Radial Thermal Conductivity Apparatus
Annular test chamber housing insulation sleeve (r_1 = 20 mm, r_2 = 50 mm, L = 500 mm).
Chemical & Process Engineering / Radial Thermal Conductivity
FREE TO EXPLORELABORATORY 13 · CHEMICAL & PROCESS ENGINEERING
Radial Steady-State Conduction & Thermal Conductivity of Process Insulation
Measure the steady-state radial temperature distribution across a cylindrical specimen of process insulation material under controlled electrical heating, verify Fourier's law in cylindrical coordinates, and determine thermal conductivity k. Explore interactive transport phenomena, unit operations simulation, and chemical engineering telemetry.
TRANSPORT PHENOMENA · UNIT OPERATIONS · PROCESS CONTROL · REACTION ENGINEERING
Your virtual chemical and process engineering laboratory.
RADIAL TEMPERATURE DIFFERENCE ΔT—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Heater Power Q_e = 60.0 W.
Adjust Heater Power Q_e, then execute chemical process trial.
Chemical and process engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity transport phenomena and unit operations modeling.
Process engineering assumptions and boundary condition limits
The transport and thermodynamic models apply within the specified calibrated operating window (20.0 to 120.0 W). Evaluated using an insulation test sleeve (inner radius r_1 = 20.0 mm, outer radius r_2 = 50.0 mm, effective length L = 500 mm). Linear regression models ΔT versus electric power Q_e to extract thermal conductivity k = 0.1450 W/(m·K).
Process apparatus & industrial sensors.
Central Coaxial Nichrome Cartridge Heater
Provides uniform radial heat flux along central core up to 150 W.
Active Guard Heaters & End Insulation Plugs
Eliminates axial conductive heat leakage, ensuring strictly one-dimensional radial heat flow.
Water-Cooled Outer Heat Sink Jacket
Maintains outer surface at constant reference temperature T_2 = 25.0 ± 0.1 °C.
Multi-Point Calibrated Thermocouple Array
Measures internal temperatures at r_1, intermediate radii, and outer radius r_2 with 0.05 °C accuracy.
Digital Regulated DC Power Supply & Precision Wattmeter
Controls and measures electrical heat dissipation Q_e with ±0.05 W precision.
FOLLOW THE METHOD
A reason behind every step.
Measure the steady-state radial temperature distribution across a cylindrical specimen of process insulation material under controlled electrical heating, verify Fourier's law in cylindrical coordinates, and determine thermal conductivity k. Standardized parameter settings: 20.0, 40.0, 60.0, 80.0, 100.0, 120.0 W.
01
Specimen Alignment & Guard Tuning
Install the cylindrical insulation sleeve over the central core; energize guard heaters and adjust differential thermocouples to read 0.0 °C to eliminate axial losses.
02
Water Jacket Cooling Initialization
Circulate cooling water through the outer jacket at 5.0 L/min to stabilize outer wall temperature at T_2 = 25.0 °C.
03
Low Power Steady-State Establishment
Set central heater power to Q_e = 20.0 W; allow 45 minutes for the low-conductivity material to reach thermal steady state (drift < 0.05 °C over 10 min).
04
Temperature Profile Logging
Record inner temperature T_1, outer temperature T_2, and intermediate radial temperatures to confirm logarithmic distribution.
05
Power Stepping Protocol
Step heater power through 40.0, 60.0, 80.0, 100.0, and 120.0 W, allowing full steady-state equilibration and recording ΔT at each level.
06
Conductivity Regression Analysis
Plot radial temperature difference ΔT versus heater power Q_e, extract the thermal resistance slope S, and compute material thermal conductivity k.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates Radial Thermal Conductivity mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
ΔT = S · Q_e = 0.3850 · Q_e
| # | Electric Heater Power Q_e (W) | Radial Temperature Difference ΔT (K) | Heater electrical power Q_e (W) | Radial temperature difference ΔT = T_1 - T_2 (K) | Remove |
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CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
In steady-state one-dimensional radial heat conduction through a hollow cylinder, the temperature varies with radius r as:
The critical radius of insulation for a circular pipe exposed to convection is given by:
If the outer radius of an insulated pipe is smaller than the critical radius (r_o < r_cr), adding more insulation will:
Guarded end heaters in radial conductivity apparatus are used to enforce the condition:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
In chemical process plants, cryogenic storage terminals, and steam distribution systems, thermal insulation materials—such as calcium silicate, mineral wool, expanded perlite, and cellular glass—are mandatory to minimize parasitic thermal losses, prevent personnel burn injuries, avoid pipeline freezing, and suppress condensation. Determining the thermal conductivity k of tubular process insulation is vital for accurate thermal design. In cylindrical geometries, heat flows radially outward from an internal coaxial heating element through an annular insulation sleeve of inner radius r_1, outer radius r_2, and length L. Applying Fourier's fundamental law of heat conduction in one-dimensional steady cylindrical coordinates yields: q_r = -k A(r) · (dT/dr) = -k (2π r L) · (dT/dr). Separating variables and integrating across the annular wall establishes the classic logarithmic temperature profile: T(r) = T_1 - (T_1 - T_2) · [ln(r/r_1) / ln(r_2/r_1)], and gives the steady radial heat flow rate: q_r = [2π k L / ln(r_2/r_1)] · (T_1 - T_2). In this laboratory experiment, an annular specimen of refractory process insulation is heated with an internal coaxial electrical element across power levels from 20 to 120 W with guarded end heaters to eliminate axial heat leakage. Measuring the radial temperature difference ΔT = T_1 - T_2 directly evaluates the thermal resistance slope S and determines the material thermal conductivity k.
ΔT = S · Q_e = 0.3850 · Q_e
Evaluated using an insulation test sleeve (inner radius r_1 = 20.0 mm, outer radius r_2 = 50.0 mm, effective length L = 500 mm). Linear regression models ΔT versus electric power Q_e to extract thermal conductivity k = 0.1450 W/(m·K).