Type your question here 1. C onsider a large plane wall of thickness L=0.4 m, th
ID: 1856527 • Letter: T
Question
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1. Consider a large plane wall of thickness L=0.4 m, thermal conductivity k =1.8 W/m.K, and surface area A=30 m2. The left side of the wall is maintained at a constant temperature of T1= 900C while the right side loses heat by convection to the surrounding air at T?= 250C with a heat transfer coefficient of h = 24 W/m2.K. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall. (b) Obtain a relation for the variation of temperature in the wall by solving the differential equation and (c) evaluate the rate of heat transfer through the wall. <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /?>
Explanation / Answer
2. Relevant equations
Q?wall=?kAdT(0)/dx
d2T/dx2=0
T(0)=900
?kdT(L)/dx=h[T(L)?Ts]
3. The attempt at a solution
Solving the differential equation and applying B.C.:
T(x)=xC1+C2
T(0)=C2=900
?kC1=hLC1+hC2?250h]
C1=?h(C2?250)k+hL
Plugging numbers in:
C2=900
C1=?136.8
T(x)=900?136.8x
Q?wall=?1.8?30?(?136.8)=7,387W
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