Question

A furnace wall consisting of 0.25 m of fire clay brick, 0.20 m of kaolin, and a 0.10-m outer layer of masonry brick is exposed to furnace gas at 1370 K with air at 300 K adjacent to the outside wall. The inside and outside convective heat transfer coefficients are 115 and 23 W/m2 K, respectively.

The outside temperature of the masonry brick cannot exceed 325 K, by how much must the thickness of kaolin be adjusted to satisfy this requirement?

Answer 1

To calculate the thickness of kaolin needed to satisfy the requirement, we can use Fourier's law of heat conduction and the convective heat transfer coefficients of the furnace wall surfaces.

Step-by-step explanation:

To calculate the thickness of kaolin needed to satisfy the requirement that the outside temperature of the masonry brick cannot exceed 325 K, we need to consider the heat transfer through the entire furnace wall. The rate of heat conduction can be calculated using Fourier's law of heat conduction:

Q = (kA * ΔT) / d

Where:

Q is the rate of heat conduction (in W)

k is the thermal conductivity (in W/m.K)

A is the cross-sectional area of the wall (in m²)

ΔT is the temperature difference across the wall (in K)

d is the thickness of the wall (in m)

By setting the heat transfer between the gas and the masonry brick surface equal to the rate of heat conduction, we can solve for the thickness of kaolin that satisfies the requirement.