Dimensional Transient Heat Conduction Research Articles

Precision controllable Gaver–Wynn–Rho algorithm in Laplace transform triple reciprocity boundary element method for three dimensional transient heat conduction problems

In this paper, Laplace transform triple reciprocity boundary element method (LT-TRBEM) is employed to solve the three dimensional transient heat conduction problems. In order to improve the accuracy of the Laplace inversion using Gaver-Wynn-Rho (GWR) algorithm in non-multi-precision computational environment, a precision controllable GWR (PCGWR) algorithm is proposed in the current study. The inversion parameter NL will be selected automatically according to inverse transform accuracy. Solutions with very poor precision in GWR will be identified and eliminated by PCGWR to guarantee the inverse transform accuracy. In LT-TRBEM, there is a non-integral term containing fundamental solution in the boundary integral equation (BIE) for domain points. The value of it is infinite and cannot be calculated directly. In order to supplement this shortcoming, a computable BIE for domain points is proposed, the term with infinite value is converted into a known amount of boundary integral. So, we can calculate the domain points’ temperature successfully, and LT-TRBEM can be employed in problems with discontinuous boundary conditions. Three numerical examples were included to demonstrate the performance of the proposed approach. In summary, LT-TRBEM combined with the PCGWR and the new BIE for domain points can capture the transient heat conduction responses efficiently and accurately.

Heat transfer distribution of premixed methane-air laminar flame jets impinging on ribbed surfaces

Heat transfer distribution of premixed methane-air laminar flame jet impinging on ribbed surfaces is presented in this work. Experiments are carried out on ribbed plates with three different geometrical shaped rib elements i.e. circular, rectangular and triangular. In addition, numerical simulations are performed to study flow field distribution near the ribs. During the experiments, Reynolds number is varied from 600 to 1800 and burner tip to target plate distance is varied from 2 to 4. An analytical inverse solution to three dimensional transient heat conduction presented in our previous work is used to obtain heat transfer parameters. Heat transfer coefficients are found lower whereas reference temperatures are observed higher on ribbed surfaces as compared with smooth surface. Obstruction to the flow, flow separation and decrease in momentum are the reasons attributed for lower heat transfer rate for ribbed surfaces.

A novel formulation and sequential solution strategy with time-space adaptive mesh refinement for efficient reconstruction of local boundary heat flux

Inverse heat conduction problems appear in a variety of applications in industry and academia. Due to their mathematical challenges, they have been studied extensively over the last decades. Nevertheless, the solution of three dimensional transient inverse heat conduction problems are still computationally expensive. Commonly used solution approaches include the regularization-based approaches such as Tikhonov regularization or iterative regularization that result in formulating and solving optimization problems. A radically different solution approach is presented in this paper to provide efficient solutions of three dimensional transient inverse heat conduction problems on thin-plates that are used very often in industrial applications. Instead of solving optimization problems subject to constraints given in terms of three dimensional partial differential equations, the suggested approach transforms the inverse problem into an easy-to-solve direct problem that only needs the reconstruction of a Dirichlet boundary condition. This yields an approximated solution. Furthermore, a new time-space adaptive mesh refinement strategy is proposed to further reduce computational effort at an acceptable level of estimation precision. The accuracy and efficiency of the proposed sequential approach as well as the time-space adaptive mesh refinement strategy are validated by four representative case studies arising from practice. Estimation results with experimental data are also presented. The current work is considered as an important step forward towards the efficient solution of transient three dimensional inverse heat conduction problems, which is particularly useful for developing heat-flux soft sensors in practical problems arising from different fields such as pool boiling, falling films and steelmaking.

Effect of Process Parameters and Material Properties on Laser Micromachining of Microchannels.

Laser micromachining has emerged as a promising technique for mass production of microfluidic devices. However, control and optimization of process parameters, and design of substrate materials are still ongoing challenges for the widespread application of laser micromachining. This article reports a systematic study on the effect of laser system parameters and thermo-physical properties of substrate materials on laser micromachining. Three dimensional transient heat conduction equation with a Gaussian laser heat source was solved using finite element based Multiphysics software COMSOL 5.2a. Large heat convection coefficients were used to consider the rapid phase transition of the material during the laser treatment. The depth of the laser cut was measured by removing material at a pre-set temperature. The grid independent analysis was performed for ensuring the accuracy of the model. The results show that laser power and scanning speed have a strong effect on the channel depth, while the level of focus of the laser beam contributes in determining both the depth and width of the channel. Higher thermal conductivity results deeper in cuts, in contrast the higher specific heat produces shallower channels for a given condition. These findings can help in designing and optimizing process parameters for laser micromachining of microfluidic devices.

Studies for aeroelastic characteristics and nonlinear response of FG-CNT reinforced composite panel considering the transient heat conduction

A solution of computing the aero-thermal-elastic problem of FG-CNT reinforced composite panel is proposed, in which the aerodynamic heating and transient heat conduction are accounted for. The Von-Karman theory and the third-order piston theory are employed to establish the motion equation of FG-CNT panel, where the thermo-mechanical properties of polymer matrix and carbon nanotubes are set to be location- and temperature-dependent. The Ecker’s reference temperature method and heat flux equation are adopted to calculate the heat flux. Two dimensional transient heat conduction including in-plane and through-thickness directions are computed using a finite difference approach. In the calculation process, the influence of elastic deformation on the aero-heating and aero-heating on panel stiffness is included. The aeroelastic stability analysis is presented for the influential parameters such as CNT volume fraction, distribution and aspect ratio of the panel. Moreover, the effects of the oblique shock wave parameters on the critical flutter pressure and dynamic response are discussed. Numerical results show that the coupled solution leads to the inhomogeneous aero-heating, which results in nonuniform temperature distributions and material property degradations. Consequently, the stability boundary and dynamic response are varied with respect to the case without considering the coupling effect.

Thermal Aspects of Environmentally Friendly-MQL Grinding Process

This study attempts to quantify the amount of heat that goes into the workpiece during grinding processes. A new two dimensional transient heat conduction finite element model (FEM) has been made for both the conventional and environmentally friendly-MQL grinding processes. The boundary conditions for this problem were established based on the results of the heat transfer studies on semi-infinite bodies with a heat source moving on its surface. The model also takes into account the convective cooling of the grinding fluid/MQL. Hence this model can be used to evaluate the cooling effectiveness of various coolant-lubricant conditions based upon their convective heat transfer coefficient and bulk temperature. The finite element results can be used to evaluate the energy partition, which is defined as the fraction of total grinding energy that goes as heat into the workpiece. These results when matched with the experimental data give the energy partition. Results show that the finite element results match well with the experimental data.

Transient response of a thermoelectric generator subjected to spatially non-uniform heating: Implications for heat and IR sensing applications

We present a combined experimental and computational investigation of the transient behavior of a thermoelectric generator (TEG) subjected to temperature gradients of less than 0.5K across its thickness. Such conditions can exist when TEGs are used as heat sensors or IR detectors. Spatially non-uniform heating was initiated by allowing light to strike the central portion of one side of the TEG or by placing a small heated probe in contact with that surface. The time-dependent, open circuit voltage output of the TEG was predicted using temperature results from a three dimensional transient heat conduction finite element model. It is shown that the transient voltage output is influenced by the configuration of the mounting hardware, by the thermal properties of the TEG’s materials of construction, and by convection. Three-dimensional heat conduction in the TEG determines the nature of the transient voltage output, which, in some cases, exhibits an overshoot.

A new meshless local B-spline basis functions-FD method for two-dimensional heat conduction problems

Purpose – The purpose of this paper is to present a new approach of meshless local B-spline based finite difference (FD) method for solving two dimensional transient heat conduction problems. Design/methodology/approach – In the present method, any governing equations are discretized by B-spline approximation which is implemented in the spirit of FD technique using a local B-spline collocation scheme. The key aspect of the method is that any derivative is stated as neighbouring nodal values based on B-spline interpolants. The set of neighbouring nodes are allowed to be randomly distributed thus enhanced flexibility in the numerical simulation can be obtained. The method requires no mesh connectivity at all for either field variable approximation or integration. Time integration is performed by using the Crank-Nicolson implicit time stepping technique. Findings – Several heat conduction problems in complex domains which represent for extended surfaces in industrial applications are examined to demonstrate the effectiveness of the present approach. Comparison of the obtained results with solutions from other numerical method available in literature is given. Excellent agreement with reference numerical method has been found. Research limitations/implications – The method is presented for 2D problems. Nevertheless, it would be also applicable for 3D problems. Practical implications – A transient two dimensional heat conduction in complex domains which represent for extended surfaces in industrial applications is presented. Originality/value – The presented new meshless local method is simple and accurate, while it is also suitable for analysis in domains of arbitrary geometries.

Development of three dimensional transient numerical heat conduction model with growth of oxide scale for steel billet reheat simulation

This paper presents development of numerical heat conduction model for prediction of transient three dimensional temperature field in the billet. The model is applied to billet heating process in the reheat furnace. The discretization of governing equation is done by control volume approach and implicit scheme of finite difference method. The model captures various time dependent boundary conditions corresponding to the billet reheat in the reheat furnace, in addition to this it also accounts for the growth of oxide scale layer on the billet surfaces during reheat simulations. The set of discretized equations is solved using own developed MATLAB® code. The proposed model is capable of predicting the temperature field in the billet and scale growth on the billet surfaces. The model is validated with analytical results and published experimental results. The results obtained through the model simulations are in concurrence with the anticipated trend. The proposed methodology of numerical modeling will be helpful for the temperature and scale growth predictions, which are vital for a variety of reasons like energy efficiency, process optimization, roll force calculations, carbon segregation control and product microstructure control, etc.

One dimensional transient heat conduction in segmented fin-like geometries with distinct discrete peripheral convection

This study presents the solution of transient heat conduction in a composite extended surface whose periphery is exposed to convection and whose thermophysical properties experience discontinuities along the longitudinal direction. The solution development uses the natural analytic approach and formats the description so that the constants of integration of each of the composite segments are expressed in terms of the previous segment's eigenfunctions. This allows the solution to be “built” in a very systematic and sequential manner. A three-segment case study is also provided to show the simplicity and applicability of the implementation of this solution.

The transient response for different types of erodable surface thermocouples using finite element analysis

The transient response of erodable surface thermocouples has been numerically assessed by using a two dimensional finite element analysis. Four types of base metal erodable surface thermocouples have been examined in this study, included type-K (alumel-chromel), type-E (chromel-constantan), type-T (copper-constantan), and type-J (iron-constantan) with 50 mm thick- ness for each. The practical importance of these types of thermocouples is to be used in internal combustion engine studies and aerodynamics experiments. The step heat flux was applied at the surface of the thermocouple model. The heat flux from the measurements of the surface temperature can be commonly identified by assuming that the heat transfer within these devices is one-dimensional. The surface temperature histories at different positions along the thermocouple are presented. The normalized surface temperature histories at the center of the thermocouple for different types at different response time are also depicted. The thermocouple response to different heat flux variations were considered by using a square heat flux with 2 ms width, a sinusoidal surface heat flux variation width 10 ms period and repeated heat flux variation with 2 ms width. The present results demonstrate that the two dimensional transient heat conduction effects have a significant influence on the surface temperature history measurements made with these devices. It was observed that the surface temperature history and the transient response for thermocouple type-E are higher than that for other types due to the thermal properties of this thermocouple. It was concluded that the thermal properties of the surrounding material do have an impact, but the properties of the thermocouple and the insulation materials also make an important contribution to the net response.

Finite element solution of transient heat conduction using iterative solvers

PurposeTo provide an analysis of transient heat conduction, which is solved using different iterative solvers for graduate and postgraduate students (researchers) which can help them develop their own research.Design/methodology/approachThree‐dimensional transient heat conduction in homogeneous materials using different time‐stepping methods such as finite difference (Θ explicit, implicit and Crank‐Nicolson) and finite element (weighted residual and least squared) methods. Iterative solvers used in the paper are conjugate gradient (CG), preconditioned gradient, least square CG, conjugate gradient squared (CGS), preconditioned CGS, bi‐conjugate gradient (BCG), preconditioned BCG, bi‐conjugate gradient stabilized (BCGSTAB), reconditioned BCGSTAB and Gaussian elimination with incomplete Cholesky factorization.FindingsProvides information on which time‐stepping method is the most accurate, which solver is the fastest to solve a symmetric and positive system of linear matrix equations of all those considered.Practical implicationsFortran 90 code given as an abstract can be very useful for graduate and postgraduate students to develop their own code.Originality/valueThis paper offers practical help to an individual starting his/her research in the finite element technique and numerical methods.

Enhancement of Heat Transfer in Hydrogen Storage Tank with Hydrogen Absorbing Alloy (Optimum Fin Arrangement)

Optimization of fin arrangement in a metal hydride (MH) bed has been sought with calculations to enhance heat transmission in a hydrogen storage tank and get the maximum hydrogen absorption rate. Two different fin configurations such as radial and circular fins in a vertical cylindrical reactor vessel using a La-Ni based AB 5 type hydrogen storage alloy were tested. Two dimensional transient heat conduction analysis in the bed coupling with exoergic hydriding reaction predicted temperature and absorption of hydrogen. Those agreed with some experimental results within 6 K and 8.5%, respectively. Hence effects of thickness, spacing and shape of fin on hydrogen absorbing rate were analytically evaluated and optimum range of the each fin arrangement was decided according to a trade off between absorption time and reduce of the MH volume due to the fin volume. At most the hydrogen absorbing time for the recommended fin layout may reduce to about one-third of that without fin.

Numerical computation of time lags and decrement factors for different building materials

In this study, time lags and decrement factors for different building materials have been investigated numerically. For this purpose, one dimensional transient heat conduction equation was solved using the Crank–Nicolson scheme under convection boundary conditions. To the outer surface of the wall, periodic boundary conditions were applied. Twenty-six different building materials were selected for analysis. The computations were repeated for eight different thickness of each material and the effects of thickness and the type of material on time lag and decrement factor were investigated. It was found that thickness of material and the type of the material have a very profound effect on the time lag and decrement factor. The results of present study are useful for designing more effective passive solar buildings and other related areas.

Application of the Laplace transform dual reciprocity boundary element method in the modelling of laser heat treatments

The Laplace Transform Dual Reciprocity Boundary Element Method (LTDRM or LT-DRBEM) provides with an alternative numerical technique to finite difference (FDM) or finite element methods (FEM) for solving transient diffusion problems. With this method, solutions are calculated directly at any specific time thus avoiding the use of time-stepping schemes. Besides, domain integrals are removed from the problem formulation. In this work we study the applicability of the LT-DRBEM method for laser heat treatment modelling purposes. A simple model was developed based on a two dimensional transient heat conduction equation, in which the laser beam is included as a heat flux boundary condition of gaussian shape. Results corresponding to a stationary and a moving beam are presented and discussed. Non-linear formulations of the problem as those given by temperature dependent material properties are also considered. Good accuracy results were obtained for the stationary beam approach, whereas severe limitations were found for the moving beam case.

A Laplace transform-based fundamental collocation method for two-dimensional transient heat flow

The fundamental collocation method (FCM) is extended to handle two dimensional transient heat conduction problems in solids. The method is applied in the Laplace transform domain, after which an inversion technique is used to retrieve the time-domain solution. Examples are used to illustrate the method and a technique for evaluating accuracy is discussed. The performance was found to be very good. The method is capable of handling regions of arbitrary shapes, subjected to constant temperature initial conditions and mixed type, time-independent boundary conditions. Due to its inherent advantages over the domain-oriented techniques like the finite element and, finite difference methods, the Laplace transform-based FCM approach presented here may be regarded as a simpler method for solving a wide variety of time-dependent problems in heat conduction and related fields.

Effects of Wall's thermophysical properties on time lag and decrement factor

In this study, the effects of thermophysical properties and thickness of a wall of a building on time lag and decrement factor have been investigated. For this purpose, one dimensional transient heat conduction equation was solved using Crank-Nicolson scheme under convection boundary conditions. To the outer surface of the wall, periodic boundary conditions were applied. A very general code which can take care of composite walls under any kind of boundary condition was developed. Single and combined effects of the thickness and thermophysical properties on the time lag and decrement factor were investigated. It was found that thermophysical properties have a very profound effect on the time lag and decrement factor. The computations were repeated for different building materials and the results are discussed.

An engineering foundation for controlling heat transfer in one-dimensional transient heat conduction problems

This paper develops an engineering foundation for controlling heat transfer in one dimensional transient heat conduction problems based upon concepts borrowed from vibration control problems. The foundation distinguishes between modal control, distributed control, discrete control and direct feedback control and then singles out direct feedback control because its simplicity. An example demonstrates modal control and direct feedback control of the variation of the transient temperature field in a one dimensional slab geometry.

Temperature in Rubber Moldings during Injection Molding Cycle: Simulation and Experimentation

Measurements of temperature traces in a rubber compound are carried out during injection molding cycle. The measurements are performed using a special temperature measuring device inserted into molds having a cylindrical cavity. The measurements indicate complex temperature traces with a minimum and a maximum during molding cycle. Calculations of tem perature field are performed based on the finite difference solution of the two- dimensional transient heat conduction equation with convective heat transfer on the boundary. The predicted temperature traces, although qualitative, cor rectly simulate experimental observations.

Heat and mass transfer analysis in air-cooling of spherical food products

The one dimensional transient heat conduction equation, in spherical co-ordinates, is solved with convective surface boundary condition, during air-cooling. The enthalpy potential concept is used to include the cooling effect of desiccation. A calculation scheme is proposed in which, up to half the cooling time, the calculation is made with both heat and mass transfer from the product surface, thereafter it is continued with heat transfer only. The calculated temperatures for apples and potatoes are compared with the measured values available in the literature, and good agreement is observed.