# Numerical Simulation of Forced Convective Heat Transfer Past a Square Diamond-Shaped Porous Cylinder

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## Abstract

Fluid flow and heat transfer around and through a porous cylinder is an important issue in engineering applications. In this paper a numerical study is carried out for simulating the fluid flow and forced convection heat transfer around and through a square diamond-shaped porous cylinder. The flow is two-dimensional, steady, and laminar. Conservation laws of mass, momentum, and heat transport equations are applied in the clear region and Darcy–Brinkman–Forchheimer model for simulating the flow in the porous medium has been used. Equations with the relevant boundary conditions are numerically solved using a finite volume approach. In this study, Reynolds and Darcy numbers are varied within the ranges of $$1<Re<45$$ and $$10^{-6}<Da<10^{- 2}$$, respectively. The porosity $$(\varepsilon )$$ is 0.5. This paper presents the effect of Reynolds and Darcy numbers on the flow structure and heat transfer characteristics. Finally, these parameters are compared among solid and porous cylinder. It was found that the drag coefficient decreases and flow separation from the cylinder is delayed with increasing Darcy number. Also the size of the thermal plume decreases by decreasing Darcy number.

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## Abbreviations

$$c_\mathrm{{p}}$$ :

Specific heat (J/kg K)

$$C_\mathrm{{D}}$$ :

Drag coefficient

$$C_\mathrm{{F}}$$ :

Forchheimer coefficient

$$D$$ :

Diameter of the cylinder (m)

$$Da$$ :

Darcy number (=$$K/D^{2}$$)

$$F_\mathrm{{d}}$$ :

Drag force (N)

$$h$$ :

Heat transfer coefficient (W/m$$^{2}$$ K)

$$k$$ :

Thermal conductivity (W/m K)

$$K$$ :

Permeability (m$$^{2}$$)

$$Nu$$ :

Nusselt number (=$$hD/k$$)

$$Nu_\mathrm{ave}$$ :

Average Nusselt number

$$P$$ :

Pressure (Pa)

$$Pe$$ :

Péclet number (=$$Re\times Pr$$)

$$Pr$$ :

Prandtl number (=$$\nu /\alpha$$)

$$q^{\prime \prime \prime }$$ :

Heat source (W/m$$^{3}$$)

$$R_\mathrm{{c}}$$ :

Thermal conductivity ratio, (=$$k_\mathrm{{eff}}/k_\mathrm{{f}}$$)

$$Re$$ :

Reynolds number (=$$U_{\infty }D/\nu$$)

$$t$$ :

Time (s)

$$T$$ :

Temperature (K)

$$x,y$$ :

Rectangular coordinates (m)

$$\overline{x} , \overline{y}$$ :

Rectangular coordinates for parallel and normal to the surfaces of cylinder (m)

$$u, v$$ :

Velocity component in $$x$$ and $$y$$ directions (m s$$^{-1}$$)

$$\overline{u} ,\overline{v}$$ :

Velocity component in $$\overline{x}$$ and $$\overline{y}$$ directions (m s$$^{-1}$$)

$$\alpha$$ :

Thermal diffusivity (m$$^{2}$$ s$$^{-1}$$)

$$\varepsilon$$ :

Porosity

$$\mu$$ :

Dynamic viscosity (kg m$$^{-1}$$ s$$^{-1}$$)

$$\nu$$ :

Fluid kinematic viscosity (m$$^{2}$$ s$$^{-1}$$)

$$\rho$$ :

Fluid density (kg m$$^{-3}$$)

ave:

Average

eff:

Effective

f:

Fluid

p:

Pressure force

r:

Ratio

s:

Solid

w:

Wall

$$\infty$$ :

Free stream

1:

Clear fluid domain

2:

Porous domain

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Correspondence to I. Pop.

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Rashidi, S., Bovand, M., Pop, I. et al. Numerical Simulation of Forced Convective Heat Transfer Past a Square Diamond-Shaped Porous Cylinder. Transp Porous Med 102, 207–225 (2014). https://doi.org/10.1007/s11242-014-0272-0