对流换热实验中忽略壁面轴向导热的误差分析

以水和空气在钢管中的热充分发展的层流过程为对象,通过数值计算分析了轴向导热给圆管内对流换热的一维壁面导热带来的误差。在二维导热模型的基础上,添加等热流、绝热边界条件,用Fortran语言编写数值计算程序进行计算,定义了相对误差。结果表明,相对误差近似和壁厚与内径的比值成正比,而不同的流体介质数值大小不同。     

A finite element analysis for inverse heat conduction problems

This paper presents an efficient inverse analysis technique based on a sensitivity coefficient algorithm to estimate the unknown boundary conditions of multidimensional steady and transient heat conduction problems. Sensitivity coefficients were used to represent the temperature response of a system under unit loading conditions. The proposed method, coupled with the sensitivity analysis in the finite element formulation, is capable of estimating both the unknown temperature and heat flux on the surface provided that temperature data are given at discrete points in the interior of a solid body. Inverse heat conduction problems are referred to as ill-posed because minor inaccuracy or error in temperature measurements cause a drastic effect on the predicted surface temperature and heat flux. To verify the accuracy and validity of the new method, two-dimensional steady and transient problems are considered. Their surface temperature and heat flux are evaluated. From a comparison with the exact solution, the effects of measurement accuracy, number and location of measuring points, a time step, and regularization terms are discussed. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(6): 345–359, 1997     

Non-Fourier heat conduction in a finite medium subjected to arbitrary non-periodic surface disturbance

The non-Fourier heat conduction equation is solved for a finite medium under arbitrarily chosen surface disturbances by utilizing the principle of superposition along with the Fourier integral representation of arbitrary non-periodic functions. The obtained solution is such that for a given non-periodic disturbance, we just have to introduce the Fourier integral coefficients of that function to the presented general solution and perform some definite integrations, analytically if possible, but in general numerically which is a straightforward computational task.     

Non-Fourier heat conduction in a hollow sphere with periodic surface heat flux

Presented is the analysis of non-Fourier effect in a hollow sphere exposed to a periodic boundary heat flux. The problem is studied by deriving an analytical solution of the hyperbolic heat conduction equation. Using the obtained analytical expression, the temperature profiles at outer and inner surfaces of the sphere are evaluated for various thermal relaxation times. By comparing the results of non-Fourier model with those obtained from Fourier heat conduction equation, the transition process from parabolic model to hyperbolic one is shown. The phase difference and amplitude ratio of boundary surfaces are calculated as functions of the thermal relaxation time and the results are depicted graphically.     

Modeling of fractal heat conduction of semi-coke bed in waste heat recovery steam generator for hydrogen production

With the steam obtained from the waste heat of high temperature semi-coke, the hydrogen production through gasification method is considered more commercial. In order to improve the efficiency of waste heat recovery, the fractional model for heat conduction of semi-coke bed in waste heat recovery process was established. The non-destructive CT was employed to obtain the inner morphology of semi-coke bed and the image binarization processing was used to segment the CT image. With the MATLAB program, the box-counting method was used to calculate the fractal dimension of semi-coke bed. The fractional model for heat conduction of semi-coke bed was established by the fractal theory. The results showed that, the CT image and bit binary image of semi-coke bed can really reflect the inner morphology of semi-coke bed, and the inner morphology of semi-coke bed can be regarded as a fractal medium. The fractal dimension of semi-coke bed is 1.7537, which is very close to golden mean, 1.618, this could be the optimal structure for the heat conduction of semi-coke bed under the condition of natural accumulation. The one-dimensional heat conduction fractional equation of semi-coke bed was established and it can be accurately solved by fractal complex transformation and traveling wave transformation.     

Integral transform solution for hyperbolic heat conduction in a finite slab

An analytical integral transformation of the thermal wave propagation problem in a finite slab is obtained through the generalized integral transform technique (GITT). The use of the GITT approach in the analysis of the hyperbolic heat conduction equation leads to a coupled system of second order ordinary differential equations in the time variable. The resulting transformed ODE system is then numerically solved by Gear's method for stiff initial value problems. Numerical results are presented for the local and average temperatures with different Biot numbers and dimensionless thermal relaxation times, permitting a critical evaluation of the technique performance. A comparison is also performed with previously reported results in the literature for special cases and with those produced through the application of the Laplace transform method (LTM), and the finite volume-Gear method (FVGM).     

A method of fundamental solutions for the radially symmetric inverse heat conduction problem

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric inverse heat conduction problem (IHCP). In the radially symmetric IHCP data on an inner fixed boundary is determined from Cauchy data given on an outer boundary. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach of Johansson et al. (2008) for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.     

Solution of inverse heat conduction problem using the lattice Boltzmann method

In this paper the D2Q9 lattice Boltzmann method (LBM) was utilized for the solution of a two-dimensional inverse heat conduction (IHCP) problem. The accuracy of the LBM results was validated against those obtained from prevalent numerical methods using a common benchmark problem. The conjugate gradient method was used in order to estimate the heat flux test case. A complete error analysis was performed. As the LBM is attuned to parallel computations, its use is recommended in conjugation with IHCP solution methods.     

Steady-state heat conduction in multi-layer bodies

The mathematical formulation of the steady-state temperature field in multi-dimensional and multi-layer bodies is presented. The numerical examples are for two-layer bodies and they include boundary conditions of the first, second, and third kind. This study includes tables to assist the selection of eigenfunctions and computation of the eigenvalues. The computations include the contribution of contact resistance to the temperature solution. An efficient computational scheme for calculating the eigenvalues is used. For multi-dimensional, multi-layer bodies, the eigenfunctions are real if each layer is homogeneous; they may become imaginary if layers are orthotropic.     

Combined heat and power considered as a virtual steam cycle heat pump

The first aim of this paper is to shed light on the thermodynamic reasons for the practical pursuit of low temperature operation by engineers involved in the design and the operation of combined heat and power (CHP) and district heating (DH) systems. The paper shows that the steam cycle of a combined heat and power generator is thermodynamically equivalent to a conventional steam cycle generator plus an additional virtual steam cycle heat pump. This apparently novel conceptualisation leads directly to (i) the observed sensitivity of coefficient of performance of CHP to supply and return temperatures in associated DH systems, and (ii) the conclusion that the performance of CHP will tend to be significantly higher than real heat pumps operating at similar temperatures. The second aim, which is pursued more qualitatively, is to show that the thermodynamic performance advantages of CHP are consistent with the goal of deep, long-term decarbonisation of industrialised economies. As an example, estimates are presented, which suggest that CHP based on combined-cycle gas turbines with carbon capture and storage has the potential to reduce the carbon intensity of delivered heat by a factor of ∼30, compared with a base case of natural gas-fired condensing boilers.     

Non-Fourier heat conduction in a finite medium with insulated boundaries and arbitrary initial conditions

The non-Fourier transient heat conduction in a finite medium with insulated boundaries under the influence of arbitrary initial conditions is investigated analytically. The solution is expressed in the form of Fourier cosine series. The obtained analytical closed-form solution can be used for validation of numerical solutions. The resulting solution is valid for any choice of integrable initial conditions. The significant feature of proposed solution is its generality. In order to show the applicability of the presented solution, two numerical examples are solved.     

Mixed nonstationary problem of heat conduction for a microperiodic two-layered half-space

The paper deals with a mixed nonstationary problem of heat conduction for a microperiodic two-layered half-space. The body is assumed to be initially at zero temperature, the boundary plane is kept at a known temperature for time 0 ≤ t ≤ t₀ and is insulated for t > t₀. The half-space is composed of periodically repeated two-layered laminae with layering parallel to the boundary. The problem is solved within the framework of homogenized model with microlocal parameters [Cz. Woźniak, A nonstandard method of modelling of thermoelastic periodic composites, International Journal of Engineering Science 25, (1987), pp. 483–499, S.J. Matysiak Cz. Woźniak, On the modelling of heat conduction problem in laminated bodies, Acta Mechanica, 65, (1986), pp. 223–238.]. The influence of thermal and geometric properties of the composite components on the temperature distribution for some special case of the boundary condition is analyzed.     

Non-Fourier heat conduction in a finite medium subjected to arbitrary periodic surface disturbance

The non-Fourier transient heat conduction in a finite medium under arbitrary periodic surface thermal disturbance is investigated analytically. In order to obtain the desired temperature field from the known solution for non-Fourier heat conduction under a harmonic disturbance, the principle of superposition along with the Fourier series representation of an arbitrary periodic function is employed. The developed method can be applied for more realistic periodic boundary conditions occurred in nature and technology.     

Peridynamic simulation of transient heat conduction problems in functionally gradient materials with cracks

In this article, a modified state-based peridynamic (PD) method is proposed to solve transient heat conduction problems in functionally gradient materials (FGMs) with extending insulated cracks. The PD formulation of transient heat conduction has been derived by using the time integration through the forward difference technique. Numerical simulations have been performed to verify the accuracy and effectiveness of the proposed method. The analytical solution and the finite element method results are used for comparison. In this work, the material properties of functionally graded materials are assumed to vary exponentially in z-direction. Our PD results show good agreement with analytical solutions and results from the finite element method. Hence the proposed PD method is suitable to deal with the transient heat conduction problem in FGMs with extending insulated cracks.     

Radial ballistic-diffusive heat conduction in nanoscale

Heat conduction in radius direction is of great importance to the use of two-dimensional materials and experiments. In this paper, radial ballistic-diffusive heat conduction in nanoscale is investigated by the phonon Monte Carlo (MC) method and phonon Boltzmann transport equation. We find that owing to the two-dimensional nature, the radial heat transport is dominated by two parameters, including the Knudsen number (Kn) and the radius ratio of the two concentric boundaries, the former of which is defined as the ratio of the phonon mean-free-path to the distance of the two boundaries. Compared with the one-dimensional cases, radial ballistic transport not only leads to boundary temperature jumps and the size effect of the effective thermal conductivity, but also results in a nonlinear temperature profile in logarithm radius coordinate, a difference of the inner and outer boundary temperature jumps, a stronger size effect, and a nonuniform local thermal conductivity within the system. When the value of Kn is far less than one, diffusive transport predominates and the effect of the radius ratio is negligible. Whereas, when Kn is comparable to or larger than one, the intensity of ballistic transport compared to diffusive transport will be increased significantly as the radius ratio decreases. In addition, the models for the temperature profile and the effective thermal conductivity are derived by an interpolation of the limit solutions and modification of the previous model, respectively. The good agreements with the phonon MC simulations demonstrate their validity.     

A technique for uncertainty analysis for inverse heat conduction problems

A technique is presented for the uncertainty analysis of the linear Inverse Heat Conduction Problem (IHCP) of estimating heat flux from interior temperature measurements. The selected IHCP algorithm is described. The uncertainty in thermal properties and temperature measurements is considered. A propagation of variance equation is used for the uncertainty analysis. An example calculation is presented. Parameter importance factors are defined and computed for the example problem; the volumetric heat capacity is the dominant parameter and an explanation is offered. Thoughts are presented on extending the analysis to include the non-linear problem of temperature dependent properties.     

Exact variational principle for 3-D unsteady heat conduction with second sound

The exact variational formulation of the extended unsteady heat conduction equation with finite propagationspeed(the 2nd sound speed)of hyperbolic type is derived herein via a systematic and natural way.Moreover,theboundary- and the physically acceptable initial-value conditions are accommodated in the variational principle bya novel method suggested just recently.In this way a perfect justification of the variational theory of transient heatconduction and a rigorous theoretical basis for the finite element analysis of heat conduction are provided.     

Use of the microscopic parabolic heat conduction model in place of the macroscopic model validation criterion under harmonic boundary heating

Parabolic heat conduction models are considered. The validity of using a microscopic under harmonic fluctuating boundary heating source is investigated. It is found that using the microscopic parabolic heat conduction model is essential when . The phase-shift between the electron gas and solid lattice temperatures is found to be . This phase-shift reaches a fixed value of 1.5708 rad at very large values of . It is found that using the microscopic parabolic heat conduction model is essential when rad/s for most metallic layers regardless of their thickness.     

A Novel Variational Formulation of Inverse Problem of Heat Conduction with Free Boundary on an Image

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Investigating heat conduction in a sphere with heat absorption using generalized Caputo fractional derivative

In this paper, we study the ρ-Laplace transform and the finite sin-Fourier transform as powerful tools in solving fractional differential equations with generalized Caputo derivative. We use these transforms to solve the time-fractional heat equation with a generalized Caputo fractional derivative associated with heat absorption in spherical coordinates. We obtain the solutions in two cases of Dirichlet boundary conditions. The effect of the parameter $\rho$, which characterizes the generalized Caputo derivative is illustrated through some numerical examples.