1. Spencer Ferguson and Natalie Siddoway April 7, 2014
Transient Conduction Approximation Calculator (Lumped Capacitance and Analytical approximations)
Spencer Ferguson and Natalie Siddoway April 7, 2014

2. Transient Conduction Approximations
Lumped Capacitance
Assumes temperature uniformity throughout the body
Valid for Bi < 0.1
Analytical approach
More accurate
More complex solution

3. Approximation Calculator
Calculates the time required for a body to reach a specified temperature
Lumped Capacitance: body temperature
Analytical method: any location on body
Inputs: h, k, ρ, c_p, temperatures, geometry, desired location (analytical only)
Output: approximated time to reach a temperature

4. Calculator layout Step 1: Input desired parameters
Step 2: Input known and desired temperatures
Step 3: Select geometry for application

5. Calculator layout Step 4: Input geometry sizes (follow layout)
Step 5: Input desired location (analytical only)
Step 6: For analytical, use linear interpolator to find c1 and ξ (also J_0 for cylinders)
Evaluate solutions

6. Example Problem
A sphere 30 mm in diameter initially at 800 K is quenched in a large bath having a constant temperature of 320 K with a convection heat transfer coefficient of 75 W/m^2-K. The thermophysical properties of the sphere material are: ρ=400 kg/m^3, c=1600 J/kg-K and k=1.7 W/m-K. Calculate the time required for the surface of the sphere to reach 415 K.
Steps 1&2: Input desired parameters and temperatures
Steps 3&4: Select geometry for application and input sizes

7. Example Problem
A sphere 30 mm in diameter initially at 800 K is quenched in a large bath having a constant temperature of 320 K with a convection heat transfer coefficient of 75 W/m^2-K. The thermophysical properties of the sphere material are: ρ=400 kg/m^3, c=1600 J/kg-K and k=1.7 W/m-K. Calculate the time required for the surface of the sphere to reach 415 K.
Steps 5&6: Input desired location, find c1 and ξ
Evaluate solutions:
Lumped Capacitance Bi > 0.1, so lumped capacitance method is invalid
Analytical Fo > 0.2, so analytical approximation is valid