The hybrid application of the Laplace transform technique and the control-volume method in conjun... more The hybrid application of the Laplace transform technique and the control-volume method in conjunction with the hyperbolic shape functions is employed to analyze the hyperbolic heat conduction problem in the film and substrate composite under a pulsed volumetric source adjacent to the exterior film surface. The model of the convective boundary condition is applied to specify the interface thermal resistance.
Numerical Heat Transfer, Part B: Fundamentals, 1994
Two-dimensional hyperbolic heat conduction (HHC) problems with temperature-dependent thermal prop... more Two-dimensional hyperbolic heat conduction (HHC) problems with temperature-dependent thermal properties are investigated numerically. The present numerical method involves the hybrid application of the Laplace transform and control-volume methods. The Laplace transform technique is used to remove time-dependent terms, and then the transformed equation is discretized in the space domain by the control-volume formulation. Nonlinear terms induced by temperature-dependent thermal properties are linearized by using the Taylor's series approximation. In general, the numerical solution of the HHC problem has the phenomenon of the jump discontinuity in the vicinity of the thermal wave front. This phenomenon easily causes numerical oscillations in this region. In order to suppress these numerical oscillations, the selection of shape functions is an important task in the present study. The bi-hyperbolic shape function is introduced in the present control-volume formulation. Three examples involving a problem with an irregular geometry are illustrated to demonstrate the accuracy and stability of the present numerical method for such problems.
Numerical Heat Transfer, Part B: Fundamentals, 2007
A hybrid numerical method involving the Laplace transform technique and finite-difference method ... more A hybrid numerical method involving the Laplace transform technique and finite-difference method in conjunction with the least-squares method and actual experimental temperature data inside the test material is proposed to estimate the unknown surface conditions of inverse heat conduction problems with the temperature-dependent thermal conductivity and heat capacity. The nonlinear terms in the differential equations are linearized using the Taylor series approximation. In this study, the functional form of the surface conditions is unknown a priori and is assumed to be a function of time before performing the inverse calculation. In addition, the whole time domain is divided into several analysis subtime intervals and then the unknown estimates on each subtime interval can be predicted. In order to show the accuracy and validity of the present inverse scheme, a comparison among the present estimates, direct solution, and actual experimental temperature data is made. The effects of the measurement errors, initial guesses, and measurement location on the estimated results are also investigated. The results show that good estimation of the surface conditions can be obtained from the present inverse scheme in conjunction with knowledge of temperature recordings inside the test material.
Numerical Heat Transfer, Part B: Fundamentals, 1988
... Hun-Taw Chen and Cha'o-Kuang Chen Department of Mechanical Engineering, National Chen Ku... more ... Hun-Taw Chen and Cha'o-Kuang Chen Department of Mechanical Engineering, National Chen Kung University, Tainan, Taiwan. ... In previous works, this required the solution of n simultaneous algebraic equations at each time step when the usual Crank-Nicolson algorithm was ...
Abstract This paper describes a novel concept of integrated on-chip fiber free laser-induced fluo... more Abstract This paper describes a novel concept of integrated on-chip fiber free laser-induced fluorescence detection system. The poly-dimethylsiloxane (PDMS) chip was fabricated using soft lithography and was bonded with a glass substrate of 150 μm thickness that reduced the distance of channel-to-sidewall to less than 180 μm. The cells and particles detection was conducted by an external single fiber close to the glass substrate that transmitted laser light for simultaneous excitation and receipt of the emission light signals. The performance of ...
Abstract A novel on-chip optical flow cytometer concept is reported for fluorescence detection, e... more Abstract A novel on-chip optical flow cytometer concept is reported for fluorescence detection, enumeration, and sizing of microparticles in a poly-dimethylsiloxane (PDMS) microchip. The detection system integrates a pair of external optical fibers and other optical components for particle counting, sizing and fluorescence analysis in each measurement simultaneously. The scattered light signal indicates the total number and the size of the particles passing through the detection window, whereas the concurrent backward ...
The problem of free convection flow of a non-Newtonian power law fluid along an isothermal vertic... more The problem of free convection flow of a non-Newtonian power law fluid along an isothermal vertical flat plate embedded in the porous medium is considered in the present study. The physical coordinate system is shown schematically in Fig 1. In the present study, it is assumed that ...
The hyperbolic heat conduction equation is applied to investigate the rapid transient heat conduc... more The hyperbolic heat conduction equation is applied to investigate the rapid transient heat conduction in IC chip instead of the classical Fourier equation. The present study applies an analytical method and a hybrid numerical scheme of the Laplace transform technique and the control volume method in conjunction with the hyperbolic shape functions to investigate the present problem. For the numerical scheme, the Laplace transform method is used to remove the time-dependent terms in the governing differential equation and the boundary conditions, and then the transformed equations are discretized by the control volume scheme. The analytical solution is obtained from a simple mathematical analysis. In order to evidence the reliability and accuracy of the present results, a comparison between the present numerical results and the analytical solution is made. The results show that the present numerical results do not exhibit numerical oscillations in the vicinity of the jump discontinuity and agree well with the analytic solution. It can also be observed that the time derivative of the heat generation and the relaxation time play the important role in the present problem and the non-Fourier effects are significant only for short times.
The hybrid application of the Laplace transform technique and the control-volume method in conjun... more The hybrid application of the Laplace transform technique and the control-volume method in conjunction with the hyperbolic shape functions is employed to analyze the hyperbolic heat conduction problem in the film and substrate composite under a pulsed volumetric source adjacent to the exterior film surface. The model of the convective boundary condition is applied to specify the interface thermal resistance.
Numerical Heat Transfer, Part B: Fundamentals, 1994
Two-dimensional hyperbolic heat conduction (HHC) problems with temperature-dependent thermal prop... more Two-dimensional hyperbolic heat conduction (HHC) problems with temperature-dependent thermal properties are investigated numerically. The present numerical method involves the hybrid application of the Laplace transform and control-volume methods. The Laplace transform technique is used to remove time-dependent terms, and then the transformed equation is discretized in the space domain by the control-volume formulation. Nonlinear terms induced by temperature-dependent thermal properties are linearized by using the Taylor's series approximation. In general, the numerical solution of the HHC problem has the phenomenon of the jump discontinuity in the vicinity of the thermal wave front. This phenomenon easily causes numerical oscillations in this region. In order to suppress these numerical oscillations, the selection of shape functions is an important task in the present study. The bi-hyperbolic shape function is introduced in the present control-volume formulation. Three examples involving a problem with an irregular geometry are illustrated to demonstrate the accuracy and stability of the present numerical method for such problems.
Numerical Heat Transfer, Part B: Fundamentals, 2007
A hybrid numerical method involving the Laplace transform technique and finite-difference method ... more A hybrid numerical method involving the Laplace transform technique and finite-difference method in conjunction with the least-squares method and actual experimental temperature data inside the test material is proposed to estimate the unknown surface conditions of inverse heat conduction problems with the temperature-dependent thermal conductivity and heat capacity. The nonlinear terms in the differential equations are linearized using the Taylor series approximation. In this study, the functional form of the surface conditions is unknown a priori and is assumed to be a function of time before performing the inverse calculation. In addition, the whole time domain is divided into several analysis subtime intervals and then the unknown estimates on each subtime interval can be predicted. In order to show the accuracy and validity of the present inverse scheme, a comparison among the present estimates, direct solution, and actual experimental temperature data is made. The effects of the measurement errors, initial guesses, and measurement location on the estimated results are also investigated. The results show that good estimation of the surface conditions can be obtained from the present inverse scheme in conjunction with knowledge of temperature recordings inside the test material.
Numerical Heat Transfer, Part B: Fundamentals, 1988
... Hun-Taw Chen and Cha'o-Kuang Chen Department of Mechanical Engineering, National Chen Ku... more ... Hun-Taw Chen and Cha'o-Kuang Chen Department of Mechanical Engineering, National Chen Kung University, Tainan, Taiwan. ... In previous works, this required the solution of n simultaneous algebraic equations at each time step when the usual Crank-Nicolson algorithm was ...
Abstract This paper describes a novel concept of integrated on-chip fiber free laser-induced fluo... more Abstract This paper describes a novel concept of integrated on-chip fiber free laser-induced fluorescence detection system. The poly-dimethylsiloxane (PDMS) chip was fabricated using soft lithography and was bonded with a glass substrate of 150 μm thickness that reduced the distance of channel-to-sidewall to less than 180 μm. The cells and particles detection was conducted by an external single fiber close to the glass substrate that transmitted laser light for simultaneous excitation and receipt of the emission light signals. The performance of ...
Abstract A novel on-chip optical flow cytometer concept is reported for fluorescence detection, e... more Abstract A novel on-chip optical flow cytometer concept is reported for fluorescence detection, enumeration, and sizing of microparticles in a poly-dimethylsiloxane (PDMS) microchip. The detection system integrates a pair of external optical fibers and other optical components for particle counting, sizing and fluorescence analysis in each measurement simultaneously. The scattered light signal indicates the total number and the size of the particles passing through the detection window, whereas the concurrent backward ...
The problem of free convection flow of a non-Newtonian power law fluid along an isothermal vertic... more The problem of free convection flow of a non-Newtonian power law fluid along an isothermal vertical flat plate embedded in the porous medium is considered in the present study. The physical coordinate system is shown schematically in Fig 1. In the present study, it is assumed that ...
The hyperbolic heat conduction equation is applied to investigate the rapid transient heat conduc... more The hyperbolic heat conduction equation is applied to investigate the rapid transient heat conduction in IC chip instead of the classical Fourier equation. The present study applies an analytical method and a hybrid numerical scheme of the Laplace transform technique and the control volume method in conjunction with the hyperbolic shape functions to investigate the present problem. For the numerical scheme, the Laplace transform method is used to remove the time-dependent terms in the governing differential equation and the boundary conditions, and then the transformed equations are discretized by the control volume scheme. The analytical solution is obtained from a simple mathematical analysis. In order to evidence the reliability and accuracy of the present results, a comparison between the present numerical results and the analytical solution is made. The results show that the present numerical results do not exhibit numerical oscillations in the vicinity of the jump discontinuity and agree well with the analytic solution. It can also be observed that the time derivative of the heat generation and the relaxation time play the important role in the present problem and the non-Fourier effects are significant only for short times.
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