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

Thermophysical Properties Research Literature Retrieval Guide Edited by Y. S. Touloukian, J. K. Gerritsen and N. Y. Moore Second edition, revised and expanded. Book 1: Pp. xxi + 819. Book 2: Pp.621. Book 3: Pp. ix + 1315. (New York: Plenum Press, 1967.) n.p.

/pdf/heat-and-mass-transfer-1yaijfx8vp.pdf

Heat and Mass Transfer

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Introduction To Electrodynamics

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Magnetic Resonance Imaging Physical Principles And Sequence Design

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The Essential Physics Of Medical Imaging

Experimental investigation of helical structures in swirling flows

In this PhD thesis, Magnetic Resonance Imaging (MRI) techniques were applied to thermofluid applications. Magnetic Resonance Velocimetry (MRV) was utilized to measure the three-dimensional, three-component mean velocity field in forced convection flows. Flow models were investigated that contain complex internal structures (e.g. compact heat exchangers) that would not be measureable with conventional optical velocity measurement techniques. The effects of the internal structures on the fluid flow were analyzed to understand the flow physics and to introduce further improvements in performance. Modern three-dimensional manufacturing processes, such as direct polyamide laser sintering, were used to manufacture MR compatible flow models of arbitrary complexity. Measuring velocity fields in such flow models highlights the unique features of MRV.
Magnetic Resonance Thermometry (MRT), based on the temperature-dependent Proton Resonance Frequency (PRF) shift of the water molecule, is a comparatively novel approach with which the scalar temperature difference field can be measured. Novel experimental setups meeting the requirements given by MRT were developed and applied to MRT and MRV. The chosen flow models were taken from thermofluid sciences and exhibit mixed convection flows, whereby temperature-induced buoyancy forces play an important role. In their velocity and temperature fields three-dimensional structures develop. The three-dimensional temperature and velocity vector fields were measured utilizing optimized adjustments of both techniques. The results show the applicability of MRT and MRV to thermofluid applications and demonstrate these MRI techniques as valuable engineering measurement tools.

Magnetic Resonance Imaging Techniques for Thermofluid Applications

PURPOSE

Proton resonance frequency thermometry is well established for monitoring small temperature changes in tissue. Application of the technique to the measurement of complex temperature distributions within fluid flow is of great interest to the engineering community and could also have medical applications. This work presents an experimental approach to reliably measure three-dimensional (3D) temperature fields in fluid flow using proton resonance frequency thermometry.

METHODS

A velocity-compensated three-dimensional gradient echo sequence was used. A flexible pumping system was attached to an MR compatible double pipe heat exchanger. The temperature of two separate flow circuits could be adjusted to produce various three-dimensional spatial temperature distributions within the fluid flow. Validation was performed using MR compatible temperature probes in a uniformly heated flow. A comparative study was conducted with thermocouples in the presence of a spatially varying temperature distribution.

RESULTS

In uniformly heated flow, temperature changes were accurately measured to within 0.5 K using proton resonance frequency thermometry, while spatially varying temperature changes measured with MR showed good qualitative agreement with pointwise measurements using thermocouples.

CONCLUSION

Proton resonance frequency thermometry can be used in a variety of complex flow situations to address medical as well as engineering questions. This work makes it possible to gain new insights into fundamental heat transfer phenomena. Magn Reson Med 76:145-155, 2016. © 2015 Wiley Periodicals, Inc.

Acquisition of 3D temperature distributions in fluid flow using proton resonance frequency thermometry.

Cyclone cooling is a promising method to enhance heat-transfer processes in future internal turbine-blade leading-edge cooling-ducts. The basic component of such cooling channels is the swirl generator, which induces a swirling movement of the coolant. The angular momentum generates stable, complex and three-dimensional flow structures of helical shape with alternating axial flow directions. Full three-dimensional and three-component velocity measurements using magnetic resonance velocimetry (3D3C-MRV) were conducted, with the aim to understand the complex structure of pipe flows with strong swirl. In order to mimic the effect of different installation concepts of the cyclone-cooling ducts an idealized bend-duct swirl-tube configuration with variable exit orifices has been investigated. Pronounced helical flow structures and distinct velocity zones could be found in this swirl flow. One substantial result is the identification of stationary helix-shaped streaks of high axial velocity in the direct vicinity of the wall. These findings are in good agreement with mass-transfer measurements that also show helix-shaped structures with increased mass transfer at the inner surface of the tube. According to the Reynolds analogy between heat and mass transfer, augmented heat-transfer processes in these areas are to be expected.Copyright © 2012 by ASME

Florian Wassermann

Papers

Experimental investigation of helical structures in swirling flows

Magnetic Resonance Imaging Techniques for Thermofluid Applications

Acquisition of 3D temperature distributions in fluid flow using proton resonance frequency thermometry.

Swirl Flow Investigations on the Enhancement of Heat Transfer Processes in Cyclone Cooling Ducts