, Volume 54, Issue 1–2, pp 135–153 | Cite as

Lattice Boltzmann simulation of nanofluid conjugate heat transfer in a wide microchannel: effect of temperature jump, axial conduction and viscous dissipation

  • Ali Alipour Lalami
  • Mohammad KaltehEmail author


In the present study, conjugate heat transfer of nanofluid in a wide microchannel with thick wall, by considering the velocity slip and temperature jump on the fluid–solid interface and also the effect of viscous dissipation is investigated. For numerical solution of velocity field, preconditioned lattice Boltzmann method (PLBM) based on standard LBM, and for temperature field, standard LBM are used. Upper wall of the microchannel is insulated and uniform heat flux is imposed on the lower wall of the solid region. For applying the temperature jump boundary condition on the fluid–solid interface, a new algorithm reported here, is used. The problem is solved for dimensionless slip coefficient 0–0.1, volume fraction 0, 0.02 and 0.04, nanoparticles diameters (10–50) nm, and also Reynolds numbers 10–150. The results of the presented algorithm for conjugate heat transfer with temperature jump at the fluid–solid interface, show good agreement with analytical and other numerical solutions. Also, it is shown that in conjugate heat transfer of nanofluid, using super hydrophobic surfaces not only has no considerable negative effect on the average Nusselt number, but also it can increase it, especially in higher Reynolds numbers. As well as, in conjugate heat transfer, unlike the conditions of ignoring the wall thickness (at constant heat flux boundary condition), temperature jump on the wall is not constant and depends on the Reynolds number. On the other hands, using super hydrophobic surfaces (considering velocity slip and temperature jump on the wall), decreases the effect of viscous dissipation, specially at higher volume fraction of nanoparticles.


LBM Conjugate heat transfer Velocity slip Temperature jump Nanofluid Viscous dissipation 

List of symbols

B = β/HC

Dimensionless slip coefficient

Br = µUin2/q″Hc

Brinkman number


Microscopic lattice velocity


Conduction number


Specific heat capacity (J/kg K)


Specific heat capacity (J/kg K)


Lattice speed of sound


Diameter (m)

Dh = 2Hc

Hydraulic diameter (m)


Density distribution function


Dimensionless temperature distribution function

Gr−1 = x/Dh Red Pr

Graetz number


Height of the microchannel (m)


Solid wall thickness (m)


Thermal conductivity coefficient (W/m K)

Kn = λ/Dh

Knudsen number


Boltzmann constant (J/K)


Length of microchannel (m)


Molecular weight (kg/k mol)


Avogadro’s number, 6.023 × 10−23 (Molecule/mol)


Nusselt number


Average Nusselt number


Fully developed Nusselt number

Pr = ν/α

Prandtl number


Heat flux (W/m2)

Re = Uin Hc/νnf

Reynolds number

Red = Uin Dhnf

Reynolds number (based on hydraulic diameter)


Specific Reynolds number


Source term


Temperature (K)


Bulk temperature


Lattice time


Horizontal velocity (m/s)

x, y

Horizontal and vertical coordinates (m)


Vertical velocity (m/s)


Velocity vector (m/s)

Greek symbols


Thermal diffusivity coefficient (m2/s)


Slip coefficient (m)


Adjustable parameter for PLBM

Γ = Cp/Cv

Specific heat capacity ratio


Temperature jump coefficient

θ = (T − Tin)/(q″Hc/kf)

Dimensionless temperature

θd = (T − Tin)/(q″Dh/kf)

Dimensionless temperature

θFD = (T − Tsint)/(q″Hc/2kf)

Dimensionless temperature


Dimensionless temperature jump


Dimensionless temp jump based on the bulk temperature


Mean free path (m)


Viscosity (Pa s)


Kinematic viscosity (m2/s)


Density (kg/m3)


Relaxation time for f


Relaxation time for g

\(\overline{{\uptau_{\text{w}} }}\)

Average shear stress (Pa)


Volume fraction of nanoparticles


Weight coefficient


Collision operator

Super- and sub-scripts




Pure fluid


Inlet of channel


Interface of fluid–solid






Solid region




Compliance with ethical standards

Conflict of interest

We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUniversity of GuilanRashtIran

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