The reliability and safety of lithium-ion batteries can be affected by overheating issues. Phase ... more 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 nanoc...
This paper presents a numerical method to address function estimation problems in inverse heat tr... more This paper presents a numerical method to address function estimation problems in inverse heat transfer problems using parameter estimation approach without prior information on the functional form of the variable to be estimated. Using an inverse analysis, the functional form of a time-dependent heat transfer coefficient is estimated efficiently and accurately. The functional form of the heat transfer coefficient is assumed unknown and the inverse heat transfer problem should be treated using a function estimation approach by solving sensitivity and adjoint problems during the minimization process. Based on proposing a new sensitivity matrix, however, the functional form can be estimated in an accurate and very efficient manner using a parameter estimation approach without the need for solving the sensitivity and adjoint problems and imposing extra computational cost, mathematical complexity, and implementation efforts. In the proposed sensitivity analysis scheme, all sensitivity c...
This study presents an extension of a previous study (On an Exact Step Length in Gradient-Based A... more 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 βexact 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 calc...
Explicit expressions are obtained for sensitivity coefficients to separately estimate temperature... more Explicit expressions are obtained for sensitivity coefficients to separately estimate temperature-dependent thermophysical properties, such as specific heat and thermal conductivity, in two-dimensional inverse transient heat conduction problems for bodies with irregular shape from temperature measurement readings of a single sensor inside the body. The proposed sensitivity analysis scheme allows for the computation of all sensitivity coefficients in only one direct problem solution at each iteration with no need to solve the sensitivity and adjoint problems. In this method, a boundary-fitted grid generation (elliptic) method is used to mesh the irregular shape of the heat conducting body. Explicit expressions are obtained to calculate the sensitivity coefficients efficiently and the conjugate gradient method as an iterative gradient-based optimization method is used to minimize the objective function and reach the solution. A test case with different initial guesses and sensor locat...
A new sensitivity analysis scheme is presented based on explicit expressions for sensitivity coef... more A new sensitivity analysis scheme is presented based on explicit expressions for sensitivity coefficients to estimate timewise varying heat flux in heat conduction problems over irregular geometries using the transient readings of a single sensor. There is no prior information available on the functional form of the unknown heat flux; hence, the inverse problem is regarded as a function estimation problem and sensitivity and adjoint problems are involved in the solution of the inverse problem to recover the unknown heat flux. However, using the proposed sensitivity analysis scheme, one can compute all sensitivity coefficients explicitly in only one direct problem solution at each iteration without the need for solving the sensitivity and adjoint problems. In other words, the functional form of the unknown heat flux can be numerically estimated by using the parameter estimation approach. In this method, the irregular shape of heat-conducting body is meshed using the boundary-fitted g...
This study proposeda novel exact expression for step length (size) in gradient-based aerodynamic ... more This study proposeda novel exact expression for step length (size) in gradient-based aerodynamic shape optimization for an airfoil in steady inviscid transonic flows. The airfoil surfaces were parameterized using Bezier curves. The Bezier curve control points were considered as design variables and the finite-difference method was used to compute the gradient of the objective function (drag-to-lift ratio) with respect to the design variables. An exact explicit expression was derived for the step length in gradient-based shape optimization problems. It was shown that the derived step length was independent of the method used for calculating the gradient (adjoint method, finite-difference method, etc.). The obtained results reveal the accuracy of the derived step length.
International Journal for Computational Methods in Engineering Science and Mechanics
Abstract This article presents an inverse problem of determination of a space-dependent heat flux... more Abstract 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 temperature distribution over the body. In this study, the simulated measured temperature distribution on part of the boundary is related to the variable heat flux imposed on a different part of the boundary through incorporating the variable thermal conductivity components into the sensitivity coefficients. To do so, a body-fitted grid generation technique is used to mesh the two-dimensional irregular body and solve the direct heat conduction problem. An efficient, accurate, robust, and easy to implement method is presented to compute the sensitivity coefficients through derived expressions. Novelty of the study is twofold: (1) Boundary-fitted grid-based sensitivity analysis in which all sensitivities can be obtained in only one direct solution (at each iteration), irrespective of the number of unknown parameters, and (2) the way the measured temperatures on part of boundary are related to a variable heat flux applied on another part of boundary through components of a variable thermal conductivity. 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.
This paper presents a novel and accurate method to implement the Kutta condition in solving subso... more 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.
A linearly temperature-dependent thermal conductivity is estimated in steady state heat conductio... more 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.
This paper proposes a new methodology to solve the inverse heat transfer problem.The methodology ... more This paper proposes a new methodology to solve the inverse heat transfer problem.The methodology is based on using 3D elliptic grid generation to map the physical domain into a computational one.A new methodology for computing the sensitivities is proposed based on explicit formulae.The method is successfully tested on a range of benchmark cases.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 ... more 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 nanoc...
This paper presents a numerical method to address function estimation problems in inverse heat tr... more This paper presents a numerical method to address function estimation problems in inverse heat transfer problems using parameter estimation approach without prior information on the functional form of the variable to be estimated. Using an inverse analysis, the functional form of a time-dependent heat transfer coefficient is estimated efficiently and accurately. The functional form of the heat transfer coefficient is assumed unknown and the inverse heat transfer problem should be treated using a function estimation approach by solving sensitivity and adjoint problems during the minimization process. Based on proposing a new sensitivity matrix, however, the functional form can be estimated in an accurate and very efficient manner using a parameter estimation approach without the need for solving the sensitivity and adjoint problems and imposing extra computational cost, mathematical complexity, and implementation efforts. In the proposed sensitivity analysis scheme, all sensitivity c...
This study presents an extension of a previous study (On an Exact Step Length in Gradient-Based A... more 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 βexact 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 calc...
Explicit expressions are obtained for sensitivity coefficients to separately estimate temperature... more Explicit expressions are obtained for sensitivity coefficients to separately estimate temperature-dependent thermophysical properties, such as specific heat and thermal conductivity, in two-dimensional inverse transient heat conduction problems for bodies with irregular shape from temperature measurement readings of a single sensor inside the body. The proposed sensitivity analysis scheme allows for the computation of all sensitivity coefficients in only one direct problem solution at each iteration with no need to solve the sensitivity and adjoint problems. In this method, a boundary-fitted grid generation (elliptic) method is used to mesh the irregular shape of the heat conducting body. Explicit expressions are obtained to calculate the sensitivity coefficients efficiently and the conjugate gradient method as an iterative gradient-based optimization method is used to minimize the objective function and reach the solution. A test case with different initial guesses and sensor locat...
A new sensitivity analysis scheme is presented based on explicit expressions for sensitivity coef... more A new sensitivity analysis scheme is presented based on explicit expressions for sensitivity coefficients to estimate timewise varying heat flux in heat conduction problems over irregular geometries using the transient readings of a single sensor. There is no prior information available on the functional form of the unknown heat flux; hence, the inverse problem is regarded as a function estimation problem and sensitivity and adjoint problems are involved in the solution of the inverse problem to recover the unknown heat flux. However, using the proposed sensitivity analysis scheme, one can compute all sensitivity coefficients explicitly in only one direct problem solution at each iteration without the need for solving the sensitivity and adjoint problems. In other words, the functional form of the unknown heat flux can be numerically estimated by using the parameter estimation approach. In this method, the irregular shape of heat-conducting body is meshed using the boundary-fitted g...
This study proposeda novel exact expression for step length (size) in gradient-based aerodynamic ... more This study proposeda novel exact expression for step length (size) in gradient-based aerodynamic shape optimization for an airfoil in steady inviscid transonic flows. The airfoil surfaces were parameterized using Bezier curves. The Bezier curve control points were considered as design variables and the finite-difference method was used to compute the gradient of the objective function (drag-to-lift ratio) with respect to the design variables. An exact explicit expression was derived for the step length in gradient-based shape optimization problems. It was shown that the derived step length was independent of the method used for calculating the gradient (adjoint method, finite-difference method, etc.). The obtained results reveal the accuracy of the derived step length.
International Journal for Computational Methods in Engineering Science and Mechanics
Abstract This article presents an inverse problem of determination of a space-dependent heat flux... more Abstract 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 temperature distribution over the body. In this study, the simulated measured temperature distribution on part of the boundary is related to the variable heat flux imposed on a different part of the boundary through incorporating the variable thermal conductivity components into the sensitivity coefficients. To do so, a body-fitted grid generation technique is used to mesh the two-dimensional irregular body and solve the direct heat conduction problem. An efficient, accurate, robust, and easy to implement method is presented to compute the sensitivity coefficients through derived expressions. Novelty of the study is twofold: (1) Boundary-fitted grid-based sensitivity analysis in which all sensitivities can be obtained in only one direct solution (at each iteration), irrespective of the number of unknown parameters, and (2) the way the measured temperatures on part of boundary are related to a variable heat flux applied on another part of boundary through components of a variable thermal conductivity. 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.
This paper presents a novel and accurate method to implement the Kutta condition in solving subso... more 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.
A linearly temperature-dependent thermal conductivity is estimated in steady state heat conductio... more 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.
This paper proposes a new methodology to solve the inverse heat transfer problem.The methodology ... more This paper proposes a new methodology to solve the inverse heat transfer problem.The methodology is based on using 3D elliptic grid generation to map the physical domain into a computational one.A new methodology for computing the sensitivities is proposed based on explicit formulae.The method is successfully tested on a range of benchmark cases.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.
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Papers by Farzad Mohebbi