Problem Solving Approaches

Problem solving process

Establishing a standardized routine for tackling technical challenges is vital for maintaining precision and clarity. Approaching conservation and accounting tasks in a systematic way ensures that your work is transparent, easy to audit, and repeatable by others. While these stages might feel redundant for basic exercises, mastering this "Avengers Assemble" framework is essential for managing the high-level complexity found in professional engineering.

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Assemble

Phase 1. Assemble. Your first task is to collect and reorganize all data related to the scenario. Start by explicitly defining your goal; for example, "Determine the velocity of..." or "Calculate the mass of...".

Visualize the System: Create a comprehensive diagram that captures all moving parts. A basic block flow diagram is often the most effective way to show materials entering or exiting the system.
Define Boundaries: Clearly mark the system limits and the surrounding environment. Include every known numerical value directly on the sketch to centralize your information.

Analyze

Phase 2. In this stage, you build a logical bridge between what is known and what remains to be found.

Document Assumptions: Biological environments are incredibly intricate, involving numerous simultaneous reactions and transport phenomena. A skilled engineer knows how to simplify these systems—such as treating a blood vessel as a rigid pipe—to focus on the most important variables.
Establish a Calculation Basis: Pick a specific starting point, such as a set time frame or a fixed flow rate. If the problem only provides relative ratios rather than absolute numbers, you must choose a basis to make the math possible.
Chemical Balances: If the scenario involves reactions, identify every participating molecule and ensure the chemical equations are stoichiometrically balanced before proceeding.

Example Problem: Balance the chemical reaction. #undefined

Balance the atoms for each element separately, starting with carbon atoms.

$$ CH_4 + O_2 \rightarrow CO_2 + H_2O $$

There is one carbon atom on each side, so that is balanced. The hydrogen atom balance has 4 of the left and 2 on the right side. We need to add a 2 to the water to balance it. There are two oxygen atoms on the left and four on the right, we need to add a 2 to the oxygen compound. Now we can check the balance and verify. Consider drawing a table to help you keep track

Element	Left Side (Reactants)	Right Side (Products)
Carbon (C)	1	1
Hydrogen (H)	4	2 -> 4
Oxygen (O)	2 -> 4	4

Calculate

Phase 3. Calculate. With the framework ready, you can now construct and solve your mathematical models.

Identify Governing Equations: List the relevant accounting or conservation formulas. You can often simplify these by evaluating the system state; for instance, if the process is at steady-state, you can immediately set the accumulation term to zero.
Execute the Math: Solve for your variables in a structured sequence. While some problems can be solved step-by-step by hand, more complex systems may require computational tools like MATLAB to handle multiple simultaneous equations.

Finalize

Phase 4. Finalize. The final step is to present your findings clearly and verify their accuracy.

Present Results: Clearly state the final values, ensuring they include the correct units and reflect the proper number of significant figures. Double-check that you have actually answered the specific question posed at the start.
Quality Assurance: Confirm the validity of your answer using these three techniques:

Inverse Verification: Plug your result back into the original formulas to see if they balance.
Rough Approximation: Perform a "back-of-the-envelope" calculation to ensure your exact answer is in the right ballpark.
The Logic Test: Ask if the number makes physical sense (e.g., a prosthetic limb shouldn't weigh more than the patient).