Solving direct and inverse heat conduction problems jan. An analytical approach for inverse heat conduction problem kevin agrawal1 1department of mechanical engineering, bits pilani, k. In this paper, an inverse heat conduction problem will be considered. On an inverse problem of reconstructing a heat conduction. The case of molten metal solidifying through cooling in a sand mold is considered. A solution to the twodimensional inverse heat conduction problem. Determination of the thermal conductivity and the specific heat capacity of neem seeds azadirachta indica a. An analytical study of sensitivity parameter is carried out in order to understand. Inverting the heat equation is a problem of great interest in the sciences and engineering, in particular for modeling and monitoring applications 2. An inverse heat conduction problem advances in algebra. Inverse heat conduction problem of an elliptical plate s. The inverse heat conduction problem of determining the unknown boundary conditions exists widely in scientific research and engineering. Firstly, inverse heat conduction model is developed based on the formulation of direct and inverse problem. The magnitude of the heat source is assumed to be unknown and vary with.
Pdf 1 inverse heat conduction problems semantic scholar. In this paper, the authors develop an inverse heat conduction problem algorithm to find the surface heat flux in green sand molds. An analysis of inverse heat conduction problem on irregular. The inverse heat conduction problem ihcp, like the vast majority of inverse problems, is known to be illposed. Pdf a gradient descent method for solving an inverse. Estimation of unknown boundary functions in an inverse heat. 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. Application of meshless methods for solving an inverse heat. Numerical solution of axisymmetric inverse heat conduction. Precise evaluation of thermal contact conductance tcc is essential for the thermal and mechanical analysis of a thermal system found in different engineering applications.
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. Heatequationexamples university of british columbia. Twodimensional inverse heat conduction problem using a. The main bottleneck of these heuristics is the high. 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. The inverse problem consists in the restoration simultaneously with the solution of an unknown righthand side of. On the contrary, the inverse heat conduction problem involves the. The tasks of inverse heat problems are detection of heat conduction properties of the medium from some information of the solution, i. A fundamental solution method for inverse heat conduction. Inverse heat conduction problem in a semiinfinite circular. 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. 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.
Nowadays, inverse analyses are encountered in single and multimode heat transfer problems, dealing with multiscale phenomena. The inverse problem consists in the restoration simultaneously with the solution of an. Determination of the thermal conductivity and specific heat. Secondly the inverse algorithm is constructed and tested. Inverse problem on heat conduction in heterogeneous medium. This problem simulates the process of heat propagation in a thin closed wire wrapped around a weakly permeable insulation. Inverse and optimization problems in heat transfer inverse. Pdf a quasireversibility regularization method for an.
Artificial data for the sand surface temperature and at two different locations below the sand surface are obtained through. Introduction the direct heat conduction problem is to obtain the interior temperature distribution of a body on the basis of the given boundary conditions. A solution to the twodimensional inverse heat conduction. Inverse heat transfer problems ihtp rely on temperature andlor heat flux measurements. 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. 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. 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. 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. The analysis is developed specifically for spheres. It is assumed that the medium is heterogeneous and contains in coefficients of heat clusions. A bayesian inference approach to the inverse heat conduction. Given an interior temperature versus time, find the surface heat flux versus time. The ihcp is frequently encountered, for example, in the estimation of surface heat transfer from. A sharp impulse form of input can be determined very precisely by means of the rlsa.
Pdf an inverse heat conduction problem is solved by using alifanovs iterative regularization method to estimate the timevarying heat transfer. Inverse heat conduction is of interest in a wide range of scienti c and. Pdf inverse heat conduction problem of estimating timevarying. 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. An exact solution of the inverse problem in heat conduction. Ihcp has numerous important applications in various sciences and engineering. A new inverse algorithm is proposed for the reconstruction of the total heat exchange factor, which is concerned with transient heat conduction problems. The stability and convergence of numerical solutions are investigated and the numerical results are presented and discussed for some test problems. We consider an inverse problem for a onedimensional heat equation with involution and with periodic boundary conditions with respect to a space variable. A gradient descent method for solving an inverse coefficient heat conduction problem, russian journal of numerical analysis and applications, 11 2008 3445. Inverse heat conduction problem in welding simulation. Uncertainty in temperature measurements is modeled as stationary zeromean white noise. Pdf we present the solution of the following inverse problems.
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 inverse heat conduction problem ihcp involves the calculation of surface heat flux andor temperature histories from transient, measured temperatures at. 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. A contribution to the solution of the inverse heat conduction. Onedimensional formulation of heat conduction problem in a sphere was used. 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 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. On account of recursive algorithm, an online estimation can be used in place of batch form offline estimation. 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. The posterior probability density function ppdf of the boundary heat flux is computed given temperature measurements within a conducting solid. 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. However, there is a fundamental difference between the direct and the inverse problem.
Inverse heat conduction problem of an elliptical plate. The optimization methods for the inverse heat conduction and solidification problems are discussed. For the inverse problem solutions, the homotopy perturbation method was also employed in works 27, 28. For the present inverse heat conduction problem, the timevarying strength g p t of the plane heat source is regarded as unknown. The introduction of complex variable to solve the gradient matrix of the objective function obtains. Inverse heat conduction problems krzysztof grysa kielce university of technology poland 1. A quasireversibility regularization method for an inverse heat conduction problem without initial data. Gupta department of mechanical engineering, the university of alabama, tuscaloosa, al, 35487, usa email. Inverse transient heat conduction problems springerlink. Reconstruction of the total heat exchange factor using the. This is due to the fact that the inverse problem is inherently illposed. Numerical methods are presented for solving an inverse problem of heat conduction. In this work, 1d inverse heat conduction method has been employed for.
Solving of twodimensional unsteady inverse heat conduction. 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 statements and use of inverse problems in studying heat transfer processes and designing engineering units. Finite difference method was adopted for the solution of the heat conduction problem. Application of repulsive particle swarm optimization for. Inverse heat conduction problems ihcps arise in many industrial and engineering appli cations where heat transfer occurs. Inverse estimation of boundary heat flux for heat conduction model 75 is required to develop an algorithm with special considerations. Solution of inverse heat conduction problem using explicit. Solution of the inverse conduction problem aiaa journal.
The book presents a solution for direct and inverse heat conduction problems. Using heating rate measurements to solve the inverse heat conduction problem for heat. Juss using the inverse method is the main subject of this work. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion. In the second part, they present selected theoretical and numerical problems in the form of exercises with their subsequent solutions. Solving direct and inverse heat conduction problems. 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. An inverse problem in unsteady heat conduction is one for which boundary conditions are prescribed internally, the surface conditions being unknown. Optimization method for an evolutional type inverse heat. Burggraf or 1964 an exact solution of the inverse problem in heat conduction theory and applications. Introduction under analysis is a nonclassical problem on heat conduction, with the known bodys surface temperature and surface heat flow. 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. Exact solutions of the inverse heat conduc tion problems are very important, because they provid e closed form expressions for the heat flux in.
In the first part, the authors discuss the theoretical basis for the heat transfer process. Inverse heat conduction problem, nonlinear, twodimensional 1. 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. 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. The accurate knowledge of heat transfer coefficients is essential for the design of precise heat transfer operations. 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.
Solution to twodimensional steady inverse heat transfer. 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. Numerical solutions to an inverse problem of heat conduction. International journal of heat and mass transfer 40. Solving the inverse heat conduction problem using nvlink. Determination of the thermal conductivity and specific. An analytical approach for inverse heat conduction problem. Sabherwal 1965, 1966, studied inverse problem in heat conduction. Estimation of unknown boundary functions in an inverse.
Siam journal on scientific and statistical computing. A hybrid regularization method for inverse heat conduction. A bayesian inference approach is presented for the solution of the inverse heat conduction problem. Estimation of thermal contact conductance using transient. Keywords inverse heat conduction nonlinear boundary condition mollification space marching method 1 introduction. An inverse heat conduction problem with heat flux measurements.
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