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MATLAB for Breakfast

MATLAB for Breakfast. Evolution of heat distribution across bottom of frying pan on spiral-shaped electric Coil stovetop Tim Nickell – EPS 109, Fall 2013 – Prof. Burkhard Militzer. Context: Spiral Stovetop. Type of electric-coil stovetop

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MATLAB for Breakfast

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  1. MATLAB for Breakfast Evolution of heat distribution across bottom of frying pan on spiral-shaped electric Coil stovetop Tim Nickell – EPS 109, Fall 2013 – Prof. Burkhard Militzer

  2. Context: Spiral Stovetop • Type of electric-coil stovetop • Made from high-resistance nichrome alloy (~80% nickel, ~20% chromium) • High electrical resistivity allows coil to rapidly heat up as electric current passes through it • Goal of simulation: to model heat distribution across bottom surface of aluminum frying pan sitting on this type of burner

  3. Coding: methods, techniques, etc. • Main method = variant of the 2D time-dependent heat equation (includes internal heat source): • Adapted this equation to 2D, using form from Lab/HW 8 (discretized form of PDE): • Pan is composed of aluminum  use the density, heat conductivity, and specific heat of Al to derive kappa (heat diffusivity = k/rho*cp)

  4. Conditions and Approximations • Approximations: • Pan is extremely thin • Heat loss to air via convection = negligible on short time scales (for rough modeling purposes) • Lip of pan = excluded – only looking at the bottom surface of pan (2D) • Spiral burner = very thin (in the simulation, approximated to width of pixel) • Source term, Q: spiral-shape (like shape of burner) • Boundary conditions (bottom of pan): insulating  shaped like a circle (see below) • cooling via convection < heat transfer through pan aluminum • For both spiral and circle BC, method from Lab 2 used (if statement with radius r):

  5. “And now, our feature presentation:”

  6. Bon Appétit! (Thanks for listening!) • You can run my code by: • 1. Setting up source distribution pattern (spiral) • First, use i, j nested loop with an n = ~201x201 matrix (e.g., for I = 1:n; for j = 1:n) • Next, use method from Lab 2 to get a radius in terms of i, j (same one for making circles) • Then, come up with theta in terms of x(i), r (two loops, one for top half, one for the other) • Finally, set matrix = 1 (or whatever source temp) for all matrix(i,j) with r close to the r-value for theta at that point (solve for rnew(theta), set equal to r-old) • 2. Running the PDE as described above • 3. Insulating boundary conditions (eight loops!)

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