Similarity of the Temperature Profile formed by Fluid Flow along a Wall

TL;DR

This paper introduces an integral-based method for assessing the similarity of temperature profiles in 2-D fluid flow along heated or cooled walls, revealing new relationships among scaling parameters and profile behaviors.

Contribution

It presents a novel integral-based approach to determine temperature profile similarity applicable to any 2-D flow along isothermal walls, establishing new theoretical relationships.

Findings

Similarity temperature and length scales are interdependent.

Thermal displacement thickness must be a similarity length scale.

Temperature scaling parameter is proportional to free stream minus wall temperature.

Abstract

A new approach to the study of similarity of temperature profiles is presented. It is applicable for any 2-D fluid flow along an isothermal heated (cooled) wall. The approach is based on a simple concept; the area under a set of scaled temperature profile curves that show similar behavior must be equal. This leads to a new integral-based definition of temperature profile similarity. By taking simple area integrals of the scaled temperature profile and its first derivative, we also obtain a number of new results pertaining to similarity of the temperature profiles. For example, it is shown that if similarity exists, then: 1) the similarity temperature and length scaling parameters are interdependent, 2) the thermal displacement thickness must be a similar length scaling parameter, and 3) the temperature scaling parameter must be proportional to the free stream minus wall temperature values.