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Simulation of Forced Convection in a Channel Containing Three Obstacles over Backward and Forward Facing Steps by LBM

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Abstract

This study describes numerically forced convection laminar fluid flow simulation in a two dimensional channel containing three obstacles over backward and forward facing steps by using the lattice Boltzmann method (LBM). The LBM and the finite difference successive over relaxation method are simultaneously used to simulate the equations which govern the flow in terms of vorticity equation and energy equation. Heated fluid is impinged to flow in the channel while the solid surfaces of obstacles and channel are maintained at a lower constant temperature. The impacts on the temperature distribution and flow for changing Reynolds number are recapitulated for a fixed Prandtl number. Also, the impacts of Prandtl numbers on the flow and temperature distribution are discussed in this study. Two levels of Nusselt numbers, the local values and the mean values on the surfaces of the three obstacles, are emphasized to illustrate heat transfer rate from fluid. It is observed that 80% increase at heat transfer is noticed due to increase of Reynolds number of 100 within the range from 100 to 300. It is also observed that 60–30% increase at heat transfer is observed due to increase of Prandtl number of unity within the range from 0.71 to 13.4.

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Abbreviations

x * :

Horizontal axis

y * :

Vertical axis

t * :

Time variable

u * :

Horizontal component of fluid velocity

v * :

Vertical component of fluid velocity

T * :

Temperature

p * :

Pressure

x :

Horizontal axis (non-dimensional)

y :

Vertical axis (non-dimensional)

t :

Time variable (non-dimensional)

u :

Fluid velocity vector (non-dimensional)

u :

Horizontal component of u

v :

Vertical component of u

T :

Temperature (non-dimensional)

p :

Pressure (non-dimensional)

H :

Channel height

U :

Reference velocity

L :

Channel length

∆t :

Time step

∆x :

Mesh size for x variable

∆y :

Mesh size for y variable

Nu :

Nusselt number

Pr :

Prandtl number

Re :

Reynolds number

Nu m :

Mean Nusselt number

T in :

Maximum inlet temperature

T w :

Wall temperature

c k :

Lattice velocity vector

c k :

Lattice speed

c s :

Speed of sound

f k :

Distribution function for ω

g k :

Distribution function for T

f eq k :

Equilibrium distribution function for ω

g eq k :

Equilibrium distribution function for T

w k :

Weighting factor

α :

Thermal diffusion co-efficient

υ :

Kinematic viscosity

ρ :

Fluid density

ψ :

Stream function

ω :

Vorticity

τ f :

Relaxation factor for fk

τ g :

Relaxation factor for gk

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Authors and Affiliations

  1. Department of Mathematics, University of Barisal, Barisal, 8200, Bangladesh

    Shujit Kumar Bala

  2. Department of Applied Mathematics, University of Dhaka, Dhaka, 1000, Bangladesh

    Litan Kumar Saha & M. Anwar Hossain

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  1. Shujit Kumar Bala
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  2. Litan Kumar Saha
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  3. M. Anwar Hossain
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Correspondence to Litan Kumar Saha.

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Bala, S.K., Saha, L.K. & Anwar Hossain, M. Simulation of Forced Convection in a Channel Containing Three Obstacles over Backward and Forward Facing Steps by LBM. Int. J. Appl. Comput. Math 5, 35 (2019). https://doi.org/10.1007/s40819-019-0622-2

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