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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
cywang@mth.msu.edu

Chien Chang

Institute of Applied Mechanics and Center for Advanced Study in Theoretical Sciences, Taiwan University, Taipei 106, Taiwan
mechang@iam.ntu.edu.tw

1Corresponding author.

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

Abstract

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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