Transient Conduction Approximation Calculator Lumped Capacitance and Analytical

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Transient Conduction Approximation Calculator (Lumped Capacitance and Analytical approximations) Spencer Ferguson and Natalie Siddoway

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

Transient Conduction Approximations Lumped Capacitance • Assumes temperature uniformity throughout the body • Valid

Transient Conduction Approximations Lumped Capacitance • Assumes temperature uniformity throughout the body • Valid for Bi < 0. 1 Analytical approach • More accurate • More complex solution

Approximation Calculator • Calculates the time required for a body to reach a specified

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

Calculator layout Step 1: Input desired parameters Step 2: Input known and desired temperatures

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

Calculator layout Step 4: Input geometry sizes (follow layout) Step 5: Input desired location

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 c 1 and ξ (also J_0 for cylinders) Evaluate solutions

Example Problem A sphere 30 mm in diameter initially at 800 K is quenched

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

Example Problem A sphere 30 mm in diameter initially at 800 K is quenched

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 c 1 and ξ Evaluate solutions: • Lumped Capacitance Bi > 0. 1, so lumped capacitance method is invalid • Analytical Fo > 0. 2, so analytical approximation is valid

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