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 diamondshaped porous cylinder. The flow is twodimensional, 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
References
Alazmi, B., Vafai, K.: Numerical analysis for the flow past a porous square cylinder based on the stressjump interfacialconditions. Int. J. Heat Mass Transf. 44, 1735–1749 (2001)
Bhattacharyya, S., Dhinakaran, S., Khalili, A.: Fluid motion around and through a porous cylinder. Chem. Eng. Sci. 61, 4451–4461 (2006)
Braeckmans, K., De Smedt, S.C., Leblans, M., Pauwels, R., Demeester, J.: Encoding microcarriers: present and future technologies. Nat. Rev. Drug Discov. 1, 447–456 (2002)
Chen, X.B., Yu, P., Winoto, S.H., Low, H.T.: Numerical analysis for the flow past a porous square cylinder based on the stressjump interfacialconditions. Int. J. Numer. Methods Heat Fluid Flow 18, 635–655 (2008)
Chen, X.B., Yu, P., Winoto, S.H.: Numerical analysis for the flow past a porous trapezoidalcylinder based on the stressjump interfacialconditions. Int. J. Numer. Methods Heat Fluid Flow 19, 223–241 (2009)
Dhinakaran, S., Ponmozhi, J.: Heat transfer from a permeable square cylinder to a flowing fluid. Energy Convers. Manag. 52, 2170–2182 (2011)
Jazebi, F., Rashidi, A.: An automated procedure for selecting project manager in construction firms. J. Civil Eng. Manag. 19, 97–106 (2013)
Jue, T.C.: Numerical analysis of vortex shedding behind a porous cylinder. Int. J. Numer. Methods Heat Fluid Flow 14, 649–663 (2004)
Leal, L.G., Acrivos, A.: The effect of base bleed on the steady separated flow past bluff objects. J. Fluid Mech. 39, 735–752 (1970)
Masliyah, J.H., Polikar, M.: Terminal velocities of porous spheres. Can. J. Chem. Eng. 58, 299–302 (1980)
Minkowycz, W.J., HajiSheikh, A., Vafai, K.: On departure from local thermal equilibrium in porous media due to a rapidly changing heat source: the Sparrow number. Int. J. Heat Mass Transf. 42, 3373–3385 (1999)
Nield, D.A., Bejan, A.: Convection in Porous Media, 4th edn. Springer, New York (2013)
Patankar, S.V.: Numerical Heat Transfer and Fluid Flow. Hemisphere, New York (1980)
Rashidi, A., Jazebi, F., Brilakis, I.: Neurofuzzy genetic system for selection of construction project managers. J. Const. Eng. Manag. 137, 17–29 (2011)
Rashidi, S., Tamayol, A., Valipour, M.S., Shokri, N.: Fluid flow and forced convection heat transfer around a solid cylinder wrapped with a porous ring. Int. J. Heat Mass Transf. 63, 91–100 (2013a)
Rashidi, S., Masoodi, R., Bovand, M., Valipour, M.S.: Numerical study of flow around and through a porous diamond cylinder with different apex angles. Int. J. Numer. Methods Heat Fluid Flow (2013b) (accepted)
Tan, H., Pillai, K.M.: Finite element implementation of stressjump and stresscontinuity conditions at porousmedium, clearfluid interface. Comput. Fluids 38, 1118–1131 (2009)
Tan, H. Chen, X. Pillai, K.M., Papathanasiou, T.D.: Evaluation of boundary conditions at the clearfluid and porousmedium interface using the boundary element method. In: Proceedings of the 9th International Conference on Flow Processes in Composite Materials (FPCM9). Montréal (Québec), Canada, 8–10 July, (2008)
Valipour, M.S., Zare Ghadi, A.: Numerical investigation of forced convective heat transfer around and through a porous circular cylinder with internal heat generation. ASME J. Heat Transf. 134 (2012)
Valipour, M.S., Rashidi, S., Masoodi, R.: MHD flow and heat transfer around a solid cylinder wrapped with a porous ring. ASME J. Heat Transf. (2013) (accepted)
White, F.M.: Fluid Mechanics, 6th edn. McGraw Hill, New York (2009)
Wu, H., Wang, R.: Convective heat transfer over a heated square porous cylinder in a channel. Int. J. Heat Mass Transf. 53, 1927–1937 (2010)
Yu, P., Zeng, Y., Lee, T.S., Bai, H.X., Low, H.T.: Wake structure for flow past and through a porous square cylinder. Int. J. Heat Fluid Flow 31, 141–153 (2010)
Yu, P., Zeng, Y., Lee, T.S., Chen, X.B., Low, H.T.: Steady flow around and through a permeable circular cylinder. Comput. Fluids 42, 1–12 (2011)
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Rashidi, S., Bovand, M., Pop, I. et al. Numerical Simulation of Forced Convective Heat Transfer Past a Square DiamondShaped Porous Cylinder. Transp Porous Med 102, 207–225 (2014). https://doi.org/10.1007/s1124201402720
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DOI: https://doi.org/10.1007/s1124201402720