(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There is a wall 100 mm thick, find the U-value. Then a plasterboard lining is added of thickness x and a gap between it and the wall of 20 mm

wall thickness [tex]b=0.1[/tex]m, thermal conductivity [tex]\kappa_1=0.5 W m^{-1} K^{-1}[/tex]

plasterboard thickness [tex]x[/tex]m, thermal conductivity [tex]\kappa_2=0.1 W m^{-1} K^{-1}[/tex]

Air gap [tex]g=0.02[/tex]m,

Heat transfer coeff inside [tex]h_{in}=10 W m^{-2} K^{-1}[/tex]

Heat transfer coeff outside [tex]h_{out}=100 W m^{-2} K^{-1}[/tex]

Combined heat transfer coeff air gap [tex]h_{c}=10 W m^{-2} K^{-1}[/tex]

Temp inside [tex]\Theta_1 = 300 K[/tex]

Temp outside [tex]h_{c}= 270 K[/tex]

Cross sectional area [tex]A[/tex]

2. Relevant equations

For just the wall

rate of heat transfer [tex]q=\frac{UA(\Theta_1-\Theta_2)}{b}[/tex] where

[tex]U=(\frac{1}{h_{in}}+\frac{b}{\kappa_1}+\frac{1}{h_{out}})^{-1}[/tex]

For wall and plasterboard

rate of heat transfer [tex]q=\frac{UA(\Theta_1-\Theta_2)}{b}[/tex] where

[tex]U=(\frac{1}{h_{in}}+\frac{b}{\kappa_1}+\frac{1}{h_{c}}+\frac{x}{\kappa_2}+\frac{1}{h_{out}})^{-1}[/tex]

3. The attempt at a solution

I can work out the U-value for the wall, but I am asked then to find the U-value for the wall after lining, I can't see how to get this without having x.

Any ideas, Thanks

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# Homework Help: Steady state heat flow

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