HeatTransfer-I-Section-5

Below we see the eect of bi for steady condions

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Unformatted text preview: rise to situa/ons where the internal thermal gradient € is small. 4 Transient Conduc/on •  When this occurs, temperature is nearly uniform throughout the wall at any instant of /me. Below, we see the effect of Bi for steady condi/ons. Conduction L / kA hL Bi = = = < 0.1 Convection 1 / hA k € 5 Transient Conduc/on •  Lumped Analysis: consider a body ini/ally at some temperature Ti which is greater than the temperature of a large thermal reservoir at Too. 6 Transient Conduc/on •  The body is suddenly immersed in this large reservoir and will cool. If we assume that it cools isothermally, i.e. at any instant we only have T(t), then we write: ˙ ˙ ˙ E stored = E in − E out or dT ρc pV = − hA(T ( t ) − T∞ ) dt •  For convenience introduce θ = T ­Too. Rearranging and integra/ng gives: € t dθ ∫ θ = − ∫ dt θi 0 or ρc pV θ i t= ln hA θ ρc pV...
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