A code-independent technique for computational verification of fluid mechanics and heat transfer problems

The goal of this paper is to present a versatile framework for solution verification of PDE＇s. We first generalize the Richardson Extrapolation technique to an optimized extrapolation solution procedure that constructs the best consistent solution from a set of two or three coarse grid solution in the discrete norm of choice. This technique generalizes the Least Square Extrapolation method introduced by one of the author and W. Shyy. We second establish the conditioning number of the problem in a reduced space that approximates the main feature of the numerical solution thanks to a sensitivity analysis. Overall our method produces an a posteriori error estimation in this reduced space of approximation. The key feature of our method is that our construction does not require an internal knowledge of the software neither the source code that produces the solution to be verified. It can be applied in principle as a postprocessing procedure to off the shelf commercial code. We demonstrate the robustness of our method with two steady problems that are separately an incompressible back step flow test case and a heat transfer problem for a battery. Our error estimate might be ultimately verified with a near by manufactured solution. While our pro- cedure is systematic and requires numerous computation of residuals, one can take advantage of distributed computing to get quickly the error estimate.

A new algorithm of global tightly-coupled transient heat transfer based on quasi-steady flow to the conjugate heat transfer problem

Concerning the specific demand on solving the long-term conjugate heat transfer （CHT） problem, a new algorithm of the global tightly-coupled transient heat transfer based on the quasi-steady flow field is further put forward. Compared to the traditional loosely-coupled algorithm, the computational efficiency is further improved with the greatly reduced update frequency of the flow field, and moreover the update step of the flow field can be reasonably determined by using the engineering empirical formula of the Nusselt number based on the changes of the inlet and outlet boundary conditions. Taking a duct heated by inner forced air flow heating process as an example, the comparing results to the tightly-coupled transient calculation by Fluent software shows that the new algorithm can significantly improve the computational efficiency with a reasonable accuracy on the transient temperature distribution, such as the computing time is reduced to 22,8% and 40% while the duct wall temperature deviation are 7% and 5% respectively using two flow update time step of 100 s and 50 s on the variable inlet-flow rate conditions.

CFD Study on Local Fluid-to-Wall Heat Transfer in Packed Beds and Field Synergy Analysis

To reach the target of smaller pressure drop and better heat transfer performance, packed beds with small tube-to-particle diameter ratio(D/dp<10) have now been considered in many areas. Fluid-to-wall heat transfer coefficient is an important factor determining the performance of this type of beds. In this work, local fluid-to-wall heat transfer characteristic in packed beds was studied by Computational Fluid Dynamics(CFD) at different Reynolds number for D/dp=1.5, 3.0 and 5.6. The results show that the fluid-to-wall heat transfer coefficient is oscillating along the bed with small tube-to-particle diameter ratio. Moreover, this phenomenon was explained by field synergy principle in detail. Two arrangement structures of particles in packed beds were recommended based on the synergy characteristic between flow and temperature fields. This study provides a new local understanding of fluid-to-wall heat transfer in packed beds with small tube-to-particle diameter ratio.

Best Practices for Thermal Modeling in Microelectronics with Natural Convection Cooling: Sensitivity Analysis

A detailed sensitivity study was carried out on various key parameters from a high precision numerical model of a microelectronic package cooled by natural convection, to provide rules for the thermal modeling of microelectronic packages subjected to natural convection heat transfer. An accurate estimate of the junction temperature, with an error of less than 1˚C, was obtained compared to the experimental data for the vertical and horizontal orientations of the test vehicle in the JEDEC Still Air configuration. The sensitivity study showed that to have an accurate estimate of the temperature, the following elements should be present in the thermal model: radiation heat transfer in natural convection cooling;a computational fluid dynamics analysis to find realistic convection coefficients;detailed models of the high conductivity elements in the direction of the heat flow towards the environment;and finally precise values for the thicknesses of layers and the thermal properties of the substrate and the printed circuit board.