The two‐dimensional steady boundary layer equations, forsimultaneous heat and fluid flow within ducts, are handled through thegeneralized integral transform technique. The…
Abstract
The two‐dimensional steady boundary layer equations, for simultaneous heat and fluid flow within ducts, are handled through the generalized integral transform technique. The momentum and energy equations are integral transformed by eliminating the transversal coordinate and reducing the PDE’s into an infinite system of coupled non‐linear ordinary differential equations for the transformed potentials. An adaptively truncated version of this ODE system is numerically handled through well known initial value problem solvers, with automatic precision control procedures. The explicit inversion formulae are then recalled to provide analytic expressions for velocity and temperature fields and related quantities of practical interest. Typical examples are presented in order to illustrate the hybrid numerical analytical approach and its convergence behaviour.
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Fausto A.A. Barbuto and Renato Machado Cotta
Employs the integral transform method in the hybrid numerical‐analytical solution of fully developed laminar flow within a class of irregularly shaped ducts, with respect to the…
Abstract
Employs the integral transform method in the hybrid numerical‐analytical solution of fully developed laminar flow within a class of irregularly shaped ducts, with respect to the co‐ordinate system chosen to represent the geometry under consideration. A quite general formulation of a two‐dimensional steady‐state diffusion problem is initially considered, and a formal solution is provided. The original partial differential equation is analytically transformed into an infinite system of ordinary differential equations for the transformed velocity field in the flow direction. On truncation to a sufficiently large finite order, adaptively chosen to meet prescribed accuracy requirements, well‐established numerical schemes for boundary value problems are utilized, readily available in scientific subroutines libraries. Illustrates convergence rates for a few typical duct geometries and critically examines previously reported numerical solutions.
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H.A. Machado and H.R.B. Orlande
Solves the inverse problem of estimating the wall heat flux in a parallel plate channel, by using the conjugate gradient method with adjoint equation. The unknown heat flux is…
Abstract
Solves the inverse problem of estimating the wall heat flux in a parallel plate channel, by using the conjugate gradient method with adjoint equation. The unknown heat flux is supposed to vary in time and along the channel flow direction. Examines the accuracy of the present function estimation approach, by using transient simulated measurements of several sensors located inside the channel. The inverse problem is solved for different functional forms of the unknown wall heat flux, including those containing sharp corners and discontinuities, which are the most difficult to be recovered by an inverse analysis. Addresses the effects on the inverse problem solution of the number of sensors, as well as their locations.
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Hosein Molavi, Javad Rezapour, Sahar Noori, Sadjad Ghasemloo and Kourosh Amir Aslani
The purpose of this paper is to present novel search formulations in gradient‐type methods for prediction of boundary heat flux distribution in two‐dimensional nonlinear heat…
Abstract
Purpose
The purpose of this paper is to present novel search formulations in gradient‐type methods for prediction of boundary heat flux distribution in two‐dimensional nonlinear heat conduction problems.
Design/methodology/approach
The performance of gradient‐type methods is strongly contingent upon the effective determination of the search direction. Based on the definition of this parameter, gradient‐based methods such as steepest descent, various versions of both conjugate gradient and quasi‐Newton can be distinguished. By introducing new search techniques, several examples in the presence of noise in data are studied and discussed to verify the accuracy and efficiency of the present strategies.
Findings
The verification of the proposed methods for recovering time and space varying heat flux. The performance of the proposed methods via comparisons with the classical methods involved in its derivation.
Originality/value
The innovation of the present method is to use a hybridization of a conjugate gradient and a quasi‐Newton method to determine the search directions in gradient‐based approaches.
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Marcos de Souza, Ricardo Fortes de Miranda and Humberto Araujo Machado
The generalized integral transform technique (GITT) is an hybrid numerical‐analytical method that has been successfully applied in convection‐diffusion problems, where the…
Abstract
The generalized integral transform technique (GITT) is an hybrid numerical‐analytical method that has been successfully applied in convection‐diffusion problems, where the original potentials are replaced by eigenexpansion series, and the system of partial differential equations is transformed into a finite system of ordinary differential equations, allowing to obtain an error controlled solution without any kind of grid generation. This paper aims at the application of GITT to the transient version of the classical differentially heated square cavity problem, considering fluid properties as functions of temperature. Comparing results to some previously reported data for constant fluid properties validates the computational procedure. The solution for variable fluid properties with Boussinesq approximation is presented for several values of inclinations, at Rayleigh number of 103 and a Prandtl number of 0.71, demonstrating GITT capability of capturing circulating cells formation and evolution at a low Rayleigh number. New correlations for leaning angle and aspect ratio are presented.
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H. Ahmadi‐Noubari, A. Pourshaghaghy, F. Kowsary and A. Hakkaki‐Fard
The purpose of this paper is to reduce the destructive effects of existing unavoidable noises contaminating temperature data in inverse heat conduction problems (IHCP) utilizing…
Abstract
Purpose
The purpose of this paper is to reduce the destructive effects of existing unavoidable noises contaminating temperature data in inverse heat conduction problems (IHCP) utilizing the wavelets.
Design/methodology/approach
For noise reduction, sensor data were treated as input to the filter bank used for signal decomposition and implementation of discrete wavelet transform. This is followed by the application of wavelet denoising algorithm that is applied on the wavelet coefficients of signal components at different resolution levels. Both noisy and de‐noised measurement temperatures are then used as input data to a numerical experiment of IHCP. The inverse problem deals with an estimation of unknown surface heat flux in a 2D slab and is solved by the variable metric method.
Findings
Comparison of estimated heat fluxes obtained using denoised data with those using original sensor data indicates that noise reduction by wavelet has a potential to be a powerful tool for improvement of IHCP results.
Originality/value
Noise reduction using wavelets, while it can be implemented very easily, may also significantly relegate (or even eliminate) conventional regularization schemes commonly used in IHCP.
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Fabio Andrade Pontes, Emanuel Negrão Macêdo, Clauderino da Silva Batista, João Alves de Lima and João Nazareno Nonato Quaresma
The purpose of this study is to show the procedure, application and main features of the hybrid numerical-analytical approach known as generalized integral transform technique by…
Abstract
Purpose
The purpose of this study is to show the procedure, application and main features of the hybrid numerical-analytical approach known as generalized integral transform technique by using it to study magnetohydrodynamic flow of electrically conductive Newtonian fluids inside flat parallel-plate channels subjected to a uniform and constant external magnetic field.
Design/methodology/approach
The mathematical formulation of the analyzed problem is given in terms of a streamfunction, obtained from the Navier–Stokes and energy equations, by considering steady state laminar and incompressible flow and constant physical properties.
Findings
Convergence analyses are performed and presented to illustrate the consistency of the integral transformation technique. The results for the velocity and temperature fields are generated and compared with those in the literature as a function of the main governing parameters.
Originality/value
A detailed analysis of the parametric sensibility of the main dimensionless parameters, such as the Reynolds number, Hartmann number, Eckert number, Prandtl number and electrical parameter, for some typical situations is performed.
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R.M. Cotta and L.C.G. Pimentel
The integral transform method is employed for the hybrid numerical‐analytical solution of the boundary layer formulation in developing turbulent flow inside channels. An algebraic…
Abstract
The integral transform method is employed for the hybrid numerical‐analytical solution of the boundary layer formulation in developing turbulent flow inside channels. An algebraic turbulence model due to Cebeci and Smith is adopted, in light of its popularity demonstrated in the recent numerical simulation literature. Numerical results for the velocity components in a parallel‐plates channel are obtained, and the automatic error control feature of the present approach is demonstrated. Critical comparisons with experimental works, as well as with previous simulations that employed differential turbulence models, are also performed.
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Diego C. Knupp, Carolina Palma Naveira-Cotta, Adrian Renfer, Manish K. Tiwari, Renato M Cotta and Dimos Poulikakos
The purpose of this paper is to employ the Generalized Integral Transform Technique in the analysis of conjugated heat transfer in micro-heat exchangers, by combining this hybrid…
Abstract
Purpose
The purpose of this paper is to employ the Generalized Integral Transform Technique in the analysis of conjugated heat transfer in micro-heat exchangers, by combining this hybrid numerical-analytical approach with a reformulation strategy into a single domain that envelopes all of the physical and geometric sub-regions in the original problem. The solution methodology advanced is carefully validated against experimental results from non-intrusive techniques, namely, infrared thermography measurements of the substrate external surface temperatures, and fluid temperature measurements obtained through micro Laser Induced Fluorescence.
Design/methodology/approach
The methodology is applied in the hybrid numerical-analytical treatment of a multi-stream micro-heat exchanger application, involving a three-dimensional configuration with triangular cross-section micro-channels. Space variable coefficients and source terms with abrupt transitions among the various sub-regions interfaces are then defined and incorporated into this single domain representation for the governing convection-diffusion equations. The application here considered for analysis is a multi-stream micro-heat exchanger designed for waste heat recovery and built on a PMMA substrate to allow for flow visualization.
Findings
The methodology here advanced is carefully validated against experimental results from non-intrusive techniques, namely, infrared thermography measurements of the substrate external surface temperatures and fluid temperature measurements obtained through Laser Induced Fluorescence. A very good agreement among the proposed hybrid methodology predictions, a finite elements solution from the COMSOL code, and the experimental findings has been achieved. The proposed methodology has been demonstrated to be quite flexible, robust, and accurate.
Originality/value
The hybrid nature of the approach, providing analytical expressions in all but one independent variable, and requiring numerical treatment at most in one single independent variable, makes it particularly well suited for computationally intensive tasks such as in optimization, inverse problem analysis, and simulation under uncertainty.
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Zhenrong Zheng, Wei Zhi, Kezhu Mao, Qian Zhang and Lijuan Luo
The purpose of this paper is to study the ablative behavior of the silicone resin-coated carbon fabric (coated fabric) that will swell significantly during ablation.
Abstract
Purpose
The purpose of this paper is to study the ablative behavior of the silicone resin-coated carbon fabric (coated fabric) that will swell significantly during ablation.
Design/methodology/approach
The ablation experiments of three coated fabrics were conducted by quartz lamp radiant. Based on the experimental analysis, a numerical model was proposed for the coated fabrics to study the ablative process in term of the energy balance, mass conservation and thermal decomposition equations.
Findings
Results showed that the average relative errors between the simulated temperatures and experimental values of back surfaces of coated fabric 1, 2 and 3 were 10.01, 7.53 and 7.32%, respectively. The average density of silicone resin of coated fabric 1 was reduced by 47.96%, and the closer the distance from the heated surface was, the more the density decreased. The thermal conductivity and specific heat capacity of silicone resin of coated fabric 1 increased with time. Before 50 s, each decomposition rate curve showed an inflection point, at which the silicone resin decomposed most intensely.
Research limitations/implications
Based on experimental observations, the ablative behavior of the material with fixed expansion layer was simulated. In the further research, the moving expansion layer could be considered.
Originality/value
This paper provides the theoretical basis to evaluate the effectiveness of thermal protection materials that will swell during ablation.