Tien-Mo Shih

AN EIGENVALUE METHOD FOR SOLVING TRANSIENT HEAT CONDUCTION PROBLEMS

Abstract The eigenvalue method, which has been used by researchers in structure mechanics, is applied to problems in heat conduction. Its formulation is described in terms of an examination of transient heat conduction in a square slab. Taking advantage of the availability of the exact solution, we compare the accuracy and other numerical properties of the eigenvalue method with those of existing numerical schemes. The comparison shows that, overall, the eigenvalue method appears to be fairly attractive. Furthermore, only a few dominant eigenvalues and their corresponding eigenvectors need to be computed and retained to yield reasonably high accuracy. Great savings are attained in the computation time for a transient problem with long time duration and a large computational domain.

HYPERGOLIC COMBUSTION MODEL FOR FOUR-STROKE HEAT-BARRIER PISTON ENGINES

A numerical model for hyperbolic combustion within a four-stroke heat-barrier piston engine has been developed. An idealized fuel injector simulates the type of injector used in current experimental hypergolic combustion research. Significant to the modeling of this injector is the need to overcome the problems posed by a unit Mach number boundary condition at the injector orifice opening. Overall, the model is used to simulate a compression stroke and fuel injection portion of a power stroke. An implicit finite-difference solution of the governing flow field equations is used. The engine is modeled with the fuel injector being colocated with a single valve, making possible an axisymmetric solution. Because of its physics, hypergolic combustion dictates an eddy dissipation combustion approach. In the final run a 20 × 26 mesh is used for the greater region, which is made up of the flow field and a thin portion of the adjacent cylinder linings and piston.

Literature Survey of Numerical Heat Transfer (2000–2009): Part II

A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted. Due to the immenseness of the literature volume, the survey was split into two parts. Part I covered publications from 2000 to 2004 and was published in Shih et al. [A]. The current work, Part II, covers publications from 2005 to 2009. The journals surveyed in this article include the following: Numerical Heat Transfer (both parts A and B), ASME Journal of Heat Transfer, International Journal of Heat and Mass Transfer, and, selectively, International Journal for Numerical Methods in Fluids. Numerous NHT–related articles published in other archive journals are referenced by those surveyed herein. It has been observed that graduate students and novice researchers sometimes encounter difficulties in understanding the technical content of research–oriented journal papers. Therefore, another objective of this survey is in an attempt to narrow the gap between the education and research communities. For some topics in this survey, simple examples are presented and solved by using Matlab codes.

COMBINED CONVECTIVE AND RADIATIVE RECIRCULATING FLOWS IN ENCLOSURES

In our attempt to numerically investigate buoyancy-induced enclosure flows in which the fluid is radiotively participating, we derive the energy conservation equation over a finite, not infinitesimal, control volume. This is an alternative to the moment method with P-N approximations. Consequently, nodal Intensities in four directions are required as additional unknowns. The system of nonlinear algebraic equations is solved using the successive under-relaxation scheme. Further application of the scheme is extended to computational domains with nonuniform grids, providing high resolution in the boundary layers. Comparison and discussion of the numerical results are presented.

A METHOD TO SOLVE TWO-POINT BOUNDARY-VALUE PROBLEMS IN BOUNDARY-LAYER FLOWS OR FLAMES

A noniterative method has been developed to solve nonlinear two-point boundary-value problems efficiently and accurately. The original ordinary differential equations are linearized by a parametric differentiation procedure and are then transformed into an initial value problem. Solutions at any value of either an inherent parameter or an artificial parameter can be obtained once first-order, second-order, and remainder terms in a Taylor series expanded with respect to the parameter are computed. To illustrate this new method, mixed-mode convection boundary-layer flows and flames and Troeschs problem are analyzed. Numerical results are presented and discussed. Application of the present method proves most beneficial when (1) solutions of many parametric values are of interest or (1) solutions are highly sensitive to the missing initial conditions.

Literature Survey of Numerical Heat Transfer (2010–2011)

Here a comprehensive survey of the literature in the area of numerical heat transfer (NHT) published in 2010 and 2011 has been conducted. Due to the immenseness of the literature volume, journals surveyed in this article include: Numerical Heat Transfer A and B, ASME Journal of Heat Transfer, International Journal of Heat and Mass Transfer, and selectively International Journal for Numerical Methods in Fluids. In addition, the literature related to the topic of thermal rectifiers has been reviewed and included. Numerous NHT-related articles published elsewhere are hopefully referenced by those surveyed herein. It has been observed that graduate students and novice researchers sometimes encounter difficulties in understanding the technical content of research-oriented journal papers. Therefore, another steadfast objective of this survey series [a, b] is in an attempt to narrow the gap between the education and research communities. In the present energy-conscious era, we choose to present a simple daily-life example with numbers to demonstrate how to extract the maximum work out from a can of Coke at 5C placed in a room at 27C. The amount is found to be exactly equal to the exergy of the Coke, as expected.

CONJUGATE CONDUCTION-CONVECTION HEAT TRANSFER MODEL FOR FOUR-STROKE HEAT-BARRIER-PISTON ENGINES

A numerical model for conjugate conduction-convection heat transfer in a four-stroke heat-barrier-piston engine has been developed. The system boundaries were extended beyond the flow to fixed distances within the piston and cylinder linings. The model was used to simulate the compression stroke and fuel injection portion of the power stroke of a four stroke engine cycle. Final runs involved a 29 x 26 mesh to solve the conjugate heat transfer problem in the large region made up of the flow field and a thin portion of the adjacent cylinder linings, A smaller mesh was used for other flow field calculations inside the interior boundary of the cylinder linings and piston. The engine was modeled with the fuel injector co-located with a single valve, making possible an axisymmetric solution. The effects of swirl were not considered. It was found to be convenient to divide the flow field into three regions: one fixed in space with time, one utilizing a stretching and compressing computational mesh, and one movin...

Time-Dependent Photovoltaic-Thermoelectric Hybrid Systems

Photovoltaic-thermoelectric hybrid systems that operate in steady state have attracted considerable attention due to the possibility of supplying more power output than the photovoltaic cell alone. In real life, however, the solar energy continually changes during a day, thus rendering the assumption of steady state unrealistic. In this study, we have investigated such time-dependent systems by following the trajectory of the sun between sunrise and sunset. Computed results of thermal efficiencies are parametrized in heat transfer coefficients, the thermal conductivities of the thermoelectric module, and Seebeck coefficients. For values of the Seebeck coefficient greater than 2.13 × 10−3 V/K thermal efficiencies of the hybrid system appear higher than those of the photovoltaic cells alone. To tackle the strong nonlinear coupling between nodal temperatures, and power outputs, we have adopted two-stage iterative schemes.

Thermal analyses of alternating current light-emitting diodes

During studies of alternating current InGaN/GaN light-emitting diodes with the focus on thermal characteristics, we have identified three shortcomings in comparison with the DC-LEDs counterpart. Via laboratory experiments using infrared thermal imagers and numerical simulations using the Galerkin finite element method, approaches of suppressing these shortcomings are first speculated, then confirmed, and finally proposed.

Non-synchronization of lattice and carrier temperatures in light-emitting diodes.

Pulse implementation or switching-off (PISO) of electrical currents has become a common operation in junction-temperature (Tj) measurements for semiconductor devices since 2004. Here we have experimentally discovered a substantial discrepancy between Tj values with, and without, PISO (e.g., 36.8 °C versus 76.5 °C above the ambient temperature at 25.0 °C). Our research indicates that methods associated with PISO are flawed due to non-synchronization of lattice temperatures and carrier temperatures in transient states. To scrutinize this discrepancy, we propose a lattice-inertia thermal anchoring mechanism that (1) explains the cause of this discrepancy, (2) helps to develop a remedy to eliminate this discrepancy by identifying three transient phases, (3) has been applied to establishing an original, accurate, and noninvasive technique for light-emitting diodes to measure Tj in the absence of PISO. Our finding may pave the foundation for LED communities to further establish reliable junction-temperature measurements based on the identified mechanism.