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Consider a small chimney constructed from two different
materials. The inner layer is constructed
from concrete with a thermal conductivity, 𝑘 = 0.07 𝐵𝑡𝑢/ℎ𝑟 𝑖𝑛 °𝐹.
The outer layer is constructed
from bricks with a thermal conductivity, 𝑘 = 0.04 𝐵𝑡𝑢/ℎ𝑟 𝑖𝑛 °𝐹. The
temperature of the hot gases
on the inside of the chimney is 𝟏𝟒𝟎 °𝑭, with a heat transfer
coefficient ℎ = 0.037 𝐵𝑡𝑢/ℎ𝑟 𝑖𝑛2 °𝐹. The
outside surface is exposed to the surrounding air, which is at 𝟏𝟎
°𝑭, with a corresponding heat
transfer coefficient, ℎ = 0.012 𝐵𝑡𝑢/ℎ𝑟𝑖𝑛2 °𝐹. The dimensions are
shown below. Determine the
temperature distribution within the concrete and brick layers and
plot the temperature gradients
along path A-A.
1. Find the temperature value at the interface (DIST=1) between the
brick and concrete.
2. Find the value of thermal gradient in the x-direction (DTDX) at
the interface between the
brick and concrete.
PLEASE SOLVE THE QUESTION ANALYTICLY :
Answers are :
116.707 F
Consider a small chimney constructed from two different materials. The inner layer is constructed from concrete with a thermal conductivity, k = 0.07 Btu/hr in °F. The outer layer is constructed from bricks with a thermal conductivity, k = 0.04 Btu/hr in °F. The temperature of the hot gases on the inside of the chimney is 140 °F, with a heat transfer coefficient h = 0.037 Btu/hr in2 °F. The outside surface is exposed to the surrounding air, which is at 10 °F, with a corresponding heat transfer coefficient, h = 0.012 Btu/hrin? °F. The dimensions are shown below. Determine the temperature distribution within the concrete and brick layers and plot the temperature gradients along path A-A. Brick O Concrete 1 in. 12 in. 26 in. A 12 in. 26 in. 1. Find the temperature value at the interface (DIST=1) between the brick and concrete. 2. Find the value of thermal gradient in the x-direction (DTDX) at the interface between the brick and concrete.