The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer

Preface to the classics edition Preface Acknowledgments Part I. The Method of Weighted Residuals: 1. Introduction 2. Boundary-value problems in heat and mass transfer 3. Eigenvalue and initial-value problems in heat and mass transfer 4. Applications to fluid mechanics 5. Chemical reaction systems 6. Convective instability problems Part II. Variational Principles: 7. Introduction to variational principles 8. Variational principles in fluid mechanics 9. Variational principles for heat and mass transfer problems 10. On the search for variational principles 11. Convergence and error bounds Author index Subject index.

The method of weighted residuals and variational principles

During hyperthermia the presence of a large vessel entering the heated volume and carrying blood at the systemic temperature can be an important source of temperature non-uniformity and possible underdosage. The minimal tumour temperature near a large vessel is determined by the vessel wall temperature: a number of factors influencing the vessel wall temperature are considered--effective tissue conductivity, flow type, vessel size, entrance effects and counter-current flow. In some specific cases, especially when tissue perfusion is high, the vessel wall temperature may reach therapeutic levels when the mean blood temperature is still low. In general, well perfused tumours have a better chance of being heated uniformly. Regional heating improves temperature uniformity by reducing entrance and equilibration effects as blood is heated before entering the tumour. Raising the core temperature also reduces temperature inhomogeneity. Spatial SAR resolution should preferably be of the order of magnitude of a centimetre or better.

https://iopscience.iop.org/article/10.1088/0031-9155/37/6/009/pdf

Temperature uniformity during hyperthermia: the impact of large vessels

The Graetz problem extended to slip-flow

http://www.ipta.demokritos.gr/CHousiadas/ChristosWeb/IJHMTSlipFlow.pdf

Myron. Tribus

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