## Related questions with answers

A concrete wall, which has a surface area of $20 \mathrm{m}^{2}$ and is 0.30 m thick, separates conditioned room air from ambient air. The temperature of the inner surface of the wall is maintained at $25^{\circ} \mathrm{C}$, and the thermal conductivity of the concrete is $1 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$. (a) Determine the heat loss through the wall for outer surface temperatures ranging from $-15^{\circ} \mathrm{C}$ to $38^{\circ} \mathrm{C}$, which correspond to winter and summer extremes, respectively. Display your results graphically. (b) On your graph, also plot the heat loss as a function of the outer surface temperature for wall materials having thermal conductivities of 0.75 and $1.25 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$. Explain the family of curves you have obtained.

Solutions

VerifiedWe are given the following data:

$\begin{align*} A&=20\mathrm{~m^2}\\\\ L &=0.30\mathrm{~m}\\\\ T_i &=25\mathrm{\degree{C}}\\\\ k&=1\:\frac{\text{W}}{\text{m}\cdot{\text{K}}}\\\\ \end{align*}$

Required: $\cdot$ The heat loss through-plane wall in extreme summer and extreme winter and plotting it on the graph. $\cdot$ Plot the heat loss as a function of the outer surface temperature for wall materials.

$\rule{430pt}{1pt}$

$\text{\textcolor{#4257b2}{\textbf{Given}}}$

-Concerete wall

-The main temprature $T=25 \text{\textdegree} \ \mathrm{C}$

-The Area f wall $A=20\ \mathrm{m^{2}}$

-The thermal conductivity $K=1\ \mathrm{W/m.\text{\textdegree} \ \mathrm{C}}$

-The length $L=3 \times10^{-2}$

$\text{\textcolor{#4257b2}{\textbf{Required}}}$

(a)The heat transfer rate at:

-The wall temprature has range $T_w=-15 : 38\text{\textdegree} \ \mathrm{C}$

(b)The heat transfer rate at:

-The thermal conductivity has range f $K=0.75 :1.25 \ \mathrm{W/m.\text{\textdegree} \ \mathrm{C}}$

$\text{\textcolor{#4257b2}{\textbf{Assumption}}}$

-One dimension heat flow

-Constant thermal conductivity

-Steady state condition

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