We may write the soluon more generally as t t exp

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Unformatted text preview: hA θ 7 8 Transient Conduc/on •  We may also write as: ȹ hA T − T∞ = expȹ − ȹ ρc V Ti − T∞ ȹ p ρc pV τt = hA ȹ ȹ t ȹ t ȹ = expȹ − ȹ ȹ ȹ τ t Ⱥ Ⱥ •  Graphically, this has the behaviour: € € Transient Conduc/on •  Validity of Lumped Capacitance Method –  We have seen that the Biot number plays a role in determining when a body is approximately isothermal at any instant. –  We may write the solu/on more generally as: T − T∞ = exp( − Bi⋅ Fo) Ti − T∞ hL Bi = k αt Fo = 2 * Fo is the Fourier number, or dimensionless /me! L •  Here L is semi ­slab length scale associated € with the body. By comparison with the exact solu/on we see that: V L= A 9 Transient Conduc/on •  Shape Effects: Geometry Plane Wall Cylinder Sphere Solution T − T∞ = exp( −Bi⋅ Fo) Ti − T∞ T − T∞ = exp( −2 Bi⋅ Fo) Ti − T∞ T − T∞ = exp( −3Bi⋅...
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