Han Taw Chen

Natural convection of a non-Newtonian fluid about a horizontal cylinder and a sphere in a porous medium

Abstract The problem of natural convection of a non-Newtonian fluid about a horizontal isothermal cylinder and an isothermal sphere in the porous medium is considered. The present study is based on the boundary layer approximation and only suitable for a high Rayleigh number. Similarity solutions are obtained by using the fourth order Runge-Kutta method. The effects of the wall temperature T W and the new power-law index n on the characteristics of heat transfer are discussed.

Estimation of surface temperature in two-dimensional inverse heat conduction problems

Abstract A hybrid numerical algorithm of the Laplace transform technique and finite-difference method with a sequential-in-time concept and the least-squares scheme is proposed to predict the unknown surface temperature in two-dimensional inverse heat conduction problems. In the present study, the expression of the surface temperature is unknown a priori. The whole time domain is divided into several analysis sub-time intervals and then the surface temperature in each analysis interval is estimated. To enhance the accuracy and efficiency of the present method, a good comparison between the present estimations and previous results is demonstrated. Results show that good estimations on the surface temperature can be obtained from the knowledge of the transient temperature recordings only at a few selected locations even for the case with measurement errors. It is worth mentioning that the unknown surface temperature can be accurately estimated even though the thermocouples are located far from the estimated surface. Due to the application of the Laplace transform technique, the unknown surface temperature distribution can be estimated from a specific time.

Estimation of two-sided boundary conditions for two-dimensional inverse heat conduction problems

Abstract A hybrid numerical algorithm of the Laplace transform technique and finite-difference method with a sequential-in-time concept and the least-squares scheme is proposed to predict the unknown surface temperature of two-sided boundary conditions for two-dimensional inverse heat conduction problems. In the present study, the functional form of the estimated surface temperatures is unknown a priori. The whole time domain is divided into several analysis sub-time intervals and then the unknown surface temperatures in each analysis interval are estimated. To enhance the accuracy and efficiency of the present method, a good comparison between the present estimations and previous results is demonstrated. The results show that good estimations on the surface temperature can be obtained from the transient temperature recordings only at a few selected locations even for the case with measurement errors. It is worth mentioning that the unknown surface temperature can be accurately estimated even though the thermocouples are located far from the estimated surface. Owing to the application of the Laplace transform technique, the unknown surface temperature distribution can be estimated from a specific time.

Application of the hybrid method to inverse heat conduction problems

Abstract The hybrid method involving the combined use of the Laplace transform method and the finite element method is considerably powerful for solving one-dimensional linear heat conduction problems. In the present method, the time-dependent terms are removed from the problem using the Laplace transform method and then the finite element method is applied to the space domain. The transformed temperature is inverted numerically to obtain the result in the physical quantity. The estimation of the surface heat flux or temperature from transient measured temperatures inside the solid agrees well with the analytical solution of the direct problem without Becks sensitivity analysis and a least square criterion. Due to no time step, the present method can directly calculate the surface conditions of an inverse problem without step by step computation in the time domain until the specific time is reached. In addition, it is also not necessary to compute all the nodal temperatures at each time step when the present method is applied to an inverse problem. It is worth mentioning that a little effect of the measurement location on the estimates is shown in the present method. Thus, it can be concluded that the present method is straightforward and efficient for such problems.

Numerical method for hyperbolic inverse heat conduction problems

Abstract The Laplace transform technique and control volume method in conjunction with the hyperbolic shape function and least-squares scheme are applied to estimate the unknown surface conditions of one-dimensional hyperbolic inverse heat conduction problems. In the present study, the expression of the unknown surface conditions is not given a priori. To obtain the more accurate estimates, the whole time domain is divided into several analysis sub-time intervals. Afterward, the unknown surface conditions in each analysis interval are estimated. To evidence the accuracy of the present method, a comparison between the present estimations and exact results is made. Results show that good estimations on the unknown surface conditions can be obtained from the transient temperature recordings only at one selected location even for the cases with measurement errors.

Simultaneous estimations of temperaturedependent thermal conductivity and heat capacity

Abstract A hybrid numerical algorithm of the Laplace transform technique and the control-volume method is proposed to simultaneously estimate the temperature-dependent thermal conductivity and heat capacity from temperature measurements inside the material. But, the functional forms of the thermal conductivity and heat capacity are unknown a priori . The whole domain is divided into several sub-layers and then the thermal properties in each sub-layer are assumed to be linear functional forms of temperature before performing the inverse calculation. The accuracy and efficiency of the predicted results can be evidenced from various illustrated cases using simulated exact and inexact temperature measurements obtained within the medium. Results show that good estimations on the thermal properties can be obtained from the knowledge of the transient temperature recordings only at two selected locations. The advantage of the present method is that the relation between the thermal properties and temperature can be determined for various types of boundary conditions even though the early temperature data cannot be obtained.

Numerical solution of hyperbolic heat conduction in cylindrical and spherical systems

Abstract Hyperbolic heat conduction problems in cylindrical and spherical coordinate systems are investigated numerically. Unlike the classical Fourier heat flux model, the thermal wave of such problems propagates with a finite speed. The major difficulty in dealing with such problems is the suppression of numerical oscillations in the vicinity of a jump discontinuity. The proposed numerical method combines the Laplace transform technique for the time domain and the control volume formulation for the space domain. The transformed nodal temperatures are inverted to the physical quantities by using numerical inversion of the Laplace transform. Due to the application of a hyperbolic shape function, it can be seen from the illustrated examples that the present numerical solutions are stable and accurate. The application of the hyperbolic shape function can successfully suppress the numerical oscillations in the vicinity of jump discontinuities. Comparisons with the results obtained from the Fourier law are also presented for some basic problems.

Numerical analysis for the hyperbolic heat conduction problem under a pulsed surface disturbance

A hybrid application of the Laplace transform method and a control-volume formulation in conjunction with the hyperbolic shape functions is applied to investigate the hyperbolic diffusion problems with the pulsed boundary conditions in various coordinate systems. The Laplace transform method is used to remove the time-dependent terms in the governing differential equations and the boundary conditions, and then the transformed equations are discretized by the control volume scheme. The primary difficulty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities. The results show that the numerical results agree well with the analytic solution and do not exhibit numerical oscillations in the vicinity of the jump discontinuity. The present method also can solve the problems with the singular point.

NUMERICAL SOLUTION OF TWO-DIMENSIONAL NONLINEAR HYPERBOLIC HEAT CONDUCTION PROBLEMS

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 Taylors 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 a...

Estimation of Heat Transfer Coefficient in Two-Dimensional Inverse Heat Conduction Problems

The finite-difference method in conjunction with the least-squares scheme, cubic spline, and temperature measurements is applied to predict the distribution of the heat transfer coefficient on a surface exposed to a moving fluid. In the present study, the functional form of the heat transfer coefficient is unknown a priori. The whole space domain of the unknown heat transfer coefficient can be divided into several analysis subintervals and then the cubic spline is introduced to estimate the unknown values. In order to show the accuracy of the present inverse method, a comparison among the present estimates, previous results, and exact solution is made. The results show that the present inverse scheme not only can reduce the number of the thermocouples but also can increase the accuracy of the estimated results. Also, the present estimates are not very sensitive to the measurement locations. Good estimation of the heat transfer coefficient can be obtained from the knowledge of the temperature recordings even for the case with measurement errors.