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By A. V. Luikov

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Extra resources for Analytical Heat Diffusion Theory

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The surface temperature is constant during the whole heat transfer process. This may be achieved by special temperature control or with special conditions of heat transfer between the surroundings and the body surface (see the boundary condition of the third kind). 4) qt(r)=Ax). The simplest case of the boundary condition of the second kind is that of a constant heat flux

In a general case, the quantity k may assume fixed values defined from boundary conditions. The constants C and D are determined from the initial conditions. The particular solution is not directly applicable to estimating the temperature field since the constants C and D cannot be determined from a particular solution. 15). If we assume τ = 0 (exp[— ak2x\ = 1 ), it follows that the constant t0 should be equal to the variable C

If the temperature t8(j) changes negligibly, then the coefficient a(t) may be approximately assumed constant. This is due to the restriction that the temperature difference (ts — ta) is small and thereby t8 may be written instead of ta. Here, the convective contribution to heat flux may be assumed equal to ak At where ak is a convective heat transfer coefficient. 11) the coefficient a is the total heat-transfer coefficient a = ak + a(t). 10) describes the radiant heat transfer law to thefirstapproximation and the contribution of convective heat transfer should be sufficiently small such that the time change of the coefficient ak and its dependence on thermal properties of the body may be neglected.

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