A heat transfer textbook

https://www.eis.hu.edu.jo/deanshipfiles/pub10311353.pdf

Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids

Correlating equations for laminar and turbulent free convection from a vertical plate

Correlating equations for laminar and turbulent free convection from a horizontal cylinder

A single comprehensive equation is developed for the rate of heat and mass transfer from a circular cylinder in crossflow, covering a complete range of Pr (or Sc) and the entire range of Re for which data are available. This expression is a lower bound (except possibly for RePr < 0.2); free-stream turbulence, end effects, channel blockage, free convection, etc., may increase the rate. In the complete absence of free convection, the theoretical expression of Nakai and Okazaki may be more accurate for RePr < 0.2. The correlating equation is based on theoretical results for the effect of Pr in the laminar boundary layer, and on both theoretical and experimental results for the effect of Re. The process of correlation reveals the need for theoretical results for the effect of Pr in the region of the wake. Additional experimental data for the effect of Pr at small Pe and for the effect of Re during the transition in the point of separation are also needed.

A Correlating Equation for Forced Convection From Gases and Liquids to a Circular Cylinder in Crossflow

The quantitative prediction of turbulent flow and convection in channels extends at least from Boussinesq, who in 1877 proposed the eddy-viscosity model, to Papavassiliou and Hanratty, who in 1997 computed the rate of transport of molecular species by the turbulent fluctuations using Lagrangian direct numerical simulation. The history and current state of the art of such predictions are examined herein. It is concluded that the eddy-diffusivity, mixing-length, and κ-e models should now be completely abandoned in favor of generalized correlating equations for the turbulent shear stress and the turbulent heat flux density based on semitheoretical asymptotic expressions, even though those for the latter quantity are yet uncertain and incomplete. Correlating equations for the time-averaged velocity distribution, the friction factor, the time-averaged temperature distribution, and the heat transfer coefficient may serve as conveniences, but such expressions are unessential since these four quantities may be determined numerically with comparable accuracy from simple, single integrals of the two more elementary quantities. Such direct numerical evaluations reveal that all of the classical algebraic analogies between heat and momentum transfer are in significant error functionally as well as numerically, in large part because of inaccurate representations of the radial variation of the total heat flux density. In the interests of simplicity and clarity, this presentation is primarily limited to fully developed heat transfer in a uniformly heated round tube, but the methodologies and formulations may readily be adapted or extended for other one-dimensional flows and other thermal boundary conditions.

Turbulent flow and convection: The prediction of turbulent flow and convection in a round tube

The MACSYMA code for symbolic manipulation was used to obtain solutions in closed form for double-spiral heat exchangers of a few turns, both with and without heat losses to the surroundings. The solutions, which are for an equal rate of flow of the same fluid in both directions, reveal the existence of an optimal number of transfer units (an optimal rate of flow) for which the temperature rise for the heated stream is a maximum for a given thermal input or temperature difference. Such anomalous behavior, which is of obvious importance in the design and operation of double-spiral exchangers, has generally been overlooked or misinterpreted in prior experimental work and numerical solutions. For realistic heat losses to the surroundings, double-spiral exchangers of multiple turns are shown to be superior to true countercurrent exchangers in terms of producing a temperature rise

Solutions in closed form for a double-spiral heat exchanger

Premixed ethane/air flames in a thermally stabilized plug-flow burner were doped with fuel-N (ammonia) and fuel-S (hydrogen sulfide) to investigate the effect of sulfur on nitrogen oxide formation. Sulfur was found to reduce both thermal NO x and fuel-NO x emissions from the thermally stabilized burner at equivalence ratios from 0.8 to 1.6. A model is proposed which correctly predicts the qualitative effect of sulfur additives on fuel-NO x emissions from both the plug-flow and conventional backmixed burners, supporting both sets of experimental results

Effect of fuel sulfur on nitrogen oxide formation in a thermally stabilized plug-flow burner

Numerical solutions were obtained for the field of velocity in angular forced flow through the annulus between two concentric cylinders of large and infinite aspect ratio with a gap-to-inner radius ratio of 0.05 using a finite-element representation and the FIDAP code. For an infinite aspect ratio, velocity vectors reveal a purely angular motion below a critical Dean number of 37.31 and a secondary motion in the form of pairs of counterrotating vortices above that value. The wavelength of these vortices and the friction factor are correlated in terms of the Dean number. For large but finite aspect ratios a weak secondary motion around the periphery is found to occur below the critical Dean number, while for greater values the vortex at each end of the channel is greatly extended. The computed patterns of flow are in good agreement with prior experimental visualizations as well as with those carried out as part of this investigation. The computed characteristics are also in good agreement with prior theoretical results for limiting cases. The adaptation of the results for flow through an Archimedean spiral is described.

Flow through curved rectangular channels of large aspect ratio

Rather than merely surveying progress in the prediction of heat transfer over the past half century, attention is focused on the factors that have led to significant advances in understanding and practice. An almost one-to-one correspondence is demonstrated between advances in heat transfer and those in computer hardware and software. However, the development of specialized algorithms for flow and heat transfer by individual investigators appears in most cases to be an essential ingredient. Direct contributions of experimentation are relatively minor, but the synergy of combined experimentation and numerical analysis is most often the key to discovery and innovation. A quiet revolution has occurred in the form of correlative equations, and the primary and almost sole contribution of closed-form analysis has been the derivation of asymptotes for that purpose. Finally, progress in heat transfer has occurred primarily in discrete steps, and most often as a consequence of exploratory research and/or the observation and pursuit of the explanation for an anomaly.

Stuart W. Churchill

Papers

Turbulent flow and convection: The prediction of turbulent flow and convection in a round tube

Solutions in closed form for a double-spiral heat exchanger

Effect of fuel sulfur on nitrogen oxide formation in a thermally stabilized plug-flow burner

Flow through curved rectangular channels of large aspect ratio

Progress in the thermal sciences: AIChE Institute Lecture