Two-dimensional steady state conduction
It is important to realize that in many cases a conduction problem is over simplified by the use of one-dimensional treatment, which means the neglect of edge and corner effects which must be present in any finite object. The error involved in this neglect will depend on the dimensions of the system. Consider, for example, the wall of a building some 6 m long and 200 mm thick. In the absence of doors and windows, conduction through such a wall will be one-dimensional over the greater part of the 6 m length and the error involved in neglecting the corner effects will not be great. In contrast, conduction through a chimney, say, 300 mm square internally and 1 m square externally, is essentially two-dimensional. Again a simplifying assumption is being made, since near the base and top of the chimney conduction will be three-dimensional. Thus those problems will be considered in this chapter which may be assumed to be two-dimensional without introducing significant error. This will cover the majority of heat conduction problems which are sufficiently simple to include in an introductory text.
KeywordsHeat Transfer Mesh Point Heat Conduction Problem Conduction Heat Transfer Convection Coefficient
Unable to display preview. Download preview PDF.
- 1.Southwell, R. V. Relaxation Methods in Theoretical Physics, Oxford University Press (1946).Google Scholar
- 2.Bayley, F. J., Owen, J. M. and Turner, A. B. Heat Transfer, Nelson (1972).Google Scholar
- 3.McCracken, D. D. and Dorn, W. S. Numerical Methods and Fortran Programming, Wiley (1966).Google Scholar
- 4.Simonson, J. R. An Electrical Analogy of Extended Surfaces, Bull. Mech. Engng. Educ., vol. 8, 215–25 (1969).Google Scholar
- 5.Karplus, W. J., and Soroka, W. W. Analogue Methods, McGraw-Hill Book Company, New York (1959).Google Scholar