---
title: "Furnace brickwork: red brick thickness without filling"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 7
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:furnace-brickwork-diatomite-filling"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/furnace-brickwork-diatomite-filling
site: BCT Engineering
---

# Furnace brickwork: red brick thickness without filling

Fundamental of Thermodynamics & Heat Transfer · Chapter 7: Introduction to Heat Transfer

- Asked in: 2069 Poush, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/furnace-brickwork-diatomite-filling
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-7

## Question

A brick work of a furnace is built up of layers laid of fire clay [k1 = 0.93 W/m°C] and red brick [k3 = 0.7 W/m°C] and the space between the two is filled with crushed diatomite brick [k2 = 0.13 W/m°C]. The thickness of fire clay, diatomite filling and red brick are 12 cm, 5cm and 25cm respectively. What should be thickness of the red brick layer if the brick-work is to be laid without diatomite filling between the two layers, so that the heat flux through the brick-work remains constant?

## Short answer

Equate total thermal resistance with and without diatomite. Without filling, fire clay resistance 0.1290 plus L/0.7 must equal 0.8708 m²·°C/W. Solving gives L = 0.5192 m, so the red brick thickness must be about 51.9 cm.

## Answer

**Condition.** The heat flux through the brickwork must stay the same. With the same inside and outside temperatures, this means the total thermal resistance (per m²) must be the same with and without the diatomite layer. Surface film resistances are not given and are neglected.

**Given:** fire clay L₁ = 0.12 m, k₁ = 0.93; diatomite L₂ = 0.05 m, k₂ = 0.13; red brick L₃ = 0.25 m, k₃ = 0.7 W/m·°C.

#### Resistance with the diatomite filling
R = L₁/k₁ + L₂/k₂ + L₃/k₃
R₁ = 0.12/0.93 = 0.1290 m²·°C/W
R₂ = 0.05/0.13 = 0.3846 m²·°C/W
R₃ = 0.25/0.7 = 0.3571 m²·°C/W
R = 0.8708 m²·°C/W

#### Without filling
Fire clay stays at 0.12 m (R₁ = 0.1290); the red brick has new thickness L:

R = R₁ + L/k₃

0.8708 = 0.1290 + L/0.7

L/0.7 = 0.7418

L = 0.7 × 0.7418 = 0.5192 m

**Answer: the red brick thickness must be about 51.9 cm (0.52 m)**, instead of 25 cm. The diatomite layer (5 cm) insulates as much as an extra 26.9 cm of red brick.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. With the same inside and outside temperatures, what keeps the heat flux constant when the diatomite is removed?
   A. Same total thickness
   B. Same total thermal resistance
   C. Same thickness of red brick
   D. Same conductivity
   Answer: B. q = ΔT/R_total, so the flux is unchanged only if R_total is unchanged. (Key point: Condition for constant flux)

2. What is the total resistance with the diatomite layer?
   A. 0.8708 m2K/W (sum of L/k for the three layers)
   B. 0.129 m2K/W
   C. 0.3846 m2K/W only
   D. 2.6 m2K/W
   Answer: A. 0.1290 + 0.3846 + 0.3571 = 0.8708 m2K/W, adding series layers. (Key point: Resistance with filling)

3. Without the filling, the red brick thickness needed is about:
   A. 25 cm
   B. 51.9 cm
   C. 26.9 cm
   D. 74.2 cm
   Answer: B. 0.8708 = 0.1290 + L/0.7 gives L = 0.52 m; the diatomite is worth about 26.9 cm of extra brick. (Key point: New red brick thickness)

## Related in Fundamental of Thermodynamics & Heat Transfer

- [Furnace wall: insulation thickness for heat loss](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Afurnace-fireclay-insulation-thickness) — Fundamental of Thermodynamics & Heat Transfer, chapter 7
- [Conduction and convection through hollow cylinder, two layers](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Acombined-conduction-convection-hollow-cylinder) — Fundamental of Thermodynamics & Heat Transfer, chapter 7
- [Steam main with two insulation layers: overall coefficients](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asteam-main-two-layer-lagging-overall-u) — Fundamental of Thermodynamics & Heat Transfer, chapter 7

## Related in other subjects

- [K1 and K2 of LLF from load pattern](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Allf-k1-k2-load-pattern) — Transmission and Distribution System Design, chapter 6, asked 2×
- [Built-up column, two channels toe-to-toe, 1500 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-1500kn-10m-toe-to-toe) — Design of Steel and Timber Structure, chapter 6
- [Building: excavation, PCC, brick, wood work](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Abuilding-f-fig3-four-items) — Estimating and Costing, chapter 6
- [Well foundation: sinking, brick, sand filling, PCC](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Awell-foundation-g-sand-filling) — Estimating and Costing, chapter 6, asked 2×