SEMI-INFINITE SOLIDS CALCULATOR

Katherine Reinke Deason

Motivation

Easily solve the complicated equations for semi-infinite solids

Accurately solve the non-linear equations to find any variable in all 3 cases

Calculator GUI

Description of application for each case

Material properties calculated at Ti of the solid

Choose one of 3 variables to calculate

If a non-linear equation is produced, a pop-up window will prompt for a guess to begin the solver

Click solve to calculate the highlighted variable!

Fill in given temperatures

Choose which case applies to problem

Example 1: Problem 5.71 in Fundamentals of Heat and Mass Transfer 6th Ed

Problem: A tile-iron consists of a massive plate maintained at 150°C by an imbedded electrical heater. The iron is placed in contact with a tile to soften the adhesive. The adhesive will soften sufficiently if heated above 50°C for at least 2 min, but its temperature should not exceed 120°C. Assume the tile and subfloor to have an initial temperature of 25°C and to have equivalent thermophysical properties of k=0.15W/m/K and ρcp = 1.5E6J/m3/K. How long will it take to soften sufficiently?

Answer:At 0.004m it will be 323K or 50°C after 48.71s.

Example 2:Problem 5.79 in Fundamentals of Heat and Mass Transfer 6th Ed

Answer:At 0.0m it will be 582.39K or 309°C which is below 325°C, so the design is acceptable.

Problem: Consider a 0.25m thick concrete wall (k=1.4 W/m/K and ρ=2300 kg/m3, c = 880 J/m3/K), which is at an initial temperature of 25°C and irradiated at one surface with a heat flux of q” = 104 W/m2. The absorptivity is = 1.0. If the building code requirements dictate that the temperatures of the irradiated and back surfaces must not exceed 325°C and 25°C , respectively, after 30 min of heating, will the requirements be met?

Example 3:Problem 5.69 in Fundamentals of Heat and Mass Transfer 6th

Ed

Answer:At 0.025m it will be 323K or 50°C after 16013.9s.

Problem: A thick steel slab (k=50 W/m/K and ρ=7800 kg/m3, c = 480 J/m3/K), is initially at 300°C and is cooled by water jets impinging on one of its surfaces. The temperature of the water is 25°C, and the jets maintain an extremely large, approximately uniform convection coefficient at the surface. Assuming that the surface is maintained at the temperature of the water throughout the cooling, how long will it take for the temperature to reach 50°C at a distance of 2 mm from the surface?