1. Heat Diffusion Equation Apply this equation to a solid undergoing conduction heat transfer: E=mc p T=(  V)c p T=  (dxdydz)c p T dy dx qxqx q x+dx x y All go to zero

2. Heat Diffusion Equation (2) Generalized to three-dimensional Note: partial differential operator is used since T=T(x,y,z,t)

3. Heat Diffusion Equation (3)

4. 1-D, Steady Heat Transfer T(x=0)=100°C=C 2 T(x=1 m)=20°C=C 1 +C 2, C 1 =-80°C T(x)=100-80x (°C) 100 20 T x

5. 1-D Heat Transfer (cont.) T1T1 T2T2 x L q (I) T 1 (V 1 ) T 2 (V 2 ) R (R) Electric circuit analogy I = (V 1 -V 2 )/R

6. Composite Wall Heat Transfer T1T1 T2T2 L1L1 L2L2 k1k1 k2k2 T2T2 T1T1 R 1 =L 1 /(k 1 A) R 2 =L 2 /(k 2 A) T Note: In the US, insulation materials are often specified in terms of their thermal resistance in (hr ft 2 °F)/Btu ----> 1 Btu=1055 J. R-value = L/k, R-11 for wall, R-19 to R-31 for ceiling. T

7. R value The thermal resistance of insulation material can be characterized by its R-value. R is defined as the temperature difference across the insulation by the heat flux going through it: The typical space inside the residential frame wall is 3.5 in. Find the R-value if the wall cavity is filled with fiberglass batt. (k=0.046 W/m.K=0.027 Btu/h.ft.R)