Computational engineering / Reproducible scientific computing
Connecting physics, mathematical models, numerical methods, and executable code through carefully verified engineering problems.
01 Energy balance
Newton’s law of cooling in a lumped thermal model.
Spatially uniform temperature. Constant ambient temperature and coefficients. Convection only; no heat generation.
02 Temperature ODE
T — body temperature, K
T∞ — ambient temperature, K
β — cooling rate constant, s−1
Dots denote time derivatives.
The initial temperature completes the model.
03 Executable step Python
# T_inf: ambient temperature
beta = h * A / (m * cp)
dT_dt = -beta * (T - T_inf)
# Explicit Euler: use the old T
T_next = T + dt * dT_dtExplicit Euler · monotone relaxation when 0 < β Δt ≤ 1.
cp is cp, T_inf is T∞, and dt = Δt > 0 (s). An illustrative step, not experimental validation.The method
Each investigation keeps its assumptions, equations, algorithms, and evidence connected.
A running program is a beginning.
It is not evidence of accuracy.
Identify the system and relevant balance laws. Make units, dimensions, and physical interactions explicit.
State assumptions, variables, parameters, and initial or boundary conditions. Define the model’s domain of validity.
Choose a discretization appropriate to the governing problem. Examine consistency, stability, and convergence.
Translate the method into readable Python, with reproducible inputs and time grids consistent with the update rule.
Compare with analytical or independent reference solutions. Quantify error and distinguish numerical verification from physical validation.
Verification checks the calculation. Validation evaluates the model against independent physical evidence.
The investigations
One problem. An explicit model.
Computation open to inspection.
A lumped-capacitance heat-transfer investigation: deriving the cooling model, implementing explicit Euler integration, and checking analytical agreement, step-size convergence, limiting behavior, and discrete energy balance. This is an idealized teaching model, not an experimental measurement.
Areas of study
Fields of interest guiding future investigations.
About the project
Equation to Code is an independent project devoted to translating governing equations into reproducible computational experiments, with particular attention to physical interpretation, numerical accuracy, and engineering relevance.
The detailed work lives in version-controlled notebooks and repositories: assumptions, derivations, implementations, experiments, and their limitations.
About the author