Heat and Mass Transfer

, Volume 50, Issue 6, pp 865–875 | Cite as

Maximum thermal conductance for a micro-channel, utilising Newtonian and non-Newtonian fluid

  • M. D. Stocks
  • T. Bello-OchendeEmail author
  • J. P. Meyer


This paper investigates the thermal behaviour of two micro-channel elements cooled by Newtonian and non-Newtonian fluids, with the objective to maximise thermal conductance subject to constraints. This is done firstly for a two-dimensional duct micro-channel and secondly for a three-dimensional complex micro-channel. A numerical model is used to solve the governing equations relating to flow and temperature fields for both cases. The geometric configuration of each cooling channel is optimised for Newtonian and non-Newtonian fluid at a fixed inlet velocity and heat flux. In addition, the effect of porosity on thermal conductance is investigated. It was found, in both cases, that the non-Newtonian fluid characteristics result in a significant variation in thermal conductance as inlet velocity is increased. The characteristics of a dilatant fluid greatly reduce thermal conductance on account of shear thickening on the boundary surface. In contrast, a pseudoplastic fluid shows increased thermal conductance. A comparison of the complex micro-channel and the duct micro-channel shows the improved thermal conductance resulting from greater flow access to the conductive area, achieved by the complex micro-channel.


Heat Transfer Rate Excess Temperature Geometric Optimisation Bejan Number Pseudoplastic Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

Latin symbols


Total channel area (m2)


Global thermal conductance


Specific heat (J/K)


Channel depth (m)


Diameter of channel before branching (m)


Diameter of channel after branching (m)


Total channel height (m)


Thermal conductivity (W/m K)


Consistency (Pa s0.5)


Total channel length (m)


Length of channel before branching (m)


Length of channel after branching (m)


Power law index


Pressure (Pa)


Total heat transfer (W)


Global thermal resistance


Reynolds number


Temperature (K)


Average velocity (m/s)

\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{U} \)

Velocity vector (m/s)


Total channel volume (m3)

Greek symbols


Ratio of L 1 to L

\( \dot{\gamma } \)

Rate of strain


Angle between branches (radians)


Viscosity (kg/m s)


Density (kg/m3)


Porosity ratio



Dimensionless variable








The authors acknowledge with gratitude the funding obtained from the NRF, TESP, University of Stellenbosch/University of Pretoria, SANERI/SANEDI, CSIR EEDSM Hub and NAC and the National Research Foundation (NRF-DST), as well as support from Aerotherm.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mechanical and Aeronautical EngineeringUniversity of PretoriaHatfield, PretoriaSouth Africa
  2. 2.Department of Mechanical EngineeringUniversity of Cape TownRondeboschSouth Africa

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