermal history of a sedimentary basin is necessary for the quantitative and qualitative estimation of hydrocarbons generated from buried organic matter. Usually, specialists use a combination of backstripping and forward temperature modelling techniques for a basin history reconstruction. However, this approach decouples the structural and thermal solutions and therefore results in the less consistent modelling. The reliability of a basin model can be increased by using coupled approaches that resolve the structural and thermal solutions simultaneously.In this work, we investigate how using a backstripping-based versus a coupled thermo-tectono-stratigraphic approach for computing basement heat flow influences the predicted total hydrocarbon generation using a 808 km transect across the West Siberian basin as an example. Both coupled and decoupled approaches are used to reconstruct a basal heat flow history for the transect. Corresponding models have identical geological parameters and are calibrated with a set of temperature and vitrinite reflectance data. Furthermore, reconstructed heat flow histories are used separately as a lower boundary condition in a petroleum system model to evaluate the consequences for hydrocarbon generation. We find that the backstripping-based approach significantly overestimates hydrocarbon generation mass with respect to the basement heat flow solution obtained from the more consistent thermo-tectono-stratigraphic model. Also, the onset and time evolution of hydrocarbon generation is substantially different. These findings, obtained for the West Siberian Basin, show that calibrating a thermal model to the wellbore temperature and vitrinite data can lead to the inaccurate interpretation of the thermal history. The study results suggest that the presented advanced basin modelling strategy can help in decreasing risks in petroleum system analysis by providing more reliable and consistent heat flow solutions.

Thermal Bridge Modeling and a Dynamic Analysis Method Using the Analogy of a Steady-State Thermal Bridge Analysis and System Identification Process for Building Energy Simulation: Methodology and Validation

It is challenging to apply heat flow through a thermal bridge, which requires the analysis of 2D or 3D heat transfer to building energy simulation (BES). Research on the dynamic analysis of thermal bridges has been underway for many years, but their utilization remains low in BESs. This paper proposes a thermal bridge modeling and a dynamic analysis method that can be easily applied to BESs. The main idea begins with an analogy of the steady-state analysis of thermal bridges. As with steady-state analysis, the proposed method first divides the thermal bridge into a clear wall, where the heat flow is uniform, and the sections that are not the clear wall (the thermal bridge part). For the clear wall part, the method used in existing BESs is applied and analyzed. The thermal bridge part (TB part) is modeled with the linear time-invariant system (LTI system) and the system identification process is performed to find the transfer function. Then, the heat flow is obtained via a linear combination of the two parts. This method is validated by comparing the step, sinusoidal and annual outdoor temperature response of the finite differential method (FDM) simulation. When the thermal bridge was modeled as a third-order model, the root mean square error (RMSE) of annual heat flow with the FDM solution of heat flow through the entire wall was about 0.1 W.

Correction to: The influence of the glass transition temperature (Tg) of polymers on early OPC hydration: a complete study of the heat flow, phase evolution, and pore solution chemistry

The article ‘‘The influence of the glass transition temperature (Tg) of polymers on early OPC hydration: a complete study of the heat flow, phase evolution, and pore solution chemistry’’, written by ‘‘D. Jansen, Z. Lu, X.-M. Kong, J. Pakusch, E. Jahns, F. Deschner, Ch. Schmidtke’’, was originally published electronically on the publisher’s internet portal (currently SpringerLink) on 11 December 2019 without open access.

Thermal Step Response of N-Layer Composite Walls—Accurate Approximative Formulas

Abstract For many industrial applications, heat flow through composites relates directly to energy usage and thus is of highest interest. For multilayer composites, the heat flow is a result of multiple variables, such as the temperature gradient over the surface boundaries and each material's thermal conductivity, specific heat, and thickness. In addition, the transient heat flux also depends on how the materials are aligned together. The heat flow through composites can be estimated using advanced computer simulations for applied heat transfer. Although these tools are powerful, they are also time consuming. Therefore, approximations that allow the estimation of heat flow through composites can be very useful. This paper presents approximations to solve transient heat transfer in multilayer composites, with and without an interior surface resistance. Since the energy use for various applications relates to the heat transferred at the surface boundary, the main focus of this paper is to define approximate solutions for interior heat flow. In other words, these approximations are found by applying a unit step change in temperature on one side of a composite and then in real-time emulating the surface heat flux on the opposite side from which the step change occurs. The approximations are presented based on lumped analyses and Laplace network solutions and are validated against analytical and numerical solutions.

Transient natural convention heat and mass transfer flow in a vertical channel in the presence of Soret and Dufour effects: An analytical approach

This paper presents an analytical solution for transient natural convection heat and mass transfer flow in a vertical channel with Soret and Dufour effects. Due to the presence of these two effects, energy and concentration equations are coupled. The dimensionless governing equations for momentum, energy and concentration are first decoupled using perturbation method and then solved using Laplace Transform Technique (LTT) under relevant initial and boundary conditions. The expressions for temperature, concentration, velocity, rate of heat transfer, rate of mass transfer and skin-friction are obtained. Numerical solutions are also obtained using pdepe in MATLAB so as to validate the accuracy of the proposed analytical method. The effects of Soret parameter, Dufour parameter, Grashof number, modified Grashof number, Prandtl number, Schmidt number and dimensionless time are presented graphically and discussed. It is observed that the temperature and velocity increase with increase in Dufour number, while concentration decreases with increase of Dufour number. The Dufour effect is more significant on the temperature and velocity in comparison to concentration. Moreover, it is observed that the concentration and velocity increase with increase in Soret number while the impact of Soret number is just contrast on temperature variation.

The influence of the glass transition temperature (Tg) of polymers on early OPC hydration: a complete study of the heat flow, phase evolution, and pore solution chemistry

The impact of two different dialyzed styrene-acrylate polymer dispersions on the early hydration of OPC was studied. The polymer particles of both dispersions show a similar particle size distribution and high charge due to carboxylic groups on the surface of the particles. Both dispersions also show similar adsorption behavior. The hydration of the OPC was studied at a polymer concentration below the initial adsorption in order to evaluate possible reasons for the interaction of the polymer particles with cement hydration. It can be shown that the polymer particle with the lower glass transition temperature Tg shows a stronger impact on cement hydration, which cannot be explained by any influence on the pore solution composition or the initial dissolution of cement phases. Hence, the adsorption mechanism seems to be the most likely cause of the interaction of the polymers with hydrating cement.

Heat flow model based on lattice Boltzmann method for modeling of heat transfer during phase transformation

PurposeA fundamental principle of materials engineering is that the microstructure of a material controls the properties. The phase transformation is an important phenomenon that determines the final microstructure. Recently, many analytical and numerical methods were used for modeling of phase transformation, but some limitations can be seen in relation to the choice of the shape of growing grains, introduction of varying grain growth rate and modeling of diffusion phenomena. There are also only few comprehensive studies that combine the final microstructure with the actual conditions of its formation. Therefore, the objective of the work is a development of a new hybrid model based on lattice Boltzmann method (LBM) and cellular automata (CA) for modeling of the diffusional phase transformations. The model has a modular structure and simulates three basic phenomena: carbon diffusion, heat flow and phase transformation. The purpose of this study is to develop a model of heat flow with consideration of enthalpy of transformation as one of the most important parts of the proposed new hybrid model. This is one of the stages in the development of the complex model, and the obtained results will be used in a combined solution of heat flow and carbon diffusion during the modeling of diffusion phase transformations.Design/methodology/approachDifferent values of overheating/overcooling affect different values in the enthalpy of transformation and thus the rate of transformation. CA and LBM are used in the hybrid model in part related to heat flow. LBM is used for modeling of heat flow, while CA is used for modeling of the microstructure evolution during the phase transformation.FindingsThe use of LBM and CA in one numerical solution creates completely new possibilities for modeling of phase transformations. CA and LBM in comparison with commonly used approaches significantly simplify interface and interaction between different parts of the model, which operates in a common domain. The CA can be used practically for all possible processes that consist of nucleation and grains growth. The advantages of the LBM method can be well used for the simulation of heat flow during the transformation, which is confirmed by numerical results.Practical implicationsThe developed heat flow model will be combined with the carbon diffusion model at the next stage of work, and the new complex hybrid model at the final stage will provide new solutions in numerical simulation of phase transformations and will allow comprehensive modeling of the diffusional phase transformations in many processes. Heating, annealing and cooling can be considered.Originality/valueThe paper presents the developed model of heat flow (temperature module), which is one of the main parts of the new hybrid model devoted to modeling of phase transformation. The model takes into account the enthalpy of transformation, and the connection with the model of microstructure evolution was obtained.

Temperature fields generated by a circular heat source (CHS) in an infinite isotropic medium: Treatment of contact resistances with application to thin films

The temperature fields and heat fluxes created by a circular heat source (CHS) are derived for the case of a CHS embedded between two identical and isotropic semi-infinite media, when different thermal contact resistances (CRs) are present on each surface of the CHS. Three different temperature fields are derived: on the CHS surface and in each one of the media surrounding the CHS. The derivation of the three-dimensional heat flow solution uses first principles with no prior assumptions, and employs the Hankel and Laplace transforms. The analytical solution presented here is exact with no approximations, but is given in integral form, which requires a facile numerical evaluation. Finite element simulations performed with COMSOL Multiphysics are provided and validate the analytical solution. The application of the solution to thin film thermal conductivity virtual measurements is demonstrated. Regressions of the numerical results yield thin film resistances in excellent agreement with the actual values (all within 1.5% error), which can readily be translated into thin film thermal conductivities.

An improved friction stir shear localization model and applications in understanding weld formation process in alloy Ti-6-4

This paper presents a coupled shear localization model incorporating both pin/workpiece contact and three-dimensional (3D) heat flow environment generated by friction heating between tool shoulder and workpiece. It represents a significant improvement over an early shear localization model presented by the same authors (2014, 2015) which was focused on shear localization process in front of pin such that shear band development can be treated as a one-dimensional (1D) thermal viscoplastic problem, without considering shoulder/workpiece heating effects and contact interactions between pin and workpiece. The current model includes a novel analytical-based 3D transient heat flow solution incorporating detailed spatial resolution regarding heat generation at shoulder/workpiece interface, which provides a transient temperature environment within which shear localization process can now be examined in a greater detail. Also, contact interactions between pin and workpiece are now treated explicitly by introducing a classical contact mechanics solution for describing contact behavior between a cylinder (pin) and cylindrical cavity (surrounding base metal). This refined shear localization model has been shown capable of providing more realistic and reasonable estimations for both temperature and welding torque when compared with available experimental data. A robust numerical procedure has also been developed and implemented for determining optimum welding speed for a given combination of stir tool rotational speed and welding travel speed, which shows a good agreement with experimental results for a number of applications.

On steady heat flow problem involving Yang-Srivastava-Machado fractional derivative without singular kernel

In this article, we present a new application for the Yang-Srivastava-Machado fractional derivative without singular kernel to the steady heat flow problem. The Sumudu transform is used to find the analytical solution of the fractional-order heat flow.

Similarity Solution of Heat and Mass Transfer Flow over an Inclined Stretching Sheet with Viscous Dissipation and Constant Heat Flux in Presence of Magnetic Field

The present analysis of this paper is to examine the similarity solution of magnetohydrodynamics (MHD) free convection heat and mass transfer flow of an incompressible, electrically conducting and viscous fluid over an inclined stretching sheet with viscous dissipation and constant heat flux. So the present work is focused of the impact of the flow parameters on the velocity, temperature, and concentration are computed, discussed and have been graphically represented in figures and also the shearing stress, and rate of concentration shown in table 1 for various values of different parameters. The results presented graphically illustrate that velocity field decrease due to increasing of magnetic parameter, Prandtl number, Grashof number, and Eckert number whereas negligible increasing effects for Soret number, Schmidt number and noticeable increasing effect for angle of inclination but there is no effect for modified Grashof number. The temperature field decreases up to certain interval then increases in the presence of Magnetic parameter and reverse trend arise for Prandtl number but the temperature field increases for the remaining entering parameters. It is interesting to note that in a certain interval of η, the concentration profile is decreased and then increased but reverse trend arises in the case of Prandtl number and angle of inclination. By considering the hot plate the numerical results for the skin friction and the local Sherwood number are compared with the results reported by the other author when the magnetic field and modified Grashof number are absent. The present results in this paper are in good agreement with the work of the previous author.

Erratum: Analytic solution for heat flow through a general harmonic network [Phys. Rev. E90, 042128 (2014)

Erratum: Analytic solution for heat flow through a general harmonic network [Phys. Rev. E<b>90</b>, 042128 (2014)

Analytic solution for heat flow through a general harmonic network.

We present an analytic expression for the heat current through a general harmonic network coupled with Ohmic reservoirs. We use a method that enables us to express the stationary state of the network in terms of the eigenvectors and eigenvalues of a generalized cubic eigenvalue problem. In this way, we obtain exact formulas for the heat current and the local temperature inside the network. Our method does not rely on the usual assumptions of weak coupling to the environments or on the existence of an infinite cutoff in the environmental spectral densities. We use this method to study nonequilibrium processes without the weak coupling and Markovian approximations. As a first application of our method, we revisit the problem of heat conduction in two- and three-dimensional crystals with binary mass disorder. We complement previous results showing that for small systems the scaling of the heat current with the system size greatly depends on the strength of the interaction between system and reservoirs. This somewhat counterintuitive result seems not to have been noticed before.