On the application of Harris hawks optimization (HHO) algorithm to the design of microchannel heat sinks

  • Ahmad Abbasi
  • Behnam FirouziEmail author
  • Polat Sendur
Original Article


A novel Harris hawks optimization algorithm is applied to microchannel heat sinks for the minimization of entropy generation. In the formulation of the heat transfer model of the microchannel, the slip flow velocity and temperature jump boundary conditions have been taken into account. A variety of materials and fluids have also been evaluated to determine the optimal design of the microchannel. Since the main objective of this paper is to assess the search and exploration ability of the novel Harris Hawks algorithm, results are also benchmarked with those of commonly used particle swarm optimization, bees optimization algorithm, grasshopper optimization algorithm, whale optimization algorithm and dragonfly algorithm. Finally, results are compared to the analytical results and results obtained by the application of genetic algorithms. Results show that the Harris hawks algorithm has a superior performance in minimizing the entropy generation of the microchannel. The algorithm is also more computationally efficient compared to the aforementioned algorithms. Moreover, optimization results indicate that the use of copper for the microchannel and ammonia as the coolant leads to minimal entropy generation and, therefore, is considered as the best design. Considering the poor corrosive characteristics of copper, aluminum as the microchannel material is proposed as an alternative.


Optimization Harris hawks optimization (HHO) Entropy generation Micro-channel heat sink Knudsen number Metaheuristic optimization 

List of symbols


Surface area of heating (mm2)


Specific heat of fluid (J kg−1 K−1)


Hydraulic diameter (mm)


Friction factor


Volume flow rate (m3 s−1)


Channel height (mm)


Average heat transfer coefficient (W m−2 K−1)


Heat transfer coefficient for base surface (W m−2 K−1)


Heat Transfer coefficient along fin surface (W m−2 K−1)


Knudsen number


Thermal conductivity of solid (W m−1 K−1)


Thermal conductivity of air (W m−1 K−1)


Sum of entrance and exit losses


Ratio of thermal conductivity of fluid to solid


Slip constant


Length of channel in flow direction (mm)


Fin parameter (m−1)


Total mass flow rate (kg s−1) (the same symbol is used for fin parameter ABOVE)


Total number of microchannels


Nusselt number based on hydraulic diameter


Peclet number based on hydraulic diameter


Prandtl number


Heat flux (W m−2)


Resistance (K W−1)


Reynolds number based on hydraulic diameter


Total entropy generation rate (W K−1)


Absolute temperature (K)


Average velocity in channels (m s−1)


Slip velocity (m s−1)


Width of heat sink (mm)


Half of the channel width (mm)

Greek symbols


Thermal diffusivity (m2 s−1)


Channel aspect ratio


Heat sink aspect ratio


Fin spacing ratio


Pressure drop across microchannel (Pa)


Fin efficiency


Ratio of specific heats


Mean free path (m)


Absolute viscosity of fluid (kg m−1 s−1)


Kinematic viscosity of fluid (m2 s−1)


Fluid density (kg m−3)


Tangential momentum accommodation coefficient


Energy accommodation coefficient


Slip velocity coefficient


Temperature jump coefficient







Base surface




Contraction and expansion






Single fin




Heat sink













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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentOzyegin UniversityIstanbulTurkey

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