In the second part, they present selected theoretical and numerical problems in the form of exercises with their subsequent solutions. Using heating rate measurements to solve the inverse heat conduction problem for heat. A bayesian inference approach is presented for the solution of the inverse heat conduction problem. Given an interior temperature versus time, find the surface heat flux versus time. Firstly, inverse heat conduction model is developed based on the formulation of direct and inverse problem. The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of twodimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. On the contrary, the inverse heat conduction problem involves the. In the heat conduction problems if the heat flux andor temperature histories at the surface of a solid body are known as functions of time, then the temperature. In this research, we use the temperature sensors on the wall surface of the heat sinks to predict the unknown heat flux boundary of the fins as shown in fig. An analytical study of sensitivity parameter is carried out in order to understand. The accurate knowledge of heat transfer coefficients is essential for the design of precise heat transfer operations. Solving direct and inverse heat conduction problems jan.
Birla goa campus 1nh 17b, bypass road, zuarinagar, sancoale, goa, india abstract the inverse method has been adopted for finding the heat flux on a plate from the temperature data. Solving of twodimensional unsteady inverse heat conduction. For the present inverse heat conduction problem, the timevarying strength g p t of the plane heat source is regarded as unknown. Introduction in the heat conduction problems if the heat fl ux andor temperature histories at the surface of a solid body are known as functions of time, then the temperature distribution can be found. The book presents a solution for direct and inverse heat conduction problems. Pdf inverse heat conduction problem of estimating timevarying. Ihcp has numerous important applications in various sciences and engineering. Estimation of unknown boundary functions in an inverse. A comparative study of explicit and implicit finite element methods applied to the solution of inverse heat conduction problem is studied under identical conditions of the sensor location. The tasks of inverse heat problems are detection of heat conduction properties of the medium from some information of the solution, i. Pdf a quasireversibility regularization method for an. The inverse problem consists in the restoration simultaneously with the solution of an.
On an inverse problem of reconstructing a heat conduction. The magnitude of the heat source is assumed to be unknown and vary with. Application of meshless methods for solving an inverse heat. The inverse heat conduction problem of determining the unknown boundary conditions exists widely in scientific research and engineering.
The main bottleneck of these heuristics is the high. Pdf statements and use of inverse problems in studying heat transfer processes and designing engineering units. A new inverse algorithm is proposed for the reconstruction of the total heat exchange factor, which is concerned with transient heat conduction problems. Neisi received 28 may 2002 and in revised form 9 may 2005 this note considers the problem of estimating unknown timevarying strength of the temporaldependent heat source, from measurements of the temperature inside the. Pdf we present the solution of the following inverse problems. A solution to the twodimensional inverse heat conduction. Inverse estimation of boundary heat flux for heat conduction model 75 is required to develop an algorithm with special considerations. Introduction under analysis is a nonclassical problem on heat conduction, with the known bodys surface temperature and surface heat flow. Gupta department of mechanical engineering, the university of alabama, tuscaloosa, al, 35487, usa email. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion. Three different methods, the tikhonov regularization method, the singular value decomposition svd method, and the levenbergmarquardt method, are discussed and their performance is assessed comparatively in the inverse heat conduction problems. Introduction the direct heat conduction problem is to obtain the interior temperature distribution of a body on the basis of the given boundary conditions.
Onedimensional formulation of heat conduction problem in a sphere was used. Inverse heat conduction problem of an elliptical plate. Finite difference method was adopted for the solution of the heat conduction problem. Inverse heat conduction problem in welding simulation. Juss using the inverse method is the main subject of this work. Artificial data for the sand surface temperature and at two different locations below the sand surface are obtained through. The inverse heat conduction problem ihcp involves the calculation of surface heat flux andor temperature histories from transient, measured temperatures at an interior point of a thermally conducting solid. This is due to the fact that the inverse problem is inherently illposed.
Secondly the inverse algorithm is constructed and tested. A sharp impulse form of input can be determined very precisely by means of the rlsa. Estimation of unknown boundary functions in an inverse heat. Abstractthis paper contains a heat conduction problem for an elliptical plate with heat transfer on the upper and lower surfaces, to determine the temperature with the help of mathieu function and integral transform technique. The ihcp is frequently encountered, for example, in the estimation of surface heat transfer from. Determination of the thermal conductivity and specific heat. A quasireversibility regularization method for an inverse heat conduction problem without initial data.
Inverse heat transfer problems ihtp rely on temperature andlor heat flux measurements. The unknown total heat exchange factor is treated as the optimization variable, and the errors to be minimized are the differences between the calculated temperatures and the measured ones. Inverting the heat equation is a problem of great interest in the sciences and engineering, in particular for modeling and monitoring applications 2. Numerical methods are presented for solving an inverse problem of heat conduction. Inverse heat conduction problem, nonlinear, twodimensional 1.
The introduction of complex variable to solve the gradient matrix of the objective function obtains. Pdf an inverse heat conduction problem is solved by using alifanovs iterative regularization method to estimate the timevarying heat transfer. Numerical solution of axisymmetric inverse heat conduction. Numerical solutions to an inverse problem of heat conduction. Uncertainty in temperature measurements is modeled as stationary zeromean white noise. The success of the inverse heat conduction problems ihcps lies largely in how the effect of noise in the measurements is regularized so that the solutions become least polluted. Precise evaluation of thermal contact conductance tcc is essential for the thermal and mechanical analysis of a thermal system found in different engineering applications. Estimation of thermal contact conductance using transient. Inverse heat conduction problems krzysztof grysa kielce university of technology poland 1. Solving the inverse heat conduction problem using nvlink. A fundamental solution method for inverse heat conduction. In this paper, the authors develop an inverse heat conduction problem algorithm to find the surface heat flux in green sand molds.
A contribution to the solution of the inverse heat conduction. By specifying the boundary conditions at a single location, an exact solution is obtained as a rapidly convergent series with the wellknown, lumped capacitance approximation as the leading term. An exact solution of the inverse problem in heat conduction. Inverse problem on heat conduction in heterogeneous medium. In the first part, the authors discuss the theoretical basis for the heat transfer process.
Application of repulsive particle swarm optimization for. The inverse thermoelastic problem consists of determination of the temperature of the heating medium, the heat flux on the boundary surfaces of the solid when the conditions of the displacement and stresses are known at the some points of the solid under consideration. The stability and convergence of numerical solutions are investigated and the numerical results are presented and discussed for some test problems. The case of molten metal solidifying through cooling in a sand mold is considered. In an attempt to stabilize the solution to the inverse heat conduction problem, frankel and keyhani 1997 introduced the idea of using temperature derivatives rather than temperature measurements. An analysis of inverse heat conduction problem on irregular. An inverse heat conduction problem advances in algebra. In 16, the method of fundamental solutions mfs is firstly proposed to tackle the inverse heat conduction problem and later applied in 24,29 to handle the inverse source problem.
A solution to the twodimensional inverse heat conduction problem. Twodimensional inverse heat conduction problem using a. Solution of inverse heat conduction problem using explicit. Pdf a gradient descent method for solving an inverse. In this work, 1d inverse heat conduction method has been employed for. Pdf 1 inverse heat conduction problems semantic scholar. Inverse heat conduction problem in a semiinfinite circular. Inverse and optimization problems in heat transfer inverse. International journal of heat and mass transfer 40. However, there is a fundamental difference between the direct and the inverse problem. The determination of these values requires inverse heat transfer calculations, which are usually based on heuristic optimisation techniques, like genetic algorithms or particle swarm optimisation. The inverse heat conduction problem ihcp involves the calculation of surface heat flux andor temperature histories from transient, measured temperatures at. Reconstruction of the total heat exchange factor using the. Solution to twodimensional steady inverse heat transfer.
The posterior probability density function ppdf of the boundary heat flux is computed given temperature measurements within a conducting solid. For the inverse problem solutions, the homotopy perturbation method was also employed in works 27, 28. An inverse problem in unsteady heat conduction is one for which boundary conditions are prescribed internally, the surface conditions being unknown. Applications range from the estimation of constant heat transfer parameters to the mapping of spatially and timely varying functions, such as heat sources, fluxes and thermophysical properties. Nowadays, inverse analyses are encountered in single and multimode heat transfer problems, dealing with multiscale phenomena. Heatequationexamples university of british columbia. It is assumed that the medium is heterogeneous and contains in coefficients of heat clusions. Determination of the thermal conductivity and the specific heat capacity of neem seeds azadirachta indica a. Optimization method for an evolutional type inverse heat. Inverse heat conduction problems ihcps arise in many industrial and engineering appli cations where heat transfer occurs.
The inverse problem consists in the restoration simultaneously with the solution of an unknown righthand side of. A hybrid regularization method for inverse heat conduction. Inverse transient heat conduction problems springerlink. Depending on the form of the plane heat source, the inverse heat conduction problem can be solved either as a parameter estimation approach or as a function estimation approach. In this paper, an inverse heat conduction problem will be considered. Inverse heat conduction is of interest in a wide range of scienti c and. We consider an inverse problem for a onedimensional heat equation with involution and with periodic boundary conditions with respect to a space variable. Determination of the thermal conductivity and specific. Sabherwal 1965, 1966, studied inverse problem in heat conduction. Solution of the inverse conduction problem aiaa journal. The analysis is developed specifically for spheres. The optimization methods for the inverse heat conduction and solidification problems are discussed. Burggraf or 1964 an exact solution of the inverse problem in heat conduction theory and applications.
By reducing this inverse problem to an integral equation and using an overspecified condition, it is shown that the solution to this problem exists, and this solution is unique. A bayesian inference approach to the inverse heat conduction. Keywords inverse heat conduction nonlinear boundary condition mollification space marching method 1 introduction. An analytical approach for inverse heat conduction problem kevin agrawal1 1department of mechanical engineering, bits pilani, k.
Solving direct and inverse heat conduction problems. Inverse heat conduction problem of an elliptical plate s. Siam journal on scientific and statistical computing. On account of recursive algorithm, an online estimation can be used in place of batch form offline estimation.
A gradient descent method for solving an inverse coefficient heat conduction problem, russian journal of numerical analysis and applications, 11 2008 3445. Although there has been much research into the problem, most of it has been focused on the one or twodimensional linear problems and little has. Exact solutions of the inverse heat conduc tion problems are very important, because they provid e closed form expressions for the heat flux in. The direct heat conduction problems are concerned with the value of heat flux on unknown boundary in interior region when the initial and boundary conditions, thermal physical properties and heat generation are acquired easily. Rate to solve the inverse heat conduction problem by paul r. Inverse heat conduction method provides an effective tool for the estimation of thermal contact conductance at the interface of two bodies in contact. The inverse heat conduction problem ihcp, like the vast majority of inverse problems, is known to be illposed. This problem simulates the process of heat propagation in a thin closed wire wrapped around a weakly permeable insulation. An inverse heat conduction problem with heat flux measurements.
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