Thermal conducvity can vary with posion due to

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 02/14/2014 for the course ENGR 6901a at Memorial University.

Ask a homework question - tutors are online