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The mathematical complexity of convection heat transfer is traced to the non-linearity of the Navier-Stokes equations of motion and the coupling of flow and thermal fields. The boundary layer concept, first introduced by Prandtl in 1904, provides major simplifications. This concept is based on the notion that under special conditions certain terms in the governing equations are much smaller than others and therefore can be neglected without significantly affecting the accuracy of the solution.

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1. Write down all the governing equations.
2. Simplify all the equations.
   1. Intuitive arguments (Guess works and hypothesis)
   2. Scale Analysis (Mostly used for verification purposes)
3. Write down all the governing Eqns and boundary conditions of problem statement. Also mention the conditions that were assumed in case of ‘sub-cases’ such as high ‘Pr’ flow and low ‘Pr’ flow.

<aside> 💡 Thermal interaction is fully characterized once fluid temperature distribution is determined. However, temperature distribution depends on velocity distribution. For the special case of constant properties, velocity distribution is independent of temperature. Since this assumption will be made throughout, in each case the solution to the velocity distribution will be determined first and used to obtain the corresponding temperature solution. The exceptions are problems involving free convection where velocity and temperature must be solved simultaneously.

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1. Blasius Solution / Similarity Eqn or Momentum Equation
   1. Non-dimentionalize the governing eqns and boundary conditions
   2. Decide the similarity variable
   3. Get the final simplified governing equation and Solve!!

Here you get to know the velocity field in the fluid domain, So now on putting the velocity in Energy equation, we get the temperature field.

1. Pohlhausen’s Solution / Similarity Equation or Energy Equation
   1. Non-dimentionalize the governing eqns and boundary conditions
   2. Decide the similarity variable
   3. Get the final simplified governing equation and Solve!!

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