: Theoretical laminar flow solutions for heat transfer and flow friction are of importance in the development of compact heat exchangers. Generally the higher the degree of compactness, the lower is the Reynolds number and the greater is the relevance of the theory solutions. In the report these solutions are compiled for twenty one straight ducts and four curved ducts. Some new analytical solutions are obtained by writing a general computer program for three ducts. Application of the analytical solutions to the gas turbine regenerator is discussed.

Laminar Flow Forced Convection Heat Transfer and Flow Friction in Straight and Curved Ducts - A Summary of Analytical Solutions

This book was developed during Professor Ghiaasiaan's twelve years of teaching a graduate-level course on convection heat and mass transfer. It is ideal for a graduate course covering the theory and practice of convection heat and mass transfer. The book treats well-established theory and practice but is also enriched by its coverage of modern areas such as flow in microchannels, computational fluid dynamics-based design and analysis methods. It is primarily concerned with convection heat transfer, with the essentials of mass transfer also covered. The mass transfer material and problems are presented in such a way that they can be skipped if not required. The book is richly enhanced by examples and end-of-chapter exercises. A complete solutions manual is available to qualified instructors. The book includes eighteen appendices providing compilations of most essential property and mathematical information for analysis of convective heat and mass transfer processes.

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Convective heat and mass transfer

Tube-fed basaltic lava flows with lengths ranging from 10 to 200 km are inferred to exhibit similar amounts of cooling. To explain the wide range of implied cooling rates, we consider forced convection as a dominant cooling process in lava tubes and present solutions that express mean temperature versus distance down the tube as a function of flow rate and flow cross section. Our models treat forced convective thermal losses in steady laminar flow through a lava tube with constant temperature walls and constant material properties. We explore the effects of different wall temperature and heat flux rate boundary conditions for circular tube and parallel plate flows over a range of tube sizes, plate spacings, eruption temperatures, and volume flow rates. Results show that nonlinear cooling rates over distance are characteristic of constant wall temperature for a piecewise parallel plate/circular tube model. This provides the best fit to temperature observations for Hawaiian tubes. Such a model may also provide an explanation for the very low (∼10°C) cooling observed in ∼10 km long Hawaii tube flows and inferred in longer ∼50 to 150 km tube-fed flows in Queensland. The forced convective cooling model may also explain similar flow morphologies for long tube-fed basaltic lava flows in a wide variety of locations, since small variations in eruption temperature or flow rate can accommodate the entire range of flow lengths and cooling rates considered. Our results are consistent with previous suggestions that long basaltic flows may be a reflection of low slopes, a particularly steady moderate eruption rate, and well-insulated flow, rather than of high discharge rates.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JB03108

Flow and convective cooling in lava tubes

A number of heat and mass transfer problems of chemical engineering interest involve the convective diffusion equation of the form



where θ = θ(X1, X2). Exact solutions for such problems are developed in terms of well-known functions which have been thoroughly studied in recent years. Several problems which have appeared in the literature, solved by completely numerical methods, are re-examined and new problems are discussed and solved. The results of the present analysis are compared with those obtained by other methods where possible. The problem of axial diffusion of heat or mass is solved in terms of known functions.

The present formulation is shown to be particularly useful in the analysis of conjugated boundary value problems, i. e. for problems involving heat or mass transfer across an interface where the interfacial boundary condition is not known a priori but is related to the temperature or concentration fields in the adjacent phases.

Exact solutions for a class of heat and mass transfer problems

The extended Graetz problem with piecewise constant wall heat flux for pipe and channel flows

A theoretical method is described for obtaining the exact solution to the problem of thermal entry region heat transfer which takes into account both transverse non-uniformity in the velocity field and axial conduction. To allow for the effect of upstream conduction, the fluid temperature was taken to be uniform at × = – ∞, and the first 20 eigenvalues and the corresponding eigenfunctions were determined separately for the heated and adiabatic regions. Both the temperatures and temperature gradients were then matched at × = 0 by constructing a pair of orthonormal functions from the nonorthogonal eigenfunctions.

Nusselt numbers calculated for pipe flow subject to the boundary condition of uniform wall heat flux show virtually perfect agreement with those reported recently by Hennecke, who solved the governing partial differential equation numerically. To illustrate its general applicability, the present method was further employed to analyze the corresponding problem in parallel-plate channel flow, for which no solution has hitherto been reported.

An exact analysis of low peclet number thermal entry region heat transfer in transversely nonuniform velocity fields

Sufficiently accurate values of first twenty eigenvalues, eigenfunctions Rn (1), and the coefficients for series expansion, as well as asymptotic expressions for these quantities, have been obtained for heat (or mass) transfer to fully developed laminar flow inside a round tube with uniform wall heat (or mass) flux. The first ten eigenfunctions are shown graphically for the radius range 0 ≤ r/ro ≤ 1.

These quantities are used to calculate the Nusselt numbers for sinusoidal wall heat flux distribution and are compared with the corresponding slug flow Nusselt numbers.

Chia-Jung Hsu

Papers

An exact analysis of low peclet number thermal entry region heat transfer in transversely nonuniform velocity fields

Heat transfer in a round tube with sinusoidal wall heat flux distribution

A method of solution for mass transfer with chemical reaction under conditions of viscous flow in a tubular reactor