共查询到20条相似文献,搜索用时 15 毫秒
1.
Steady-periodic heat conduction with relaxation time in an infinitely long hollow cylinder is considered. Four boundary value
problems, with boundary conditions of the first and of the second kind, are solved analytically. The solution for a solid
cylinder with a sinusoidally varying surface temperature is obtained as a special case of a solution found for the hollow
cylinder. The effects of the relaxation time on the steady-periodic temperature field are analysed, in details, for a solid
cylinder with a sinusoidally varying surface temperature and for a hollow cylinder with a sinusoidally varying heat flux at
the inner surface and with a constant temperature at the outer surface. The results show that thermal resonances may occur
and suggest that accurate measurements of the relaxation time could be obtained by means of experiments on steady-periodic
heat conduction in cylindrical geometry.
Received on 15 April 1997 相似文献
2.
The non-stationary heat conduction in an infinitely wide plane slab with a prescribed boundary heat flux is studied. An arbitrary time dependent boundary heat flux is considered and a non-vanishing thermal relaxation time is assumed. The temperature and the heat flux density distributions are determined analytically by employing Cattaneo-Vernotte's constitutive equation for the heat flux density. It is proved that the temperature and the heat flux density distributions can be incompatible with the hypothesis of local thermodynamic equilibrium. A comparison with the solution which would be obtained by means of Fourier's law is performed by considering the limit of a vanishing thermal relaxation time. 相似文献
3.
Two space marching methods for solving the one-dimensional nonlinear inverse heat conduction problems are presented. The
temperature-dependent thermal properties and the boundary condition on the accessible part of the boundary of the body are
known. Additional temperature measurements in time are taken with a sensor located in an arbitrary position within the solid,
and the objective is to determine the surface temperature and heat flux on the remaining part of the unspecified boundary.
The methods have the advantage that time derivatives are not replaced by finite differences and the good accuracy of the method
results from an appropriate approximation of the first time derivative using smoothing polynomials. The extension of the first
method presented in this study to higher dimensions inverse heat conduction problems is straightforward.
Received on 3 May 1999 相似文献
4.
The non-stationary heat conduction in an infinite solid medium internally bounded by an infinitely long cylindrical surface
is considered. A uniform and time- dependent temperature is prescribed on the boundary surface. An analytical solution of
the hyperbolic heat conduction equation is obtained. The solution describes the wave nature of the temperature field in the
geometry under consideration. A detailed analysis of the cases in which the temperature imposed on the boundary surface behaves
as a square pulse or as an exponentially decaying pulse is provided. The evolution of the temperature field in the case of
hyperbolic heat conduction is compared with that obtained by solving Fourier's equation.
Received on 28 January 1998 相似文献
5.
A boundary identification method for an inverse heat conduction problem with an application in ironmaking 总被引:1,自引:0,他引:1
A boundary identification problem in inverse heat conduction is studied, based on data from internal measurement of temperature and heat flux. Formulated as a sideways heat conduction equation, a spatial continuation technique is applied to extend the solution to a known boundary condition at the desired boundary position. Recording the positions traversed in the continuation for each time instant yields the boundary position trajectory and hence the solution of the identification problem. A prospective application of the method can be found in the ironmaking blast furnace, where it is desired to monitor the thickness of the accreted refractory wall based on measurement of its internal state. Simulations featuring noisy measurement data demonstrate the feasibility of the identification method for blast furnace wall thickness estimation. 相似文献
6.
The effect of periodic Ohm??s heating on hyperbolic heat conduction in porous media is studied analytically with the objective of identifying the thermal resonance conditions. Local thermal equilibrium conditions are assumed to apply. The paper focuses initially on the temperature solution and looks at the conditions required for resonating the temperature signal. The heat flux solution is then evaluated. While a discrete infinite set of modes can be resonated, it is shown that in practice the resonance in the temperature signal is felt starting from moderately small values of Fourier numbers and becomes too small to be noticed if the Fourier number is extremely small. The temperature solution is shown to represent a standing wave the amplitude of which is strongly affected by the Fourier number. While the heat flux solution is shown to differ from the one obtained for the temperature, it also shows similar features such as the standing wave behavior the amplitude of which is strongly affected by the Fourier number. 相似文献
7.
The inverse problem of determining time-variable surface heat flux in a plane wall, with constant or temperature dependent thermal properties, is numerically studied. Different kinds of incident heat flux, including rectangular waveform, are assumed. The solution is numerically solved as a function estimation problem, so that no a priori information for the functional waveforms of the unknown heat flux is needed. In all cases, a solution in the form of a piece-wise function is used to approach the incident flux. Transient temperature measurements at the boundary, from the solution of the direct problem, served as the simulated experimental data needed as input for the inverse analysis. Both direct and inverse heat conduction problems are solved using the network simulation method. The solution is obtained step-by-step by minimising the classical functional that compares the above input data with those obtained from the solution of the inverse problem. A straight line of variable slope and length is used for each one of the stretches of the desired solution. The influence of random error, number of functional terms and the effect of sensor location are studied. In all cases, the results closely agree with the solution. 相似文献
8.
M. Mosaad 《Heat and Mass Transfer》1999,35(5):371-375
Coupled heat transfer between laminar forced convection along and conduction inside a flat plate wall is theoretically studied.
The laminar convective boundary layer is analyzed by employing the integral technique. The energy equations for the fluid
and the plate wall are combined under the condition of the continuity in the temperature and heat flux at the fluid-solid
interface. The analysis results in a simple formal solution. Expressions have been obtained for calculating local Nusselt
number, wall heat flux and temperature along the plate, all are functions of the local Brun number, Br
x
, which is a measure of the ratio of the thermal resistance of the plate to that of the convective boundary layer. The results
indicate that for Br
x
≥0.15, neglecting the plate resistance will results in an error of more than 5% in Nusselt number. Comparison of the present
solution with other previous studies has been made. The solution may be of a considerable theoretical and practical interest.
Received on 19 August 1998 相似文献
9.
Mohammad Reza Talaee Gholamali Atefi 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(12):1793-1806
Analytical solution of the non-Fourier axisymmetric temperature field within a finite hollow cylinder exposed to a periodic
boundary heat flux is investigated. The problem studied considering the Cattaneo–Vernotte (CV) constitutive heat flux relation.
The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method
of separation of variables is used for solving the problem with time-independent boundary conditions, and the Duhamel integral
is used for applying the time dependency. The solution is applied for the special cases of harmonic uniform heat flux and
an exponentially pulsed heat flux with Gaussian distribution in outer surface for modeling a laser pulse, and their respective
non-Fourier thermal behavior is studied. 相似文献
10.
The two-dimensional (2D) transient heat conduction problems with/without heat sources in a rectangular domain under different combinations of temperature and heat flux boundary conditions are studied by a novel symplectic superposition method (SSM). The solution process is within the Hamiltonian system framework such that the mathematical procedures in the symplectic space can be implemented, which provides an exceptional direct rigorous derivation without any assumptions or predetermination of the solution forms compared with the conventional inverse/semi-inverse methods. The distinctive advantage of the SSM offers an access to new analytic heat conduction solutions. The results obtained by the SSM agree well with those obtained from the finite element method (FEM), which confirms the accuracy of the SSM. 相似文献
11.
This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer, which is also an exact solution to the unsteady Navier-Stokes(NS) equations. The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions. The wall temperature and heat flux have power dependence on both time and spatial distance. The solution domain, the velocity distribution, the flow field, ... 相似文献
12.
A numerical solution, for incompressible, steady-state, laminar flow heat transfer in the combined entrance region of a circular tube is presented for the case of constant wall heat flux and constant wall temperature. The development of velocity profile is obtained from Sparrow's entrance region solution. This velocity distribution is used in solving the energy equation numerically to obtain temperature profiles. Variation of the heat transfer coefficient for these two different boundary conditions for the early stages of boundary layer formation on the pipe wall is obtained. Local Nusselt numbers are calculated and the results are compared with those given byUlrichson andSchmitz. The effect of the thermal boundary conditions is studied by comparing the uniform wall heat flux results with uniform wall temperature. 相似文献
13.
14.
Planar solidification of a warm flowing liquid with the convective heat transfer to the growing solid layer, has been analysed for the boundary conditions of constant temperature, constant heat flux and convective heat flux at the surface respectively. The mathematical formulation of the problem resulted in a coupled set of two differential equations in temperature and solid thickness as function of position, time and the problem parameters. Analytical expressions for the temperature distribution within the growing solid layer, the rate of solidification and the solidification time are obtained. The perturbation techniques employed here is simple and straight forward in contrast with the earlier techniques. Good agreement between the experimental results and the present solutions is obtained for the convective heat flux boundary condition. The results of this analysis are useful in the design and analysis of experiments dealing with freezing/melting in one dimension. The role of the parameter Stefan number which is small for phase change materials, is discussed in context with the storage of thermal energy. 相似文献
15.
Retrieving the heat transfer coefficient for jet impingement from transient temperature measurements
Arkadiusz Ryfa Ryszard A. Bialecki 《International Journal of Heat and Fluid Flow》2011,32(5):1024-1035
Algorithm of retrieving the heat transfer coefficient (HTC) from transient temperature measurements is presented. The unknown distributions of two types of boundary conditions: the temperature and heat flux are parameterized using a small number of user defined functions. The solutions of the direct heat conduction problems with known boundary temperature and flux are expressed as a superposition of auxiliary temperature fields multiplied by unknown parameters. Inverse problem is formulated as a least squares fit of calculated and measured temperatures and is cast in a form of a sum of two objective functions. The first results originates from an inverse problem for retrieving the boundary temperature the second comes from the inverse problem for reproducing the boundary heat flux. The final form of the objective function is obtained by enforcing constant in time value of the heat transfer coefficient. This approach leads to substantial regularization of the results, when compared with the standard technique, where HTC is calculated from separately reconstructed temperature and heat flux on the boundary. The validation of the numerical procedure is carried out by reconstructing a known distribution of the HTC using simulated measurements laden by stochastic error. The proposed approach is also used to reconstruct the distribution of the HTC in a physical experiment of heating a cylindrical sample using an impinging jet. 相似文献
16.
A. C. Giere 《Applied Scientific Research》1965,14(1):191-198
Summary The time-dependent, one-dimensional equation of heat conduction is solved for a slab of two layers in perfect thermal contact. At one boundary there is a constant heat flux into the slab, and at the other boundary there is a zero flux. The solution for the temperature distribution is obtained with the aid of the Laplace transformation.This work was supported by the U.S. Naval Weapons Evaluation Facility, Albuquerque, N. M., U.S.A. 相似文献
17.
Yuriy Povstenko 《Meccanica》2012,47(1):23-29
The theory of thermoelasticity based on the heat conduction equation with the Caputo time-fractional derivative of order α is used to study thermal stress in an infinite medium with a cylindrical hole. Two types of Neumann boundary conditions are
considered: the constant value of the normal derivative of the temperature and constant heat flux at the surface of a cavity.
The solution is obtained applying Laplace and Weber integral transforms. Numerical results are illustrated graphically. 相似文献
18.
The interfacial heat transfer coefficient (IHTC) is necessary for accurate simulation of the casting process. In this study,
a cylindrical geometry is selected for the determination of the IHTC between aluminum alloy casting and the surrounding sand
mold. The mold surface heat flux and temperature are estimated by two inverse heat conduction techniques, namely Beck’s algorithm
and control volume technique. The instantaneous cast and mold temperatures are measured experimentally and these values are
used in the theoretical investigations. In the control volume technique, partial differential heat conduction equation is
reduced to ordinary differential equations in time, which are then solved sequentially. In Beck’s method, solution algorithm
is developed under the function specification method to solve the inverse heat conduction equations. The IHTC was determined
from the surface heat flux and the mold surface temperature by both the techniques and the results are compared. 相似文献
19.
Michael Shusser 《Shock Waves》2010,20(4):323-331
The paper presents an approximate kinetic theory model of ablation of carbon by a nanosecond laser pulse. The model approximates
the process as sublimation and combines conduction heat transfer in the target with the gas dynamics of the ablated plume
which are coupled through the boundary conditions at the interface. The ablated mass flux and the temperature of the ablating
material are obtained from the assumption that the ablation rate is restricted by the kinetic theory limitation on the maximum
mass flux that can be attained in a phase-change process. To account for non-uniform distribution of the laser intensity while
keeping the calculation simple the quasi-one-dimensional approximation is used in both gas and solid phases. The results are
compared with the predictions of the exact axisymmetric model that uses the conservation relations at the interface derived
from the momentum solution of the Boltzmann equation for arbitrary strong evaporation. It is seen that the simpler approximate
model provides good accuracy. 相似文献
20.
Yuriy Povstenko 《Archive of Applied Mechanics (Ingenieur Archiv)》2012,82(3):345-362
The theory of thermal stresses based on the heat conduction equation with the Caputo time-fractional derivative of order 0 < α ≤ 2 is used to investigate axisymmetic thermal stresses in a cylinder. The solution is obtained applying the Laplace and
finite Hankel integral transforms. The Dirichlet and two types of Neumann problems with the prescribed boundary value of the
temperature, the normal derivative of the temperature, and the heat flux are considered. Numerical results are illustrated
graphically. 相似文献