Inverse Heat Convection Problem Research Articles

Solving an inverse heat convection problem with an implicit forward operator by using a projected quasi-Newton method

We consider the quasilinear 1D inverse heat convection problem of determining the enthalpy-dependent heat fluxes from noisy internal enthalpy measurements. This problem arises in the accelerated cooling process of producing thermomechanically controlled processed heavy plates made of steel. In order to adjust the complex microstructure of the underlying material, the Leidenfrost behavior of the hot surfaces with respect to the application of the cooling fluid has to be studied. Since the heat fluxes depend on the enthalpy and hence on the solution of the underlying initial boundary value problem (IBVP), the parameter-to-solution operator, and thus the forward operator of the inverse problem, can only be defined implicitly. To guarantee well-defined operators, we study two approaches for showing existence and uniqueness of solutions of the IBVP. One approach deals with the theory of pseudomonotone operators and so-called strong solutions in Sobolev–Bochner spaces. The other theory uses classical solutions in Hölder spaces. Whereas the first approach yields a solution under milder assumptions, it fails to show the uniqueness result in contrast to the second approach. Furthermore, we propose a convenient parametrization approach for the nonlinear heat fluxes in order to decouple the parameter-to-solution relation and use an iterative solver based on a projected quasi-Newton (PQN) method together with box-constraints to solve the inverse problem. For numerical experiments, we derive the necessary gradient information of the objective functional and use the discrepancy principle as a stopping rule. Numerical tests show that the PQN method outperforms the Landweber method with respect to computing time and approximation accuracy.

Inverse identification of viscosity coefficient for Newtonian and non‐Newtonian slurries during the turbulent pipeline transportation

AbstractSlurry viscosity is an important parameter that can be used for slurry characterization and pipeline design. This study proposed an inversion method to identify the viscosity coefficient of slurries in turbulent pipeline flow. An inverse heat convection problem with unknown viscosity for Newtonian and non‐Newtonian slurries was solved in a fully developed turbulent pipe flow, and a modified mixing length theory in the turbulent model was applied to improve the estimation accuracy. Through the inversion calculation, the viscosity coefficient was obtained by temperature profile at several measurement positions. An experimental setup was established, and several experiments were conducted to verify the viscosity estimations for slurry flow in this study. The results showed that the method was reliable for identifying the slurry viscosities in the turbulent state and the modified mixing length model can effectively improve the inversion accuracy. This method provided an effective way to detect the rheological properties for determining the operation mode of turbulent slurry pipelines.

Identification of viscosity and solid fraction in slurry pipeline transportation based on the inverse heat transfer theory

A method based on the inverse heat transfer theory for identifying the viscosity coefficient and solid volume fraction of slurries is proposed in this study. An inverse heat convection problem for non-Newtonian fluid is solved in a fully developed laminar circular pipe flow based on temperature measurements obtained at several radial locations in the stream. An optimal estimation of the apparent viscosity of slurries is obtained by the relationship between temperature profile and apparent viscosity. The solid volume fraction in the pipe can be eventually determined through the applicable relation between solid loading and viscosity. Several experiments were conducted to verify the accuracy of the method. Coal-water slurry and coal-slime slurry were considered for the validation. Comparisons between the estimated values and experimental data showed that this method was reliable for predicting viscosity coefficient and solid fraction in slurry fluid. It is expected to be useful in detecting the rheological properties for determining operation mode of slurry pipelines.

Development of the ball-spine algorithm for the shape optimization of ducts containing nanofluid

ABSTRACTIn this paper a novel shape design method is introduced for the numerical solution of inverse heat convection problems (IHCPs) of nanofluids. The proposed method is a novel extension of the ball-spine algorithm (BSA) inverse method, which is recently adapted for inverse heat transfer problems (IHTPs). Here it is shown how, by a novel physical-sense remedy, the method is applicable to IHCPs as well. In this respect, after validation of the proposed method, two types of IHCPs are introduced and numerically solved. In both types of introduced inverse problems, the objective is shape optimization of a duct containing such steady-state incompressible laminar nanofluid flow that it satisfies a prescribed heat flux distribution along the walls of the geometry. The results show merits and robustness of the BSA application in capturing the target geometry corresponding to a given heat flux distribution in forced heat convection problems with a low computational cost.

On the inverse heat convection problem of the flow over a cascade of rectangular blades

In this study, an inverse algorithm based on the conjugate gradient method is applied to a steady flow over a cascade of rectangular blades to estimate the inlet flow temperature. The objective is to study the difficulties associated with inverse heat convection problems. Therefore, the measurement quantity has been deliberately placed at five different locations over the domain, each of them covered by a unique flow feature. The computation shows that at very low Reynolds number, the accuracy of the inverse method is not affected by the relative position between the estimated and measurement quantities. At a higher Reynolds number, however, the accuracy of the inverse method strongly depends on the relative position between the two quantities. The inverse method only returns satisfactory estimation for some cases but not others.

Resolution of linear inverse forced convection problems using model reduction by the Modal Identification Method: application to turbulent flow in parallel-plate duct

Inverse Heat Convection Problems have received attention only recently. They usually involve the use of a high order model corresponding to the spatial discretization of the domain. In this numerical study, the possibility to quickly solve such a problem with a low order model is analysed. The proposed method can be applied to any forced convection problem, whatever the geometry, as far as it is linear. Starting from a Detailed Model (DM) of the system, the Modal Identification Method is applied to build a Reduced Model (RM), which can be used to solve the inverse problem. The inversion procedure is sequential and requires no iterations. The function specification method is used to stabilize the inverse problem. An illustrative application is given. Turbulent forced convection is considered, with a hydrodynamically fully developed, thermally developing, incompressible, turbulent flow of a newtonian and constant property fluid inside a parallel-plate duct. Axial conduction in the flow is neglected. Two wall heat flux densities, varying with time, are estimated from the knowledge of simulated transient temperature measurements inside the fluid. When solving the inverse problem with RM instead of DM, a drastic reduction of computing time is obtained (with a reduction factor up to 11,000 in the present study), without significant loss of accuracy. Effects of functional form of the unknowns, sensors number and position, measurement error, on the accuracy of estimates are examined.

Identification of velocity distribution in a turbulent flow inside parallel-plate ducts from wall temperature measurements

An Inverse Heat Convection Problem is investigated in this numerical study. Turbulent forced convection is considered, with a hydrodynamically fully developed, thermally developing, incompressible, constant property flow inside a parallel-plate duct. Velocity and effective diffusivity distributions of the turbulent model are characterised by a Reynolds number b + based on the shear stress velocity. The identification of b + from simulated wall temperature measurements is presented. A heat flux density is applied along the channel length and temperature responses are taken at the wall external surface. Heat transfer has to act as a small but measurable perturbation of the flow. The inverse problem is recast into an optimisation problem solved with a Quasi-Newton method. Reynolds numbers 105 and 106, corresponding to two different values of b + , are considered. Effects of sensor number and location, as well as magnitude of measurement error on the estimation accuracy, are examined.

Nonlinear parameter estimation in laminar forced convection within a circular sector tube

In this article we examine an inverse heat convection problem of estimating unknown parameters of a parameterized variable boundary heat flux. The physical problem is a hydrodynamically developed, thermally developing, three-dimensional steady state laminar flow of a Newtonian fluid inside a circular sector duct, insulated in the flat walls and subject to unknown wall heat flux at the curved wall. Results are presented for polynomial and sinusoidal trial functions, and the unknown parameters as well as surface heat fluxes are determined. Depending on the nature of the flow, on the position of experimental points the inverse problem sometimes could not be solved. Therefore, an identification condition is defined to specify a condition under which the inverse problem can be solved. Once the parameters have been computed it is possible to obtain the statistical significance of the inverse problem solution. Therefore, approximate confidence bounds based on standard statistical linear procedure, for the estimated parameters, are analyzed and presented.

SIMULTANEOUS ESTIMATION OF INLET TEMPERATURE AND WALL HEAT FLUX IN TURBULENT CIRCULAR PIPE FLOW

An inverse heat convection problem is solved for simultaneous estimation of unknown inlet temperature and wall heat flux in a thermally developing, hydrodynamically developed turbulent flow in a circular pipe based on temperature measurements obtained at several different locations in the stream. The direct problem of turbulent forced convection is solved with a finite difference method with appropriate algebraic turbulence modelling. Although we seek for two unknown functions, we formulate the inverse problem as one of parameter estimation through the representation of the unknown inlet temperature profile and the wall heat flux distribution by one-dimensional finite element interpolation. Nodal values of the inlet temperature and the wall heat flux at chosen positions are determined as unknown parameters through the Levenberg–Marquardt algorithm for minimization procedure. Numerical results for several testing cases with different magnitudes of measurement errors are examined by using simulated experimental data. The effects of the number and the locations of the temperature measurement points are discussed.

Estimation of unknown wall heat flux in turbulent circular pipe flow

An inverse heat convection problem is solved for the estimation of a nonuniform wall heat flux in a thermally developing, hydrodynamically developed turbulent flow in a circular pipe based on temperature measurements obtained at several different locations in the stream. The direct problem of turbulent forced convection is solved with a finite difference method with appropriate algebraic turbulence modelling. The unknown wall heat flux is represented by a one-dimensional finite element interpolation. Nodal values at several chosen points are determined as unknown parameters by the Levenberg-Marquardt algorithm. The effects of sensor number and position are examined.

A method of solving inverse convection problems by means of mode reduction

Determination of wall heat flux for laminar flow inside a duct from the temperature measurement within the flow is a typical inverse heat convection problem which is ill-posed. In the present paper, an efficient method based on the Karhunen–Loève Galerkin procedure (Park and Cho, 1996, Chem. Engng Sci. 51, 81–98) is proposed for the solution of this kind of inverse heat transfer problems. Employing the Karhunen–Loève Galerkin procedure, which is a Galerkin method employing empirical eigenfunctions of the Karhunen–Loève decomposition, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and thus convert a given system into a model with a minimum degree of freedom, resulting in drastic reduction of computation time. The performance of the present technique of inverse analysis using the Karhunen–Loève Galerkin procedure is evaluated by numerical experiments on the identification of unknown functions of wall heat flux, and is found to be very accurate as well as efficient.

Utilization Of The Algor Package In Solution OfThe Inverse Heat Convection Problems

This paper presents the method of application of the commercial package Algor in the inverse heat convection problems solutions. Due to the Algor functions it has to be supplemented by additional modules which allows us to solve full inverse problem. Constructed hybrid program make it possible to solve various formulations of inverse problems. Two of them are dealt with here. These are evaluating boundary heat flux from the internal temperature measurements (inverse formulation of energy equation), and estimation of inlet velocity profile from internal velocity measurements (inverse formulation of momentum equation).