# The effect of obstacles’ characteristics on heat transfer and fluid flow in a porous channel

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## Abstract

The fluid flow and heat transfer around obstacles are an engineering and research interest. This paper dealt with this matter in a porous channel. It explained the features of the presence of hot solid obstacles in porous media. These obstacles were located at different positions inside the medium. The particularity of this work is coupling two complex phenomena: the heat transfer in porous media and the presence of hot solid obstacles. This is the first time that these phenomenona were studied. The diffusion–convection equation is adopted to calculate the temperature. The viscous heat dissipation and compression work due to the pressure were not taken into consideration. This choice and assumptions were based on our previous work. The numerical simulation was done using the generalized lattice Boltzmann method. To ensure that our numerical code is free of errors, we resorted to benchmark cases. Then, we were interested in the effect of triangular and rectangular obstacles on the heat transfer and fluid flow in a porous channel. The isotherms and the velocity contours were studied for several dynamic parameters. The fluid behavior was described by the streamlines and the velocity fields. The velocity profile was followed along the porous channel. These results allow concluding that the Reynolds number increment led to the increase in the heat transfer and the fluid velocity. The increment of the distance between the inlet and the obstacle generates the same conclusion.

## Keywords

Thermal lattice Boltzmann method Porous channel Laminar fluid flow Convection Obstacle position and geometries## List of symbols

*c*Lattice spacing

*c*_{i}Discrete velocity for D2Q9 model

*c*_{pf}Specific heat capacity of fluid

*c*_{pc}Specific heat capacity of solid

*c*_{0}Coefficient

*c*_{1}Coefficient

*Da*Darcy number

- d
*x*, d*y* Spatial step

*f*Density distribution function

*f*^{eq}Density equilibrium distribution function

*F*Total body force

- \(F_{\varepsilon }\)
Geometric factor

*G*An external force

*g*_{0}Gravity acceleration

*g*Thermal distribution function

*g*^{eq}Thermal equilibrium distribution function

*H*Channel width

*i*Lattice index in the

*x*direction*j*Lattice index in the

*y*direction*K*Permeability

*k*Thermal conductivity

*m*Fluid particle mass

*n*The position on the right boundary

*p*Pressure

*Pr*Prandtl number

*Ra*Rayleigh number

*Re*Reynolds number

*T*Fluid temperature

*t*Time

*T*_{c}Cold temperature

*T*_{h}Hot temperature

*U*Fluid velocity

*U*_{in}*X*-Component velocity in the inlet*U*_{0}Top wall velocity

- \(\nu\)
Temporal velocity

- \(\nu_{n}\)
*Y*-Component velocity of the upper plate- \(\nu_{0}\)
Injection velocity

## Greek letters

*α*Thermal diffusivity

*β*Thermal expansion

- \(\Gamma_{c}\)
Thermal relaxation time

- \(\Gamma_{\nu }\)
Density relaxation time

*δt*Time step

*ε*Porosity

- \(\upsilon\)
Viscosity

- \(\upsilon_{\text{e}}\)
Effective viscosity

*ρ*Density

*ρ*_{f}Fluid density

*ρ*_{s}Solid density

*ρ*_{in}Inlet density

*ρ*_{N}Density of the upper plate

*σ*The ratio between

*c*_{pc}and*c*_{pf}- Σ
Internal energy

- Ω
Collision operator

*ω*_{i}Weight coefficient in the direction

*i*

## Subscripts

- e
Effective

- f
Fluid

*i*Discrete velocity direction

- in
Inlet

*m*Average

## Superscript

- eq
Equilibrium

## PACS No.

44.05.+e 44.25.+f 44.30.+v 02.70.−c## References

- [1]
- [2]
- [3]
- [4]
- [5]
- [6]M Farhadi, A A Mehrizi, K Sedighi and H H Afrouzi
*J. Technol. (Sci. Eng.)***58**59 (2012)Google Scholar - [7]
- [8]A Nabovati and A C M Sousa
*New Trends in Fluid Mechanics Research*Fifth International Conference on Fluid Mechanics**518**(2007)Google Scholar - [9]
- [10]
- [11]A A Mohamad
*Lattice Boltzmann Method Fundamentals and Engineering Applications with Computer Codes*(ed.) A A Mohamad, April 12, 2011,**18**(London: Springer) (2011)Google Scholar - [12]
- [13]S Chatti, C Ghabi and A Mhimid
*Lecture Notes in Mechanical Engineering book series (LNME)***2015**823 (2015)Google Scholar - [14]S. Succi
*The Lattice Boltzmann Equation for Fluid Dynamics and Beyond*, 1st edn. (Oxford : Clarendon Press) p 3 (2001)zbMATHGoogle Scholar - [15]
- [16]
- [17]Z Guo and T S Zhao
*Phys. Rev. E Stat. Nonlinear Soft Matter Phys.***66**036304 (2002)ADSCrossRefGoogle Scholar - [18]T Seta, E Takegoshi, K Kitano and K. Okui
*J. Therm. Sci. Technol.***1**90 (2006)ADSCrossRefGoogle Scholar - [19]A Haghshenas, M Rafati Nasr and M H Rahimian
*International Communications in Heat and Mass Transfer***37**1513 (2010)Google Scholar - [20]
- [21]L Chen, Y L He, Q Kang and W Q Tao
*J. Comput. Phys.***255**83 (2013)ADSMathSciNetCrossRefGoogle Scholar - [22]
- [23]
- [24]
- [25]
- [26]M A Mussa, S Abdullah, C S Nor Azwadi and N Muhamad
*Comput. Fluids***44**162 (2011)CrossRefGoogle Scholar - [27]
- [28]H Shokouhmand, F Jam and M R Salimpour
*Int. Commun. Heat Mass Transf.***38**1162 (2011)CrossRefGoogle Scholar - [29]