Technical Brief

New Closed-Form Thermal Boundary Layer Solutions in Shear Flow with Power-Law Velocity

[+] Author and Article Information
C.Y. Wang

Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA

Chien Chang

Institute of Applied Mechanics and Center for Advanced Study in Theoretical Sciences, Taiwan University, Taipei 106, Taiwan

1Corresponding author.

ASME doi:10.1115/1.4042489 History: Received May 30, 2018; Revised January 07, 2019


The forced convection problem for a developing thermal boundary layer in a parallel shear flow is studied. If the shear flow has a power-law velocity profile, exact similarity thermal boundary layer solutions in terms of Gamma functions can be found. Specifically, three types of thermal boundary conditions are considered: a step temperature change, a step flux change, and a concentrated heat source. The latter is also analogous to mass diffusion form an isolated source. The mixing index for mass diffusion is found exactly.

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