Steady heat conduction from an infinite row of holes in a half-space or a uniform slab (Q5966230)

The steady heat conduction problem is analyzed in a half-space or in a uniform slab with an infinite row of circular holes equally spaced at fixed distance below the surface of the half-space or along the midplane of the slab. All boundaries are supposed to be isothermal, the temperature on each hole being higher than that on the other surfaces. The problem is reduced to a special boundary integral equation and numerical results are given based on the periodicity of the solution in both bodies under consideration. These results are then used to evaluate the exactness of standard handbook approximations for the total heat flux from any hole. The new approximation proposed recently for the half-space [see \textit{M. R. Barone} and the author, Q. J. Mech. Appl. Math. 34, 265- 286 (1981; Zbl 0461.73067)] is shown to offer a substantial improvement in accuracy. In conclusion the case when one surface of the slab is completely insulated is also discussed.