Heat and Mass Transfer Research Journal (HMTRJ)

Research Article

Power-Law Heat Transfer on Linearly Stretching or Shrinking Surfaces

Patrick Weidman

Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427, USA

Submitted: January 30, 2018; Revised: July 11, 2018; Accepted: July 12, 2018

Abstract

The heat transfer from a linearly stretching surface with power-law temperature variation along the surface is considered for both stretching and shrinking surfaces. For stretching sheets this extends previous works to large temperature exponents and reveals new exact solutions. Here for the first time shrinking sheets are considered for the dual solutions that exist in the presence of suction. It is proven that only the upper branch of the dual solutions is stable. Thus only the upper branch is viable and results are given at various points along this branch which exhibit discontinuities with increasing values of the temperature exponent. These discontinuities separate heat transfer away from the wall to heat transfer to the wall.

Keywords

stretching/shrinking surface; power-law temperature; shear stress; heat transfer.

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