{
  "model": "One-dimensional constant-property inert slab; two fixed-temperature faces; analytical Fourier series",
  "parameters": {
    "thermal_diffusivity_m2_s": 1e-07,
    "half_thickness_m": 0.01,
    "initial_temperature_C": 20.0,
    "fixed_face_temperature_C": 5.0,
    "characteristic_time_s": 1000.0000000000001
  },
  "series_terms": 64,
  "minimum_Fo": 0.001,
  "formula": "theta=sum_n 4*(-1)^n/((2*n+1)*pi)*cos((2*n+1)*pi*x/(2*L))*exp(-(2*n+1)^2*pi^2*Fo/4)",
  "validation": {
    "64_vs_128_terms_max_difference_C": 0.0,
    "explicit_finite_difference": [
      {
        "intervals": 100,
        "results": [
          {
            "fourier_number": 0.01,
            "max_temperature_error_C": 0.03036833371477532,
            "centre_temperature_error_C": 4.505229522777654e-11,
            "time_step_Fo": 0.00015873015873015873,
            "stability_ratio": 0.3968253968253968
          },
          {
            "fourier_number": 0.05,
            "max_temperature_error_C": 0.0061329611265248385,
            "centre_temperature_error_C": 0.0006621932850109369,
            "time_step_Fo": 0.00016,
            "stability_ratio": 0.4
          },
          {
            "fourier_number": 0.2,
            "max_temperature_error_C": 0.0014407419680034783,
            "centre_temperature_error_C": 0.0012215021902478584,
            "time_step_Fo": 0.00015991471215351814,
            "stability_ratio": 0.39978678038379534
          },
          {
            "fourier_number": 1.0,
            "max_temperature_error_C": 0.0005932333962439112,
            "centre_temperature_error_C": 0.0005932333962439112,
            "time_step_Fo": 0.00016,
            "stability_ratio": 0.4
          }
        ]
      },
      {
        "intervals": 200,
        "results": [
          {
            "fourier_number": 0.01,
            "max_temperature_error_C": 0.0076683861196569225,
            "centre_temperature_error_C": 2.381261854367267e-11,
            "time_step_Fo": 4e-05,
            "stability_ratio": 0.4
          },
          {
            "fourier_number": 0.05,
            "max_temperature_error_C": 0.0015361172063887985,
            "centre_temperature_error_C": 0.00016584675226805068,
            "time_step_Fo": 4e-05,
            "stability_ratio": 0.4
          },
          {
            "fourier_number": 0.2,
            "max_temperature_error_C": 0.00036038667183491135,
            "centre_temperature_error_C": 0.00030536250835100365,
            "time_step_Fo": 3.998933617701947e-05,
            "stability_ratio": 0.3998933617701947
          },
          {
            "fourier_number": 1.0,
            "max_temperature_error_C": 0.00014833419951343352,
            "centre_temperature_error_C": 0.00014833419951343352,
            "time_step_Fo": 4e-05,
            "stability_ratio": 0.4
          }
        ]
      },
      {
        "intervals": 400,
        "results": [
          {
            "fourier_number": 0.01,
            "max_temperature_error_C": 0.0019206509363550728,
            "centre_temperature_error_C": 7.309153282619718e-12,
            "time_step_Fo": 1e-05,
            "stability_ratio": 0.4
          },
          {
            "fourier_number": 0.05,
            "max_temperature_error_C": 0.0003841604219101402,
            "centre_temperature_error_C": 4.144488347512798e-05,
            "time_step_Fo": 1e-05,
            "stability_ratio": 0.4
          },
          {
            "fourier_number": 0.2,
            "max_temperature_error_C": 9.011366879696503e-05,
            "centre_temperature_error_C": 7.633982932131467e-05,
            "time_step_Fo": 9.999333377774817e-06,
            "stability_ratio": 0.39997333511099264
          },
          {
            "fourier_number": 1.0,
            "max_temperature_error_C": 3.7085173244591485e-05,
            "centre_temperature_error_C": 3.7085173244591485e-05,
            "time_step_Fo": 1e-05,
            "stability_ratio": 0.4
          }
        ]
      }
    ],
    "bounds_and_monotonic_centre_checks": "passed"
  },
  "limitations": [
    "Synthetic calculation, not experimental measurements.",
    "No phase change, fluid motion, heat production, finite convection resistance or temperature-dependent properties.",
    "The surface jumps instantaneously at t=0; plotted domain is t>0.",
    "An infinitely wide plane wall removes lateral edge losses.",
    "No biological, food safety or cryopreservation claims."
  ],
  "source": "https://ocw.mit.edu/courses/3-044-materials-processing-spring-2013/6b75f358c8da03e1a3ea70a6e2098dd5_MIT3_044S13_TranHeaCondSol.pdf"
}