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Heat Diffusion Equation

All go to zero. Heat Diffusion Equation. Apply this equation to a solid undergoing conduction heat transfer:. E=mc p T=( r V)c p T= r (dxdydz)c p T. dx. q x+dx. dy. q x. y. x. Heat Diffusion Equation (2). Note: partial differential operator is used since T=T(x,y,z,t).

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Heat Diffusion Equation

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  1. All go to zero Heat Diffusion Equation Apply this equation to a solid undergoing conduction heat transfer: E=mcpT=(rV)cpT=r(dxdydz)cpT dx qx+dx dy qx y x

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

  3. Heat Diffusion Equation (3)

  4. 1-D, Steady Heat Transfer T T(x=0)=100°C=C2 T(x=1 m)=20°C=C1+C2, C1=-80°C T(x)=100-80x (°C) 100 20 x

  5. 1-D Heat Transfer (cont.) T1 T2 q (I) Electric circuit analogy x T2 (V2) I = (V1-V2)/R T1 (V1) L R (R)

  6. T k2 k1 Composite Wall Heat Transfer T1 T2 R1=L1/(k1A) R2=L2/(k2A) T1 T2 T L1 L2 Note: In the US, insulation materials are often specified in terms of their thermal resistance in (hr ft2 °F)/Btu ----> 1 Btu=1055 J. R-value = L/k, R-11 for wall, R-19 to R-31 for ceiling.

  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)

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