Determination of Local Heat Transfer Coefficients and Friction Factors at Variable Temperature and Velocity Boundary Conditions for Complex Flows

Transient conjugate heat transfer measurements under varying temperature and velocity inlet boundary conditions at incompressible flow conditions were performed for flat plate and ribbed channel geometries. Therefrom, local adiabatic wall temperatures and heat transfer coefficients were determined. The data were analyzed using typical heat transfer correlations, e.g., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Nu</mi><mo>=</mo><mi>C</mi><msup><mrow><mi>Re</mi></mrow><mi>m</mi></msup><msup><mrow><mi>Pr</mi></mrow><mi>n</mi></msup></mrow></semantics></math></inline-formula>, determining the local distributions of <i>C</i> and <i>m</i>. It is shown that they are closely linked. A relationship <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">ln</mo><mfenced open="(" close=")"><mi>C</mi></mfenced><mo>=</mo><mi>A</mi><mo>−</mo><mi>m</mi><mi>B</mi></mrow></semantics></math></inline-formula> is observed, with <i>A</i> and <i>B</i> as modeling parameters. They could be related to parameters in log-law or power-law representations for turbulent boundary layer flows. The parameter <i>m</i> is shown to have a close link to local pressure gradients and, therewith, near wall streamlines as well as friction factor distributions. A normalization of the <i>C</i> parameter allows one to derive a Reynolds analogy factor and, therefrom, local wall shear stresses.