One-dimensional Inverse Heat Conduction Problem Research Articles

Analytical solution of the one-dimensional nonlinear inverse heat conduction problem and its applications

An analytical solution of the nonlinear inverse heat conduction problem is obtained and its application to identification of the boundary conditions on the components of the flow-through part of a gas turbine engine is demonstrated.

A simple inverse heat conduction method with optimization

A simple numerical method for one-dimensional nonlinear inverse heat conduction problem solving based on finite difference principle is presented. Time-step size is variable and chosen in such a way ensuring optimal results. Numerical stability analysis is derived and stochastic error contributions to the solution quality and inversely computed distance influence are demonstrated. Simulated experiments using inexact data illustrate usability of the method.

An Adaptive Inverse Heat Conduction Method With Automatic Control

An adaptive sequential method is presented for solving the one-dimensional inverse heat conduction problem. The step size, order of parameterization, and amount of the step retained are variable and chosen automatically for each sequence such that optimal, stable results are obtained. A statistical analysis accounting for the stochastic error contributions from both the measured and initial temperatures is derived. Results from the statistical analysis are used to predict stability or instability for a given selection of parameters controlling the inverse method. Simulated experimental applications using inexact data illustrate the practicality of the approach and the effectiveness of the automatic control criteria.

The two transition boiling curves and solid-liquid contact on a horizontal surface

Transition pool boiling heat transfer from a horizontal circular surface is studied experimentally. Deionized water and refrigerant 113 are the working liquids at 1 atm pressure. The solution of the one-dimensional inverse heat conduction problem by Kastelin is extended to include a polynomial function of any degree for temperature versus time data. The existence of two transition boiling curves, i.e., separate transient heating and transient cooling curves, is confirmed. This finding is supported by independent measurement of solid-liquid contact. The heating transition boiling curve is higher than the cooling curve. Surface wettability has the same effect on both curves. As the contact angle increases, the transition boiling heat flux decreases. The two transition boiling curves are distinct even at zero contact angle. The steady-state measurements are generally higher than the transient measurements. There is no evidence of any jump among the steady-state, heating, and cooling curves.

A mollified space marching finite differences algorithm for the inverse heat conduction problem with slab symmetry

The one-dimensional inverse heat conduction problem (IHCP) for a slab is considered. A new solution algorithm based on a data filtering interpretation of the mollification method is presented and a fully explicit space marching finite differences scheme is developed. After showing the numerical stability of the algorithm, the efficiency of the method is demonstrated by means of several examples. The numerical results show the procedure to be very useful in the presence of noisy data, even for some nonlinear cases.

A stable space marching finite differences algorithm for the inverse heat conduction problem with no initial filtering procedure

We consider the one-dimensional semi-infinite linear inverse heat conduction problem (IHCP) and present a new solution algorithm based on singular perturbation techniques. The new method successfully incorporates the needed initial filtering procedure of the noisy data into the marching scheme. The concept of formal stability for the IHCP is analyzed and its relationship with the high frequency components of the measured data funciton is further studied by comparing the new method with the mollification method and the method of Weber. A fully explicit space marching finite differences scheme is developed and several numerical experiments of interest, showing the accuracy and stability properties of the algorithm in the presence of noisy data and for small dimensionless time steps, are investigated.

Emissivity estimation through the solution of an inverse heat-conduction problem

A new transient calorimetric method to measure the total hemispherical emissivity of opaque surfaces as a function of temperature is presented. A disk-shaped specimen for which the emissivity is required to be measured is placed in an evacuated vessel. One of its two surfaces is heated uniformly by means of an electrical resistance. The total hemispherical emissivity of the other—free—surface, which is parallel and very near to a uniformly cooled plate, can then be estimated using only transient temperature measurements at two locations inside the specimen. A model based on the solution of a one-dimensional inverse heat-conduction problem is used. This model allows one to estimate the surface temperature and net radiative heat flux from which the emissivity can be obtained. This property can also be estimated for paints and other surface coatings by covering the free surface with a thin layer of the coating concerned.

Parameter selection by discrete mollification and the numerical solution of the inverse heat conduction problem

A procedure for the numerical solution of the one-dimensional inverse heat conduction problem, based on the computaion of the solution associated with a suitable filtered version of the noisy data by discrete mollification is presented and a parameter choice criterion, which automatically determines the radius of mollification as a function of the amount of noise in the data, is introduced. Several numerical examples of interest are also analyzed, showing the accuracy and stability properties of the method.

SURFACE VARIANCE ESTIMATES USING AN ADJOINT FORMULATION FOR A ONE-DIMENSIONAL NONLINEAR INVERSE HEAT CONDUCTION TECHNIQUE

The one-dimensional nonlinear inverse heat conduction problem is considered. A new technique for estimating the surface variances of the predicted surface fluxes and temperatures based on an adjoint formulation is presented. The surface variances are related to the measurement variances and to an estimate of the initial condition variances. The only assumption necessary to apply the technique is that of additive measurement errors. Two test cases with three sets of boundary conditions are studied. The surface variance estimates given by the adjoint formulation and direct estimation are shown to be in good agreement.

Estimation of aerodynamic heat transfer in free flight at Mach number up to 4.7

A one-dimensional inverse transient heat conduction problem with a radiation boundary condition is analysed using implicit finite difference approximation. An iterative procedure is described which predicts unknown surface conditions from the measured thermocouple temperature. A unified thermal analysis (temperature/heat flux prediction) of the sounding rocket aerothermodynamic environment is presented using flight data which are transmitted to ground test station.

Critical heat flux and transition to film boiling in a subcooled flow boiling system.

Wall temperature fluctuations at the CHF condition are measured for subcooled flow boiling. From the measured inner wall temperature history, the surface heat flux and the outer wall temperature are computed by a numerical method for one-dimensional inverse heat conduction problem. Heat transfer characteristics during overheating and quenching periods at the CHF condition and the wall superheats at rewetting point and minimum heat flux point are presented. The results show that the wall temperature rise at the CHF condition consists of the temperature fluctuations accompanied with passage of large coalescent bubbles and a subsequent sharp increase under film boiling condition.

A transient one-dimensional inverse heat conduction problem with overspecified data at one boundary

For one-dimensional transient heat conduction, a procedure is developed to estimate the temperature at one boundary when both the temperature and heat flux are measured at the other boundary. The Laplace transform technique is employed and the inverse Laplace transform is carried out by using a novel technique. Exact and noisy data are used to infer the unknown boundary temperature. It is shown that the present procedure is accurate and also stable to measurement errors.

Solution of the linear one-dimensional inverse heat-conduction problem on the basis of a hyperbolic equation

The linear problem of determining the temperature in an infinite one-dimensional plate with a stationary heat sensor and a stationary boundary is solved. The allowable approximation time steps in the calculations can be diminished by using a hyperbolic heat-conduction equation with a suitably chosen hyperbolicity parameter.

Determination of boundary thermal regime from the solution of an inverse heat-conduction problem

We consider control schemes for the solution of a one-dimensional inverse heat-conduction problem in a region with moving boundaries. We investigate the computational aspects of the construction of effective algorithms.