Current trends in heat transfer computations

Introduction H EAT transfer is usually thought of as being composed of convection, conduction, and radiation with certain applications (e.g., structural heating and boiling), evidencing aspects of all three. Until recent years the computational aspects were usually anchored in the finite difference or finite volume methods and other esoteric methods were seen only in the context of solutions to very special problems, normally involving stiff equations or pertubation analyses. The physical models which underlay the computations ranged from simple to complex, but were most frequently based upon correlations of experimental data gathered slowly and with frequent inadequate resolution. During the last decade heat transfer computations have undergone remarkable changes. Improved computer architecture, particularly work stations with graphical output, have led to significantly more complex codes and static or animated graphical displays for interpretation. Hardware implementation of formerly slow software processing has enabled the construction and visualization of twoand three-dimensional grids for problems that were up to now intractable, and the development of improved algorithms which relied upon finite Fourier (FFT) and other transforms. At the same time, high frequency, programmable data acquisition systems have led to the measurement of data of unusually high resolution and accuracy and have permitted the construction of sophisticated models to buttress the computations. In this paper we wish to describe a variety of different problems which are being aggressively attacked computationally and the computational trends which they suggest. It is not our intent to describe the heat transfer modeling and computations in as much detail as the papers of the 50th anniversary of the Journal of Heat Transfer which should be consulted for complete coverage and extensive bibliographies. Neither do we suggest that our descriptions constitute critical reviews of the works to be discussed nor that we possess any specific or unusual intellectual skills in these areas. Rather we hope to give a flavor of the different problems and ap-