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1.
This paper is concerned with a method for solving inverse heat conduction problem. The method is based on the controlled random
search (CRS) technique in conjunction with modified Newton–Raphson method. The random search procedure does not need the computation
of derivative of the function to be evaluated. Therefore, it is independent of the calculation of the sensitivity coefficient
for nonlinear parameter estimation. The algorithm does not depend on the future-temperature information and can predict convective
heat transfer coefficient with random errors in the input temperature data. The technique is first validated against an analytical
solution of heat conduction equation for a typical rocket nozzle. Comparison with an earlier analysis of inverse heat conduction
problem of a similar experiment shows that the present method provides solutions, which are fully consistent with the earlier
results. Once validated, the technique is used to investigate another estimation of heat transfer coefficient for an experiment
of short duration, high heating rate, and employing indepth temperature measurement. The CRS procedure, in conjunction with
modified Newton–Raphson method, is quite useful in estimating the value of the convective heat-transfer coefficient from the
measured transient temperature data on the outer surface or imbedded thermocouple inside the rocket nozzle. Some practical
examples are illustrated, which demonstrate the stability and accuracy of the method to predict the surface heat flux. 相似文献
2.
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
3.
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
4.
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
5.
Hugo D. Fernández Sare Reinhard Racke 《Archive for Rational Mechanics and Analysis》2009,194(1):221-251
We consider hyperbolic Timoshenko-type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative
effect through heat conduction. While exponential stability under the Fourier law of heat conduction holds, it turns out that
the coupling via the Cattaneo law does not yield an exponentially stable system. This seems to be the first example that a
removal of the paradox of infinite propagation speed inherent in Fourier’s law by changing to the Cattaneo law causes a loss
of the exponential stability property. Actually, for systems with history, the Fourier law keeps the exponential stability
known for the pure Timoshenko system without heat conduction, but introducing the Cattaneo coupling even destroys this property.
This work was supported by the DFG-project “Hyperbolic Thermoelasticity” (RA 504/3-1). 相似文献
6.
Hyperbolic heat conduction in a plane slab, infinitely long solid cylinder and solid sphere with a time dependent boundary
heat flux is analytically studied. The solution is based on the separation of variables method and Duhamel’s principle. The
temperature distribution, the propagation and reflection of the temperature wave and the effect of geometry on the shape of
the wave front are studied for the case of a rectangular pulsed boundary heat flux. Comparisons with the solution obtained
for Fourier heat conduction are performed by considering the limit of a vanishing thermal relaxation time. 相似文献
7.
It is considered a heat conduction in a layer made of two conductors distributed in the form of laminas with varied thicknesses.
Macroscopic (averaged) properties of the layer are continuously “transversally” graded across its thickness (TGL layer), cf.
Fig. 1. The aim of the paper is to present and apply an averaged model of the heat conduction, obtained within the tolerance
averaging technique, discussed in the book edited by Woźniak et al. (Thermomechanics of microheterogeneous solids and structures. Tolerance averaging approach, Łódź, Wydawnictwo Politechniki Łódzkiej, 2008). It is shown that the proposed model describes the microstructural effect on the heat conduction of the TGL layer. Moreover,
results obtained within this model are compared to results by the higher order theory (cf. Aboudi et al., Composites B, 30:777–832,
1999). 相似文献
8.
M. Thiele 《Heat and Mass Transfer》1997,33(1-2):7-16
An analysis has been performed to study the influence of velocity dependent dispersion on transverse heat transfer in mixed
convection flow above a horizontal wall of prescribed temperature in a saturated porous medium. The Boussinesq approximation
and boundary layer analysis were used to numerically obtain gravity affected temperature and velocity distributions within
the frames of Darcy's law and a total thermal diffusivity tensor comprising both of constant coefficient heat conduction and
velocity proportional mechanical heat dispersion. Dependending on Pe∞, the molecular Peclét number basing on the effective thermal diffusivity and the velocity of the oncoming flow, density coupling
has distinct influences on heat transfer rates between the wall surface and the porous medium flow region. For small Peclét
numbers, when heat conduction is the prevailing mechanism, wall heat fluxes are the higher the larger the density difference
between the oncoming and the near wall fluid is. The opposite is true for larger Peclét numbers, when mechanical heat dispersion
is the main cause of heat spreading. For Pe∞ tending to infinity these wall heat fluxes approach finite maximum values in the total heat diffusivity model, they grow
beyond any limit if only constant coefficient heat conduction is considered. Thus, the inclusion of mechanical heat dispersion
effects yields physically more realistic predictions.
Received on 18 September 1996 相似文献
9.
袁镒吾 《应用数学和力学(英文版)》1995,16(9):905-912
THESIMILARSOLUTIONSOFNONLINEARHEATCONDUCTIONEQUATIONYuanYiwu(袁镒吾)(CentralSouthUniversityofTechnology,Changsha410012.P.R.China... 相似文献
10.
In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve the timefractional heat conduction equation.The Caputo fractional derivative of the order 0 < α≤ 1 is used.The solution is presented in terms of the Mittag-Leffler functions.Numerical results are illustrated graphically for various values of fractional derivative. 相似文献
11.
The crosslinking of the unsaturated polyester was studied by using experiments and a model of the process. The kinetic parameters
were calculated from the heat flux–time curves obtained by differential scanning calorimetry (DSC, Netzsch–Simultaneous Thermal
Analyser DSC 200), working in DSC (dynamic) mode. The temperature–time histories were studied in plain sheet copper mould.
The mathematical model was constructed by taking into account the heat transferred by conduction through the resin, as well
as the kinetics of heat generated by the crosslinking reaction. The contributions to the rise in temperature from heat conduction
and chemical reaction are different in different parts of the composite, and can explain the temperature-, or degree of crosslinking
(DOC)–time histories. By considering temperature–time histories developed within the sample, more extensive knowledge of the
process can be obtained. The effect of the heat transfer by conduction through the composite as well as the internal heat
generated by the cure reaction is clearly shown, despite the complexity of the process. Finally, good agreement between experimental
data and predicted mathematical model of the crosslinking process in plane sheet mould was shown. 相似文献
12.
In this paper, a variable heating strength model (VHS model) is developed to predict transient heat conduction from a vertical
rod buried in a semi-infinite medium. Unlike past studies, the current VHS model permits a VHS along the rod. Both axial heat
conduction through the rod and lateral heat conduction to the surrounding ground are modeled. A derived distribution of axial
heating strength is then applied to a finite line heat source model to predict transient temperature changes in the surrounding
medium. The predicted results show how the rod’s radius and ground’s thermal conductivity affect the vertical variation of
heating strength and temperature response. Additional simulations predict the long-term temperature increase in the ground,
due to a power transmission tower installed in a region of initially frozen ground. 相似文献
13.
Comparative numerical study of laminar heat transfer characteristics of annular tubes with sinusoidal wavy fins has been conducted
both experimentally and numerically with Re = 299–1,475. The uniform heat flux is imposed on the tube outside wall surface.
Two tube materials (copper and stainless steel) are considered. It is found that the fluid temperature profile is not linear
but convex along the flow direction due to the axial heat conduction in tube wall, and the effects of axial heat conduction
on the heat transfer decreases with an increase in Reynolds number or decrease in tube wall thermal conductivity. The axial
distributions of local Nusselt number could reach periodically fully developed after 3–5 cycles. The convectional data reduction
method based on the traditional method should be improved for tube with high thermal conductivity or low Reynolds numbers,
Otherwise, the heat transfer performance of internally finned tube may be underestimated. 相似文献
14.
A theoretical solution is presented for the convective heat transfer of Giesekus viscoelastic fluid in pipes and channels,
under fully developed thermal and hydrodynamic flow conditions, for an imposed constant heat flux at the wall. The fluid properties
are taken as constant and axial conduction is negligible. The effect of Weissenberg number (We), mobility parameter (α) and Brinkman number (Br) on the temperature profile and Nusselt number are investigated. The results emphasize the significant effect of viscous
dissipation and fluid elasticity on the Nusselt number in all circumstances. For wall cooling and the Brinkman number exceeds
a critical value (Br
1), the heat generated by viscous dissipation overcomes the heat removed at the wall and fluid heats up longitudinally. Fluid
elasticity shifts this critical Brinkman number to higher values. 相似文献
15.
Experimental study on axial wall heat conduction for convective heat transfer in stainless steel microtube 总被引:1,自引:0,他引:1
Distilled water and nitrogen gas used as the working fluids flow through the stainless steel microtube with inner diameter
168 μm outer diameter 406 μm. Using the Joule heating, the wall temperature field photos of the microtube is acquired by employing
an IR camera and the temperature and the volume flow rate of the inlet and the outlet of microtube are measured. A correlation
between the axial wall heat conduction and the convective heat transfer is obtained by theoretical analysis based on the experimental
results. The investigative results clearly show that the axial heat conduction can reduce the convective heat transfer in
the stainless steel microtube and the decrement may reach 2% compared to the convective heat transfer when the working fluid
is nitrogen gas, however, the decrement can be neglected for distilled water as the working fluid. 相似文献
16.
We present the theory of space–time elasticity and demonstrate that it is the extended reversible thermodynamics and gives the coupled model of thermoelasticity and heat conductivity and involves traditional thermoelasticity. We formulate the generally covariant variational model’s dynamic thermoelasticity and heat conductivity in which the basic kinematic and static variables are unified tensor objects (subject, matter). Variation statement defines the whole set of the initial-boundary problems for the 4D vector governing equation (Euler equation), the spatial projections of which define motion equations and the time projection gives the heat conductivity equation. We show that space–time elasticity directly implies the Fourier and the Maxwell–Cattaneo laws of heat conduction. However, space–time elasticity is richer than classical thermoelasticity, and it advocates its own equations of motion for coupled thermoelasticity. Moreover, we establish that the Maxwell–Cattaneo law and Fourier law can be defined for the reversible processes as compatibility equations without introducing dissipation. We argue that the present framework of space–time elasticity should prove adequate to describe the thermoelastic phenomena at low temperatures for interpreting the results of molecular simulations of heat conduction in solids and for the optimal heat and stress management in the microelectronic components and the thermoelectric devices. 相似文献
17.
In this paper, the authors introduce a robust numerical technique for radiation–conduction heat transfer in the high temperature
fields of gas turbine combustors. The conduction and radiation effects are analyzed by a differential and an integral equation,
respectively. Using discrete ordinates for the angular discretization of the integral equation for the radiation effects and
a Galerkin discretization for the heat equation, the authors propose a fast multilevel algorithm to solve the fully discretized
problem. The algorithm uses the same mesh hierarchy for both radiation and conduction effects, but with two different smoothing
operators. Numerical results are shown for test problems in three space dimensions, and comparisons to other methods are also
given. 相似文献
18.
The two-dimensional quasi-steady conduction equation governing conduction controlled rewetting of an infinite tube, with
outer surface flooded and the inside surface subjected to a constant heat flux, has been solved by Wiener–Hopf technique.
The solution yields the quench front temperature as a function of various model parameters such as Peclet number, Biot number
and dimensionless heat flux. Also, the dryout heat flux is obtained by setting the Peclet number equal to zero, which gives
the maximum sustainable heat flux to prevent the dryout of the coolant.
Received on 6 September 2000 / Published online: 29 November 2001 相似文献
19.
The transient heat conduction equation in a finite slab undergoing phase change (two-phase problem of melting and solidification),
with isothermal, adiabatic or convective boundary conduction is studied by the network simulation method; solid phase conductivity
and specific heat are assumed to be dependent on temperature. Ablation, as a particular case, is also analysed. A network
model is established for a cell and boundary conditions are added to complete the whole network model. No restrictions exist,
as to the kinds of linear and non-linear boundary conditions, Stefan number values or the initial conditions (when hypotheses
concern of the Stefan problem, numerical and exact solutions are compared for a large interval of Stefan numbers; simulation
values show good agreement). Movement of the solid–liquid boundary and thermal fields are determined in all cases.
Received on 10 May 2000 / Published online: 29 November 2001 相似文献
20.
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