Read e-book online Analytical Heat Diffusion Theory PDF

By A. V. Luikov

ISBN-10: 0124597564

ISBN-13: 9780124597563

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The width (2A) and length (21) of the plate are considerably greater than its thickness, so that the temperature gradient along the length and over the width of the plate is zero (a one-dimensional case). , t(x, τ). If the coordinate origin is in the center of the plate, then the mean integral temperature will be i(T) = Smt{x'T)dv -^ = 2 ^ J* Ä '(* *) dx = -^- j * t(x, T) dx. 11) Example 2. , t(r9 τ). Then the mean temperature (over the volume) ί(τ) will be f(vT) = — ^ j - 3 f* f ** Γ i(r, r)r2 sin Θ d6 dw ψ dr ' 4nR Jo J Jv=o v } = i JT r2 ' (r T)dr> (L912) since the volume element is dv = r2 sin Θ dB dtp dr.

6) The total heat amount AQ which was supplied for heating for the time Ax will be found after integration over the whole volume AQ = Q2-Qi = tx. 9) where t0 is the mean (integral) temperature. 9 Methods for Calculating the Heat Flow AQv = cy(t-t0). 10) Thus the main problem in this calculation method is to find ί(τ). Consider some examples. Example 1. We have a plate 2R in thickness. The width (2A) and length (21) of the plate are considerably greater than its thickness, so that the temperature gradient along the length and over the width of the plate is zero (a one-dimensional case).

The heat transfer coefficient may be approximately assumed constant, independent of the temperature, and uniform over the whole surface. In unsteady heat transfer processes between the body surface and the fluid flow, a conventional thickness of a boundary layer will depend not only on the fluid velocity and its physical properties, but also on thermal properties of a body and will continuously change with time: ô =f(r). 6a) the relation may be taken as a boundary condition and as a predicting formula to the first approximation, but not as a relation of the convectivetransfer law.

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Analytical Heat Diffusion Theory by A. V. Luikov


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