The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Recently, the demand for data center computing has surged, increasing the total energy footprint of data centers worldwide. Data centers typically comprise three subsystems: IT equipment provides services to customers; power infrastructure supports the IT and cooling equipment; and the cooling infrastructure removes heat generated by these subsystems. This work presents a novel approach to model the energy flows in a data center and optimize its operation. Traditionally, supply-side constraints such as energy or cooling availability were treated independently from IT workload management. This work reduces electricity cost and environmental impact using a holistic approach that integrates renewable supply, dynamic pricing, and cooling supply including chiller and outside air cooling, with IT workload planning to improve the overall sustainability of data center operations. Specifically, we first predict renewable energy as well as IT demand. Then we use these predictions to generate an IT workload management plan that schedules IT workload and allocates IT resources within a data center according to time varying power supply and cooling efficiency. We have implemented and evaluated our approach using traces from real data centers and production systems. The results demonstrate that our approach can reduce both the recurring power costs and the use of non-renewable energy by as much as 60% compared to existing techniques, while still meeting the Service Level Agreements.

/pdf/renewable-and-cooling-aware-workload-management-for-21f3o272ec.pdf

Renewable and cooling aware workload management for sustainable data centers

Micropumps, microvalves, and micromixers within PCR microfluidic chips: Advances and trends.

Thermal performance of phase change material (PCM) based pin-finned heat sinks for electronics devices: Effect of pin thickness and PCM volume fraction

Experimental investigations on phase change material based finned heat sinks for electronic equipment cooling

To achieve reductions in the power consumption of the data center cooling infrastructure, the current strategy in data center design is to increase the inlet temperature to the rack, while the current strategy for energy-efficient system thermal design is to allow increased temperature rise across the rack. Either strategy, or a combination of both, intuitively provides enhancements in the coefficient of performance (COP) of the data center in terms of computing energy usage relative to cooling energy consumption. However, this strategy is currently more of an empirically based approach from practical experience, rather than a result of a good understanding of how the impact of varying temperatures and flow rates at rack level influences each component in the chain from the chip level to the cooling tower. The aim of this paper is to provide a model to represent the physics of this strategy by developing a modeling tool that represents the heat flow from the rack level to the cooling tower for an air cooled data center with chillers. This model presents the performance of a complete data center cooling system infrastructure. After detailing the model, two parametric studies are presented that illustrate the influence of increasing rack inlet air temperature, and temperature rise across the rack, on different components in the data center cooling architecture. By considering the total data center, and each component's influence on the greater infrastructure, it is possible to identify the components that contribute most to the resulting inefficiencies in the heat flow from chip to cooling tower and thereby identify the components in need of possible redesign. For the data center model considered here it is shown that the strategy of increasing temperature rise across the rack may be a better strategy than increasing inlet temperature to the rack. Part II of this work expands on this paper with further parametric studies to evaluate the robustness of this data center cooling strategy, with conditions for optimal strategy deployment.

From chip to cooling tower data center modeling: Part I Influence of server inlet temperature and temperature rise across cabinet

Pressure drop in two phase slug/bubble flows in mini scale capillaries

https://ulir.ul.ie/bitstream/handle/10344/2398/Grimes,%20Ronan.pdf;sequence=2

Active cooling of a mobile phone handset

Low profile fan and heat sink thermal management solution for portable applications

An experimental study is performed on one of the smallest commercially available miniature fans, suitable for cooling portable electronic devices, used in conjunction with both finned and finless heat sinks of equal exterior dimensions. The maximum overall footprint area of the cooling solution is 534 mm 2 with a profile height of 5 mm. Previous analysis has shown that due to fan exit angle, flow does not enter the heat sinks parallel to the fins or bounding walls. This results in a nonuniform flow rate within the channels of the finned and finless heat sinks along with impingement of the flow at the entrance giving rise to large entrance pressure losses. In this paper straightening diffusers were attached at the exit of the fan, which resulted in aligning the flow entering the heat sinks with the fins and channel walls. Detailed velocity measurements were obtained using particle image velocimetry, which provided a further insight into the physics of the flow in such miniature geometries and in designing the straightening diffusers. The thermal analysis results indicate that the cooling power of the solution is increased by up to 20% through the introduction of a diffuser, hence demonstrating the need for integrated fan and heat sink design of low profile applications.

Ed Walsh

Papers

From chip to cooling tower data center modeling: Part I Influence of server inlet temperature and temperature rise across cabinet

Pressure drop in two phase slug/bubble flows in mini scale capillaries

Active cooling of a mobile phone handset

Low profile fan and heat sink thermal management solution for portable applications

An Experimental Study on the Design of Miniature Heat Sinks for Forced Convection Air Cooling