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A numerical inverse analysis based on explicit sensitivity coefficients is developed for the simultaneous estimation of heat flux and heat transfer coefficient imposed on different parts of boundary of a general irregular heat conducting body made of functionally graded materials with spatially varying thermal conductivity. It is assumed that the thermal conductivity varies exponentially with position in the body. The body considered in this study is an eccentric hollow cylinder. The heat flux is applied on the cylinder inner surface and the heat is dissipated to the surroundings through the outer surface. The numerical method used in this study consists of three steps: 1) to apply a boundary-fitted grid generation (elliptic) method to generate grid over eccentric hollow cylinder (an irregular shape) and then solve for the steady-state heat conduction equation with variable thermal conductivity to compute the temperature values in the cylinder, 2) to propose a new explicit sensitivity analysis scheme used in inverse analysis, and 3) to apply a gradient-based optimization method (in this study, conjugate gradient method) to minimize the mismatch between the computed temperature on the outer surface of the cylinder and simulated measured temperature distribution. The inverse analysis presented here is not involved with an adjoint equation and all the sensitivity coefficients can be computed in only one direct solution, without the need for the solution of the adjoint equation. The accuracy, efficiency, and robustness of the developed inverse analysis are demonstrated through presenting a test case with different initial guesses.

The aim of this paper is to present a very efficient and accurate numerical algorithm to identify a variable (space- and temperature-dependent) heat transfer coefficient in two-dimensional inverse steady-state heat conduction problems involving irregular heat-conducting body shapes in the presence of Dirichlet, Neumann, and Robin boundary conditions. In this numerical method, a boundary-fitted grid generation technique (elliptic) is used to discretize the physical domain (heat-conducting body) and solve for the steady-state heat conduction equation by approximating the derivatives of the field variable (temperature) by algebraic ones. This paper describes a very accurate and efficient sensitivity analysis scheme to compute the sensitivity of the temperatures to variation of the variable heat transfer coefficient. The main advantage of the sensitivity analysis scheme is that it does not require the solution of adjoint equation. The conjugate gradient method (CGM) is used to reduce the mismatch between the computed temperature on part of the boundary and the simulated measured temperature distribution. The obtained results confirm that the proposed algorithm is very accurate, efficient, and robust.

A linearly temperature-dependent thermal conductivity is estimated in steady state heat conduction problems using an inverse analysis. A body fitted grid generation technique is employed to mesh the two-dimensional body and solve the direct heat conduction problem. An efficient, accurate, and easy to implement method is presented to compute the sensitivity coefficients through derived expressions. The main feature of the sensitivity analysis is that all sensitivities can be obtained in one solve, irrespective of the number of unknown parameters. The conjugate gradient method along with the discrepancy principle is used in the inverse analysis to minimize the objective function and achieve the desired solution. The ability to efficiently and accurately recover the non-constant thermal conductivity is demonstrated through a number of benchmark problems.

An inverse analysis is used to simultaneously estimate the thermal conductivity and the boundary shape in steady-state heat conduction problems. The numerical scheme consists of a body-fitted grid generation technique to mesh the heat conducting body and solve the heat conduction equation – a novel, efficient, and easy to implement sensitivity analysis scheme to compute the sensitivity coefficients, and the conjugate gradient method as an optimization method to minimize the mismatch between the computed temperature distribution on some part of the body boundary and the measured temperatures. Using the proposed scheme, all sensitivity coefficients can be obtained in one solution of the direct heat conduction problem, irrespective of the large number of unknown parameters for the boundary shape. The obtained results reveal the accuracy, efficiency, and robustness of the proposed algorithm.

This article presents an inverse problem of determination of a space-dependent heat flux in steady-state heat conduction problems. The thermal conductivity of a heat conducting body depends on the ...

In this study we present a numerical approach to solve steady-state heat conduction problems in functionally graded materials (FGMs). Two different types of material gradations are considered for spatially varying thermal conductivity of FGM: (1) Quadratic material gradation; (2) Exponential material gradation. The proposed numerical procedure is based on finite-difference method and is developed to solve the steady-state heat conduction equation over a general two-dimensional (irregular) heat conducting body (FGM) with Dirichlet, Neumann, and Robin boundary conditions. In addition to presenting an accurate heat conduction equation solution considering an irregular shape and a variety of boundary conditions, the other novel aspect of this study is to identify the constant parameters in the material gradations accurately by an inverse analysis thereby determining the accurate form of gradation. The novelty of the inverse analysis lies in proposing an accurate and efficient explicit sensitivity analysis scheme. The main advantage of the sensitivity analysis scheme is that it is not involved with an adjoint equation and all the sensitivity coefficients can be explicitly computed in only one direct solution. The conjugate gradient method (CGM) is used to reduce the mismatch between the computed temperature on part of the boundary and the simulated measured temperature distribution. The accuracy, efficiency, and robustness of the proposed numerical approach are demonstrated through presenting two test cases.

This article is concerned with a two-dimensional inverse steady-state heat conduction problem. The aim of this study is to estimate the thermal conductivity, the heat transfer coefficient, and the heat flux in irregular bodies (both separately and simultaneously) using a two-dimensional inverse analysis. The numerical procedure consists of an elliptic grid generation technique to generate a mesh over the irregular body and solve for the heat conduction equation. This article describes a novel sensitivity analysis scheme to compute the sensitivity of the temperatures to variation of the thermal conductivity, the heat transfer coefficient, and the heat flux. This sensitivity analysis scheme allows for the solution of inverse problem without requiring solution of adjoint equation even for a large number of unknown variables. The conjugate gradient method (CGM) is used to minimize the difference between the computed temperature on part of the boundary and the simulated measured temperature distributio...

This paper presents a numerical inverse analysis to estimate the thermal conductivity, the heat transfer coefficient, and the heat flux in three dimensional irregular bodies in steady state heat conduction problems. In this study, a 3-D elliptic grid generation technique is used to mesh the irregular body. The 3-D Laplace equation is solved in the computational domain to compute the temperature at any grid point in the meshed body. A novel and very efficient sensitivity analysis scheme is introduced to compute the sensitivity coefficients in gradient based optimization method. Using this sensitivity analysis scheme, one can solve the inverse problem without need to the solution of adjoint equation. The main advantages of the sensitivity analysis scheme are its simplicity, accuracy, and independency of the number of the direct problem solution from the number of the unknown variables which makes the numerical inverse analysis presented here very accurate and efficient. The conjugate gradient method (CGM) is used to minimize the objective function which is the difference between the computed temperature on part of the boundary and the measured temperature. The obtained results confirm that the proposed algorithm is very accurate, robust, and efficient.

The reliability and safety of lithium-ion batteries can be affected by overheating issues. Phase change materials like paraffin due to their large heat capacities are among the best solutions for the thermal management of batteries. In this investigation, multiscale modelling techniques were developed to explore the efficiency in the thermal management of rechargeable batteries through employing the paraffin composite structures. A combined atomistic-continuum multiscale modelling was conducted to evaluate the thermal conductivity of paraffin reinforced with graphene or hexagonal boron-nitride nanosheet additives. In addition, heat generation during a battery service was simulated using the Newman's electrochemical model. Finally, three-dimensional heat transfer models were constructed to investigate the effectiveness of various paraffin composite structures in the thermal management of a battery system. Interestingly, it was found that the thermal conductivity of paraffin nanocomposites can be enhanced by several times but that does not yield significant improvement in the batteries thermal management over the pure paraffin. The acquired findings can be useful not only for the modelling of nanocomposites but more importantly for the improvement of phase change materials design to enhance the thermal management of rechargeable batteries and other electronic devices.

This paper proposes a novel method to implement the Kutta condition in irrotational, inviscid, incompressible flow (potential flow) over an airfoil. In contrast to common practice, this method is not based on the panel method. It is based on a finite difference scheme formulated on a boundary-fitted grid using an O-type elliptic grid generation technique. The proposed algorithm uses a novel and fast procedure to implement the Kutta condition by calculating the stream function over the airfoil surface through the derived expression for the airfoils with both finite trailing edge angle and cusped trailing edge. The results obtained show the excellent agreement with the results from analytical and panel methods thereby confirming the accuracy and correctness of the proposed method.

This paper presents a novel and accurate method to implement the Kutta condition in solving subsonic (subcritical) inviscid isentropic compressible flow over isolated airfoils using the stream function equation. The proposed method relies on body-fitted grid generation and solving the stream function equation for compressible flows in computational domain using finite-difference method. An expression is derived for implementing the Kutta condition for the airfoils with both finite angles and cusped trailing edges. A comparison of the results obtained from the proposed numerical method and the results from experimental and other numerical methods reveals that they are in excellent agreement, which confirms the accuracy and correctness of the proposed method.

This paper is concerned with an optimal shape design (shape optimization) problem in heat transfer. As an inverse steady-state heat transfer problem, given a body locally heated by a specified heat flux and exposed to convective heat transfer on parts of its boundary, the aim is to find the optimal shape of this body such that the temperature is constant on a desired subset of its boundary. The numerical method to achieve this aim consists of a three-dimensional elliptic grid generation technique to generate a mesh over the body and solve for a heat conduction equation. This paper describes a novel sensitivity analysis scheme to compute the sensitivity of the temperatures to variation of grid node positions and the conjugate gradient method (CGM) is used as an optimization algorithm to minimize the difference between the computed temperature on the boundary and desired temperature. The elliptic grid generation technique allows us to map the physical domain (body) onto a fixed computational domain and to d...

This paper deals with an inverse steady-state heat transfer problem. We develop in this work a new numerical methodology to infer the shape a heated body should have for the temperature distribution on part of its boundary to match a prescribed one. This new numerical methodology solves this shape optimization problem using body-fitted grid generation to map the unknown optimal shape onto a fixed computational domain. This mapping enables a simple discretization of the Heat Equation using finite differences and allows us to remesh the physical domain, which varies at each optimization iteration. A novel aspect of this work is the sensitivity analysis, which is expressed explicitly in the fixed computational domain. This allows a very efficient evaluation of the sensitivities. The Conjugate Gradient method is used to minimize the objective function and this work proposes an efficient redistribution method to maintain the quality of the mesh throughout the optimization procedure.

Lithium-ion (Li-ion) batteries are currently considered as vital components for advances in mobile technologies such as those in communications and transport. Nonetheless, Li-ion batteries suffer from temperature rises which sometimes lead to operational damages or may even cause fire. An appropriate solution to control the temperature changes during the operation of Li-ion batteries is to embed batteries inside a paraffin matrix to absorb and dissipate heat. In the present work, we aimed to investigate the possibility of making paraffin nanocomposites for better heat management of a Li-ion battery pack. To fulfill this aim, heat generation during a battery charging/discharging cycles was simulated using Newman’s well established electrochemical pseudo-2D model. We couple this model to a 3D heat transfer model to predict the temperature evolution during the battery operation. In the later model, we considered different paraffin nanocomposites structures made by the addition of graphene, carbon nanotubes, and fullerene by assuming the same thermal conductivity for all fillers. This way, our results mainly correlate with the geometry of the fillers. Our results assess the degree of enhancement in heat dissipation of Li-ion batteries through the use of paraffin nanocomposites. Our results may be used as a guide for experimental set-ups to improve the heat management of Li-ion batteries.

This paper is concerned with an optimal shape design problem in aerodynamics. The inverse problem in question consists in finding the optimal shape an airfoil placed in a potential flow at a given angle of attack should have such that the pressure distribution on its surface matches a desired one. The numerical method to achieve this aim is based on a body-fitted grid generation technique (elliptic, O-type) to generate a mesh over the airfoil surface and solve for the flow equation. The O-type scheme is used due to its ability to generate a high quality (fine and orthogonal) grid around the airfoil surface. This paper describes a novel and very efficient sensitivity analysis scheme to compute the sensitivity of the pressure distribution to variation of grid node positions and both the conjugate gradient method (CGM) and a version of the quasi-Newton method (i.e., BFGS) are used as optimization algorithms to minimize the difference between the computed pressure distribution on the airfoil surface and desired one. The elliptic grid generation technique allows us to map the physical domain (body) onto a fixed computational domain and to discretize the flow equation using the finite difference method (FDM).

This study presents an extension of a previous study (On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization) to viscous transonic flows. In this work, we showed that the same procedure to derive an explicit expression for an exact step length &nbsp, βexact &nbsp, in a gradient-based optimization method for inviscid transonic flows can be employed for viscous transonic flows. The extended numerical method was evaluated for the viscous flows over the transonic RAE 2822 airfoil at two common flow conditions in the transonic regime. To do so, the RAE 2822 airfoil was reconstructed by a Bezier curve of degree 16. The numerical solution of the transonic turbulent flow over the airfoil was performed using the solver ANSYS Fluent (using the Spalart–Allmaras turbulence model). Using the proposed step length, a gradient-based optimization method was employed to minimize the drag-to-lift ratio of the airfoil. The gradient of the objective function with respect to design variables was calculated by the finite-difference method. Efficiency and accuracy of the proposed method were investigated through two test cases.