Conduction in rectangular plates with boundary temperatures specified

Beck, James V.; Wright, Neil T.; Haji‐Sheikh, A.; Cole, Kevin D.; Amos, Donald E.

doi:10.1016/j.ijheatmasstransfer.2008.02.020

Cited by 20 publications

(12 citation statements)

References 15 publications

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“…Comparison of the solutions computed from the modified LIP scheme with the analytical solutions of a heat conduction in rectangular plates with boundary temperatures specified problem was adopted for the verification. The analytical solutions reported by Beck et al [8] are the well-known solutions of the problem. An in-house code was developed based on how to solve the problem by using the modified LIP scheme with the FDM.…”

Section: Modification Of the Lip Scheme For Using With The Finite Difmentioning

confidence: 94%

“…The contour values in Figure 3. are specified according to the contour values shown in [8], and the contour pattern displayed in Figure 3. is similar to the contour pattern exhibited in [8].…”

Section: Modification Of the Lip Scheme For Using With The Finite Difmentioning

confidence: 99%

“…are specified according to the contour values shown in [8], and the contour pattern displayed in Figure 3. is similar to the contour pattern exhibited in [8]. solving between using the FDM with the modified LIP scheme and using the FVM with the LIP scheme at different grid sizes for 5 cases.…”

Section: Modification Of the Lip Scheme For Using With The Finite Difmentioning

confidence: 99%

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Modification of the Lagrange Interpolating Polynomial Scheme for Using with the Finite Difference Method

Prasopchingchana

2017

MATEC Web Conf.

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Abstract. Modification of the Lagrange interpolating polynomial (LIP) scheme for using with the finite difference method is proposed. Merits of the modified LIP scheme used with the finite difference method for problem solving are facile to discretize equations, and fast to obtain solutions. Verification of the modified LIP scheme was performed by comparison of the solutions computed from the modified LIP scheme with the analytical solutions of a heat conduction problem. The verification gives credence to the modified LIP scheme for correctness of the solutions. In addition, the comparison results of solution accuracy and computational time of problem solving between using of the finite difference method with the modified LIP scheme and the finite volume method with the LIP scheme are exhibited.

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Section: Modification Of the Lip Scheme For Using With The Finite Difmentioning

confidence: 94%

Section: Modification Of the Lip Scheme For Using With The Finite Difmentioning

confidence: 99%

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Modification of the Lagrange Interpolating Polynomial Scheme for Using with the Finite Difference Method

Prasopchingchana

2017

MATEC Web Conf.

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“…Existing analytical results (Carslaw and Jaeger, 1959;Beck et al, 2008) and numerical results obtained by finite difference method (FDM) are given also. It is seen from the tabular data that our results are in excellent agreement with the analytical solutions (Cases 1 and 2) and are very closed to the numerical solutions (Case 3).…”

Section: Examplementioning

confidence: 99%

A novel Hamiltonian-based method for two-dimensional transient heat conduction in a rectangle with specific mixed boundary conditions

Rong

Zhou

et al. 2017

JTST

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A novel Hamiltonian-based method is introduced to the two-dimensional (2-D) transient heat conduction in a rectangular domain with partial temperature and partial heat flux density on one boundary. This boundary condition is very difficult to deal with in the classical Lagrangian solving system. Because of this, a total unknown vector consisting of both temperature and heat flux density is regarded as the primary unknown so that the problem is converted to the Hamiltonian form. By using the Laplace transform and method of separation of variables, the total unknown vector is solved and expressed in terms of symplectic eigensolutions in the complex frequency domain (s-domain). The undetermined coefficients of the symplectic series are obtained according to a generalized adjoint symplectic orthogonality. In this manner, analytical expressions for the rectangular domain with specific mixed boundary conditions are achieved in the s-domain. Highly accurate numerical results in the time domain (t-domain) are then obtained by using inverse Laplace transform. Numerical examples are given to demonstrate the efficiency and accuracy of the proposed method.

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“…Analytical solutions are an important tool for solution of engineering problems [1], since they can be used: to validate approximate solutions; to facilitate the analysis and understanding of physical problems; in construction of physical problems; in construction of new numerical algorithms such as the transient method of surface element [2] or in direct application in real problems reducing the computational cost and allowing exact solutions of the model studied be obtained.…”

Section: Introductionmentioning

confidence: 99%

Use of 3D-transient analytical solution based on Green’s function to reduce computational time in inverse heat conduction problems

Fernandes

Sousa

Borges

et al. 2010

Applied Mathematical Modelling

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a b s t r a c tInverse problems can be found in many areas of science and engineering and can be applied in different ways. Two examples can be cited: thermal properties estimation or heat flux function estimation in some engineering thermal process. Different techniques for the solution of inverse heat conduction problem (IHCP) can be found in literature. However, any inverse or optimization technique has a basic and common characteristic: the need to solve the direct problem solution several times. This characteristic is the cause of the great computational time consumed. In heat conduction problem, the time consumed is, usually, due to the use of numerical solutions of multidimensional models with refined mesh. In this case, if analytical solutions are available the computational time can be reduced drastically. This study presents the development and application of a 3D-transient analytical solution based on Green's function. The inverse problem is due to the thermal properties estimation of conductors. The method is based on experimental determination of thermal conductivity and diffusivity using partially heated surface method without heat flux transducer. Originally developed to use numerical solution, this technique can, using analytical solution, estimate thermal properties faster and with better accuracy.

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Conduction in rectangular plates with boundary temperatures specified

Cited by 20 publications

References 15 publications

Modification of the Lagrange Interpolating Polynomial Scheme for Using with the Finite Difference Method

Modification of the Lagrange Interpolating Polynomial Scheme for Using with the Finite Difference Method

A novel Hamiltonian-based method for two-dimensional transient heat conduction in a rectangle with specific mixed boundary conditions

Use of 3D-transient analytical solution based on Green’s function to reduce computational time in inverse heat conduction problems

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