Cha'o-Kuang Chen

Heat transfer of a continuous, stretching surface with suction or blowing

Abstract An analysis has been carried out to determine the heat transfer occurring in the laminar boundary layer on a linearly stretching, continuous surface subject to suction or blowing. Two cases are considered: the sheet with prescribed wall temperature and heat flux. The results are expressed in terms of Kummers functions. For specified conditions, the solutions reduced to the published results. Additionally, the results of an impermeable stretching plate with variable wall heat flux are also obtained. Finally, the effects of Prandtl number, suction or blowing parameter, temperature parameter, and heat flux parameter on the temperature distribution are discussed in detail.

Solving partial differential equations by two-dimensional differential transform method

Using two-dimensional differential transform to solve Partial Differential Equations (PDE) is proposed in this study. First, the theory of two-dimensional differential transform is introduced. Second, taking two-dimensional differential transform of a PDE problem, a set of difference equations is derived. Doing some simple mathematical operations on these equations, we can get a closed form series solution or an approximate solution quickly. Finally, three PDE problems with constant and variable coefficients are solved by the present method. The calculated results are compared very well with those obtained by other analytical or approximate methods.

Application of differential transformation to eigenvalue problems

Using differential transformation to solve eigenvalue problems is introduced in this study. First, differential transformation is introduced briefly. Second, taking differential transformation of the Strum-Liouville problem, a set of difference equations is derived. Doing some simple mathematics operations on these operations, we can get any ith eigenvalue and eigenfunction at a time. Finally, two eigenvalue problems are solved by the present method. The calculated results are compared closely with the results obtained by another analytical method.

Free Convection Flow of Non-Newtonian Fluids Along a Vertical Plate Embedded in a Porous Medium

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 modified Darcy law and the boundary layer approximation are applicable. This implies that the present solutions are valid at a high Rayleigh number. With these simplifications, the governing partial nonlinear differential equations can be transformed into a set of coupled ordinary differential equations which can be solved by the fourth-order Runge-Kutta method. Algebraic equations for heat transfer rate and boundary layer thickness as a function of the prescribed wall temperature and physical properties of liquid-porous medium are obtained. The similarity solutions can be applied to problems in geophysics and engineering. The primary purpose of the present study is to predict the characteristics of steady natural convection heat transfer using the model of the flow of a non-Newtonian power law fluid in a porous medium given by Dharmadhikari and Kale (1985). Secondly, the effects of the new power law index n on heat transfer are investigated.

A decomposition method for solving the convective longitudinal fins with variable thermal conductivity

Abstract In this paper the Adomian decomposition method is used to evaluate the efficiency and the optimal length of a convective rectangular fin with variable thermal conductivity, and to determine the temperature distribution within the fin. It is a useful and practical method, which can be used to solve the nonlinear energy balance equations which are associated with variable thermal conductivity conditions. The Adomian decomposition method provides an analytical solution in the form of an infinite power series. From a practical perspective, it is necessary to evaluate this analytical solution, and to obtain numerical values from the infinite power series. This requires series truncation, and a practical procedure to accomplish the task. Together, these transform the analytical results into a solution with a finite degree of accuracy. The accuracy of the Adomian decomposition method with a varying number of terms in the series is investigated by comparing its results with those generated by a finite-difference method which uses a Newton linearization scheme.

Ecological optimization of an endoreversible Brayton cycle

In this paper, finite-time thermodynamics has been applied to ecologically optimize the power output of closed Brayton cycles for infinite thermal capacitance rates of the heat reservoirs. The optimum values of power, thermal efficiency and second-law efficiency of Brayton cycles are presented. The ratio of ecologically optimum power to maximum power is independent of the numbers of transfer units of the hot-side and the cold-side heat exchangers, and this ratio is much higher than the ratio of the entropy generation rate at maximum ecological function to that at maximum power. With the introduction of the ecological function, the improvement in second-law efficiency and in thermal efficiency is evident, especially for low hot-cold temperature ratios. Moreover, the thermal efficiency at maximum ecological function is about the average of the maximum-power efficiency and the reversible Carnot efficiency.

Influence of hydrogen functionalization on thermal conductivity of graphene: Nonequilibrium molecular dynamics simulations

The influence of hydrogen coverage on the thermal conductivity of typical armchair hydrogen functionalized graphene is investigated using a nonequilibrium molecular dynamics simulation. We also study the effects of easy-rotation of unsupported sp3 bonds. We find that the system exhibits a rapid drop in thermal conductivity with hydrogen coverage, where hydrogen coverage down to as little as 2.5% of the graphene carbon atoms reduces the thermal conductivity by about 40%. The simulation results indicate that the effect is due to a reduction in the phonon mean free path.

The ecological optimization of an irreversible Carnot heat engine

Finite-time thermodynamics with an ecological criterion is applied to an irreversible Carnot heat engine with finite thermal capacitance rates of the heat reservoirs and finite total conductance of the heat exchangers. The ecological function is defined as the power output minus the loss power or the product of the environmental temperature and the entropy production rate. The ecological function is optimized with respect to the cycle temperature ratio and the heat conductance ratio. It is shown that the ecological function is a useful and important criterion for the design of an irreversible Carnot heat engine, considering not only power output but also entropy generation and thermal efficiency. The optimum values of cycle temperature ratios and conductance ratios of irreversible Carnot heat engines are presented. Moreover, from the viewpoint of the ecological function, the thermal capacitance of the cold external fluid should be larger than that of the hot external fluid and the heat conductance of the hot-end heat exchanger should be smaller than that of the cold-end heat exchanger.

Application of differential transformation to transient advective-dispersive transport equation

In this paper, a simulation method called the differential transform or Taylor transform method is employed to predict the advective-dispersive transport problems. Such problems are usually met when dealing with the contaminant transport in groundwater. The differential transform method is introduced briefly. A hybrid method of differential transform and finite difference method is employed to solve the transient advective-dispersive transport problems. The parameters of the equation are varied and different kinds of input sources are engaged to verify that the differential transform method is suitable for the problem. Some simulation results are illustrated and discussed in compare with the analytic solutions. The results show that the differential transform method can achieve good results in predicting the solution of such problems.

Sliding mode control of chaos in the cubic Chua's circuit system

In this paper, a sliding mode controller is applied to control the cubic Chua’s circuit system. The sliding surface of this paper used is one dimension higher than the traditional surface and guarantees its passage through the initial states of the controlled system. Therefore, using the characteristic of this sliding mode we aim to design a controller that can meet the desired specication and use less control energy by comparing with the result in the current existing literature. The results show that the proposed controller can steer Chua’s circuit system to the desired state without the chattering phenomenon and abrupt state change.