This means that the eld beyond will be undisturbed

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Unformatted text preview: m diameter and ini/ally at 1000 C, cools in an environment of 25 C with a heat transfer coefficient of 50 W/m2K. Determine what the centerline and surface temperature are aeer 4 hours. 23 Transient Conduc/on •  Solu/ons for semi ­infinite solid regions have prac/cal applica/ons when heat does not penetrate deeply into a body, i.e. surface of the earth, or ini/al contact (very short /me). •  There are three fundamental solu/ons: –  Constant Surface Temperature •  T(x,t)  ­> surface flux –  Constant Surface Heat Flux •  T(x,t)  ­> surface temperature –  Constant Surface Convec/on •  T(x,t)  ­> surface flux and surface temperature 24 Transient Conduc/on 25 Transient Conduc/on •  Constant Surface Temperature (Ts) ȹ x ȹ T - Ts = erf ȹ ȹ Ti − Ts ȹ 2 αt Ⱥ k (Ts − Ti ) Surface Heat Flux q's' ( t ) = παt Temperature •  Constant Surface Flux (q’’o) ȹ x 2 ȹ q'o' x ȹ x ȹ 2q'o' αt / π Temperature T - Ti = expȹ − − erfcȹ ȹ ȹ k ȹ 2 αt Ⱥ ȹ 4 αt Ⱥ k 2q'o' αt Surface Temperature Ts ( t ) − Ti = πk € •  Constant Surface Convec/on (h, Too) ȹ x ȹ x ȹ Ⱥ ȹ hx h 2αt ȹ ȺȺ T - Ti h αt ȹ Ⱥ Temperature = erfcȹ + ȹ Ⱥ ȹ − Ⱥexpȹ + 2 ȹ ȺȺerfcȹ T∞ - Ti ȹ 2 αt Ⱥ Ⱥ ȹ k k Ⱥ ȺȺ k Ⱥ Ⱥ ȹ 2 αt Ⱥ Ⱥ ȹ h αt ȹ ȹ h 2αt ȹ Ts ( t ) - Ti Surfa...
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This document was uploaded on 02/14/2014 for the course ENGR 6901a at Memorial University.

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