- 2069 Poush · 8 marks
Furnace brickwork: red brick thickness without filling
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.
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?
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Furnace wall: insulation thickness for heat loss · Fundamental of Thermodynamics & Heat Transfer, chapter 7
- Conduction and convection through hollow cylinder, two layers · Fundamental of Thermodynamics & Heat Transfer, chapter 7
- Steam main with two insulation layers: overall coefficients · Fundamental of Thermodynamics & Heat Transfer, chapter 7
- K1 and K2 of LLF from load pattern · Transmission and Distribution System Design, chapter 6 · asked 2×
- Built-up column, two channels toe-to-toe, 1500 kN · Design of Steel and Timber Structure, chapter 6
- Building: excavation, PCC, brick, wood work · Estimating and Costing, chapter 6
- Well foundation: sinking, brick, sand filling, PCC · Estimating and Costing, chapter 6 · asked 2×
All Fundamental of Thermodynamics & Heat Transfer chapter 7 questions →