HeatTransfer-I-Section-2

# Thermal conducvity can vary with posion due to

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Unformatted text preview: e to the temperature gradient normal to the € surface. 3 Conduc'on Equa'on •  Thermal conduc'vity ranges of maPer. There are numerous tabulated values given in your book for metals, non ­metals, gases, and liquids. •  Thermal conduc'vity can vary with posi'on due to temperature and can also be direc'onal (kx, ky, kz) if the material is not isotropic. Note: Ⱥ W Ⱥ k Ⱥ Ⱥ mK Ⱥ Ⱥ € 4 Conduc'on Equa'on •  Deriva'on of the conduc'on equa'on: –  deﬁne a basic control volume 5 Conduc'on Equa'on •  For the control volume shown earlier, we apply conserva'on of energy and consider ˙ ˙ ˙ ˙ E stored = E in − E out + E generated –  heat ﬂow into and out of each face, € ∂T ∂T ∂T dydz qy = −k dxdz qz = − k dxdy ∂x ∂y ∂z ∂qy ∂q ∂qx = qx + dx qy + dy = qy + dy qz + dz = qz + z dz ∂x ∂y ∂z qx = −k qx + dx € –  heat generated uniformly in the CV due to sources such as electrical hea'ng [q’’’ = q/Volume], € ˙ E generated = q' ' ' dxdydz –  heat energy stored at any point in 'me, € ˙ stored = ρc p ∂T dxdydz E ∂t 6 Conduc'on Equa'on •  Combining all terms we get: ȹ ∂qx ∂qy ∂qz ȹ ∂T ρc p dxdydz = −ȹ dx + dy + dzȹ + q' ' ' dxdydz ∂t ∂y ∂z Ⱥ ȹ ∂x Subs'tu'ng in the heat ﬂow rates in each € direc'on and simplifyi...
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## This document was uploaded on 02/14/2014 for the course ENGR 6901a at Memorial University.

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