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Combined Mixed Convection and Radiation Heat Transfer in the Presence of Participating Medium in a Square Cavity with an Inside Heated Plate

  • Research Article-Chemical Engineering
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Abstract

The present paper analyses the interaction between thermal radiation and mixed convection inside a square vented enclosure containing a thin heated plate. The cavity walls are assumed to be diffuse, grey and opaque, while the working fluid is considered to be a radiatively absorbing, emitting and scattering medium. The main attention is focused on the effect of plate inclination angle and radiative parameters on the thermal field, fluid flow and heat transfer rate. The mixed convection governing equations are discretised using the finite volume method and are solved using the SIMPLE algorithm, whereas the solution of the radiative transfer equation is obtained using the discrete ordinate method (DO). Flow parameters such as Grashof number Gr and Richardson number Ri, and geometrical parameters like heated plate inclination are varied to show their impact on heat transfer enhancements. The effect of radiation parameters namely the radiation–conduction parameter RC and fluid optical thickness τ are also discussed while the walls emissivity and single scattering albedo were kept constant. The obtained results show that there is not a limited angle which improves heat transfer for all considered cases, but for every Gr and Ri value, there is a specific inclination which gives the most efficient rate of heat transfer, regardless of other considered parameters. The findings also highlight the influence of thermal radiation on heat transfer behaviour within the enclosure.

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Abbreviations

C p :

Specific heat at constant pressure (J kg−1 K−1)

g :

Gravitational acceleration (m s−2)

h :

Plate length (m)

h′:

Plate midsection distance to vertical left wall (m)

I :

Radiation intensity (w m−2 sr−1)

I b :

Radiation intensity of black body (w m−2 sr−1)

Gr:

Grashof number \({\text{Gr}} = g\beta \Delta TH^{3} /\upsilon^{2}\)

H :

Height (m)

k :

Thermal conductivity (W m−1 K−1)

\(\vec{n}\) :

Normal to surface unit vector

Nu:

Local Nusselt number

\(\overline{\text{Nu}}\) :

Average Nusselt number

p (P):

Dimensional pressure (dimensionless) (Pa)

Pr:

Prandtl number (Pr = υ/α)

qr, Qr :

Dimensional net radiative flux density (dimensionless \(Q_{\text{r}} = q_{\text{r}} /\sigma T_{\text{h}}^{4}\)Qr = qr/σTH4) (W m−2)

\(\vec{r}\) :

Position vector

RC:

Radiation–conduction parameter

Re:

Reynolds number (\(\text{Re} = u_{0} H/\upsilon\))

Ri:

Richardson number (\({\text{Ri}} = {\text{Gr}}/\text{Re}^{2}\))

\(\vec{s},\vec{s}^{{^{{\prime }} }}\) :

Direction vector

S(S*):

Source term (dimensionless \(S^{*} = S/\sigma T_{\text{h}}^{4}\)) (W m−2)

T :

Dimensional temperature (K)

v (V):

Dimensional velocity component (dimensionless) (m s−1)

uo(U0):

Dimensional inlet fluid velocity (dimensionless) (m s−1)

W(w):

Inlet height (dimensionless) (m)

w :

Weight of angular quadrature (sr)

xi, (Xi):

Dimensional Cartesian coordinates (x1 = x, x2 = y) (dimensionless) (m)

α :

Thermal diffusivity (m2 s−1)

β :

Thermal expansion coefficient (K−1)

ΔT :

Temperature difference (\(\Delta T = T_{\text{h}} - T_{\text{c}}\)) (K)

ε :

Emissivity

θ1, θ2 :

Dimensionless temperature parameters (\(\theta_{1} = T_{\text{c}} /\left( {T_{\text{h}} - T_{\text{c}} } \right)\), \(\theta_{2} = T_{\text{h}} /T_{\text{c}}\))

\(\varTheta\) :

Dimensionless temperature (\(\varTheta = T - T_{\text{c}} /T_{\text{h}} - T_{\text{c}}\))

λ :

Thermal conductivity (W m−1 K−1)

μ, ν :

Dynamic viscosity, kinematic viscosity (kg m−1 s−1), (m s−1)

ρ :

Density (kg m−3)

σ :

Stefan–Boltzmann constant, σ = 5.67 × 10−8 (W m−2 K−4)

σ a :

Absorption coefficient (m−1)

σ s :

Scattering coefficient (m−1)

τ :

Optical thickness (m−1)

φ :

Thin inclination angle (°)

\(\varPhi\) :

Scattering phase function

ω :

Scattering albedo

\(\varOmega , \, \vec{\varOmega }^{{^{{\prime }} }}\) :

Solid angle (sr)

δ ij :

Delta Kronecker

b:

Black wall

h, c:

Hot and cold

cv, rd:

Convection and radiation

Tot:

Total

w:

Wall

References

  1. De Kumar, A.; Dalal, A.: A numerical study of natural convection around a square, horizontal, heated cylinder placed in an enclosure. Int. J. Heat Mass Transf. 49, 4608–4623 (2006). https://doi.org/10.1016/j.ijheatmasstransfer.2006.04.020

    Article  MATH  Google Scholar 

  2. Kim, B.S.; Lee, D.S.; Ha, M.Y.; Yoon, H.S.: A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations. Int. J. Heat Mass Transf. 51, 1888–1906 (2008). https://doi.org/10.1016/j.ijheatmasstransfer.2007.06.033

    Article  MATH  Google Scholar 

  3. Selimefendigil, F.; Öztop, H.F.: Natural convection and entropy generation of nanofluid filled cavity having different shaped obstacles under the influence of magnetic field and internal heat generation. J. Taiwan Inst. Chem. Eng. 56, 42–56 (2015). https://doi.org/10.1016/j.jtice.2015.04.018

    Article  Google Scholar 

  4. Khozeymehnezhad, H.; Ali Mirbozorgi, S.: Comparison of natural convection around a circular cylinder with a square cylinder inside a square enclosure. J. Mech. Eng. Autom. 2, 176–183 (2012). https://doi.org/10.5923/j.jmea.20120206.08

    Article  Google Scholar 

  5. Lee, H.J.; Doo, J.H.; Ha, M.Y.; Yoon, H.S.: Effects of thermal boundary conditions on natural convection in a square enclosure with an inner circular cylinder locally heated from the bottom wall. Int. J. Heat Mass Transf. 65, 435–450 (2013). https://doi.org/10.1016/j.ijheatmasstransfer.2013.06.031

    Article  Google Scholar 

  6. Roslan, R.; Saleh, H.; Hashim, I.: Natural convection in a differentially heated square enclosure with a solid polygon. Sci. World J. (2014). https://doi.org/10.1155/2014/617492

    Article  Google Scholar 

  7. Hu, J.T.; Ren, X.H.; Liu, D.; Zhao, F.Y.; Wang, H.Q.: Conjugate natural convection inside a vertical enclosure with solid obstacles of unique volume and multiple morphologies. Int. J. Heat Mass Transf. 95, 1096–1114 (2016). https://doi.org/10.1016/j.ijheatmasstransfer.2015.12.070

    Article  Google Scholar 

  8. Garoosi, F.; Bagheri, G.; Talebi, F.: Numerical simulation of natural convection of nanofluids in a square cavity with several pairs of heaters and coolers (HACs) inside. Int. J. Heat Mass Transf. 67, 362–376 (2013). https://doi.org/10.1016/j.ijheatmasstransfer.2013.08.034

    Article  Google Scholar 

  9. Tasnim, S.H.; Collins, M.R.: Suppressing natural convection in a differentially heated square cavity with an arc shaped baffle. Int. Commun. Heat Mass Transf. 32, 94–106 (2005). https://doi.org/10.1016/j.icheatmasstransfer.2004.05.022

    Article  Google Scholar 

  10. Garoosi, F.; Hoseininejad, F.: Numerical study of natural and mixed convection heat transfer between differentially heated cylinders in an adiabatic enclosure filled with nanofluid. J. Mol. Liq. 215, 1–17 (2016). https://doi.org/10.1016/j.molliq.2015.12.016

    Article  Google Scholar 

  11. Öztop, H.; Dağtekin, İ.; Bahloul, A.: Comparison of position of a heated thin plate located in a cavity for natural convection. Int. Commun. Heat Mass Transf. 31, 121–132 (2003). https://doi.org/10.1016/S0735-1933(03)00207-0

    Article  Google Scholar 

  12. Mahmoodi, M.: Numerical simulation of free convection of nanofluid in a square cavity with an inside heater. Int. J. Therm. Sci. 50, 2161–2175 (2011). https://doi.org/10.1016/j.ijthermalsci.2011.05.008

    Article  Google Scholar 

  13. Sadaoui, D.; Sahi, A.; Nadjib, H.; Meziani, B.; Amoura, T.: Free convection in a square enclosure with a finned plate. Mech. Ind. 16, 310 (2015). https://doi.org/10.1051/meca/2015005

    Article  Google Scholar 

  14. Waheb, J.H.; Jalil, S.M.; Ibrahim, M.: The natural convective heat transfer in rectangular enclosure containing two inclined partitions. Int. J. Sci. Eng. Res. 2, 36–43 (2015)

    Google Scholar 

  15. Purusothaman, A.; Baïri, A.; Nithyadevi, N.: Natural convection on a horizontal and vertical thermally active plate in a closed cubical cavity. Int. J. Numer. Methods Heat Fluid Flow 26, 2528–2542 (2016). https://doi.org/10.1108/hff-08-2015-0341

    Article  Google Scholar 

  16. Hussain, S.H.; Jabbar, M.Y.; Mohamad, A.S.: Influence of presence of inclined centered baffle and corrugation frequency on natural convection heat transfer flow of air inside a square enclosure with corrugated side walls. Int. J. Therm. Sci. 50, 1799–1808 (2011). https://doi.org/10.1016/j.ijthermalsci.2011.03.016

    Article  Google Scholar 

  17. Ben-Nakhi, A.; Chamkha, A.J.: Conjugate natural convection around a finned pipe in a square enclosure with internal heat generation. Int. J. Heat Mass Transf. 50, 2260–2271 (2007). https://doi.org/10.1016/j.ijheatmasstransfer.2006.10.036

    Article  MATH  Google Scholar 

  18. Ridouane, E.H.; Hasnaoui, M.; Amahmid, A.; Raji, A.: Interaction between natural convection and radiation in a square cavity heated from below. Numer. Heat Transf. Part A Appl. 45, 289–311 (2004). https://doi.org/10.1080/10407780490250373

    Article  Google Scholar 

  19. Diaz, G.; Winston, R.: Effect of surface radiation on natural convection in parabolic enclosures. Numer. Heat Transf. Part A Appl. 53, 891–906 (2008). https://doi.org/10.1080/10407780701789518

    Article  Google Scholar 

  20. Saravanan, S.; Sivaraj, C.: Combined thermal radiation and natural convection in a cavity containing a discrete heater: effects of nature of heating and heater aspect ratio. Int. J. Heat Fluid Flow 66, 1339–1351 (2017). https://doi.org/10.1016/j.ijheatfluidflow.2017.05.004

    Article  Google Scholar 

  21. Sadaoui, D.; Sahi, A.; Djerrada, A.; Mansouri, K.: Coupled radiation and natural convection within an inclined sinusoidal solar collector heated from below. Mech. Ind. 17, 302 (2016). https://doi.org/10.1051/meca/2015060

    Article  Google Scholar 

  22. Meng, X.; Wang, Y.; Liu, T.; Xing, X.; Cao, Y.; Zhao, J.: Influence of radiation on predictive accuracy in numerical simulations of the thermal environment in industrial buildings with buoyancy-driven natural ventilation. Appl. Therm. Eng. 96, 473–480 (2016). https://doi.org/10.1016/j.applthermaleng.2015.11.105

    Article  Google Scholar 

  23. Vivek, V.; Sharma, A.K.; Balaji, C.: Interaction effects between laminar natural convection and surface radiation in tilted square and shallow enclosures. Int. J. Therm. Sci. 60, 70–84 (2012). https://doi.org/10.1016/j.ijthermalsci.2012.04.021

    Article  Google Scholar 

  24. Singh, D.K.; Singh, S.N.: Combined free convection and surface radiation in tilted open cavity. Int. J. Therm. Sci. 107, 111–120 (2016). https://doi.org/10.1016/j.ijthermalsci.2016.04.001

    Article  Google Scholar 

  25. Lari, K.; Baneshi, M.; Gandjalikhan Nassab, S.A.; Komiya, A.; Maruyama, S.: Combined heat transfer of radiation and natural convection in a square cavity containing participating gases. Int. J. Heat Mass Transf. 54, 5087–5099 (2011). https://doi.org/10.1016/j.ijheatmasstransfer.2011.07.026

    Article  MATH  Google Scholar 

  26. Mahapatra, S.K.; Dandapat, B.K.; Sarkar, A.: Analysis of combined conduction and radiation heat transfer in presence of participating medium by the development of hybrid method. J. Quant. Spectrosc. Radiat. Transf. 102, 277–292 (2006). https://doi.org/10.1016/j.jqsrt.2006.02.015

    Article  Google Scholar 

  27. Zhang, J.-K.; Li, B.-W.; Hu, Z.-M.: Effects of optical parameters on fluid flow and heat transfer of participating magnetic fluid. Int. J. Heat Mass Transf. 59, 126–136 (2013). https://doi.org/10.1016/j.ijheatmasstransfer.2012.12.004

    Article  Google Scholar 

  28. Cho, Y.H.; Seung, W.B.: The effect of radiation on natural convection in a rectangular enclosure divided by two partitions. Numer. Heat Transf. Part A Appl. 37, 249–270 (2000). https://doi.org/10.1080/104077800274280

    Article  MathSciNet  Google Scholar 

  29. Kumar, P.; Eswaran, V.: The effect of radiation on natural convection in slanted cavities of angle γ = 45 deg and 60 deg. Int. J. Therm. Sci. 67, 96–106 (2013). https://doi.org/10.1016/j.ijthermalsci.2012.12.009

    Article  Google Scholar 

  30. Saeidi, S.M.; Khodadadi, J.M.: Forced convection in a square cavity with inlet and outlet ports. Int. J. Heat Mass Transf. 49, 1896–1906 (2006). https://doi.org/10.1016/j.ijheatmasstransfer.2005.10.033

    Article  MATH  Google Scholar 

  31. Mahmoudi, A.H.; Shahi, M.; Talebi, F.: Effect of inlet and outlet location on the mixed convective cooling inside the ventilated cavity subjected to an external nanofluid. Int. Commun. Heat Mass Transf. 37, 1158–1173 (2010). https://doi.org/10.1016/j.icheatmasstransfer.2010.04.004

    Article  Google Scholar 

  32. Al-Salem, K.; Öztop, H.F.; Pop, I.; Varol, Y.: Effects of moving lid direction on MHD mixed convection in a linearly heated cavity. Int. J. Heat Mass Transf. 55(4), 1103–1112 (2011). https://doi.org/10.1016/j.ijheatmasstransfer.2011.09.062

    Article  MATH  Google Scholar 

  33. Mehrizi, A.A.; Farhadi, M.; Afroozi, H.H.; Sedighi, K.; Darz, A.A.R.: Mixed convection heat transfer in a ventilated cavity with hot obstacle: effect of nanofluid and outlet port location. Int. Commun. Heat Mass Transf. 39, 1000–1008 (2012). https://doi.org/10.1016/j.icheatmasstransfer.2012.04.002

    Article  Google Scholar 

  34. Rahma, M.M.; Öztop, H.F.; Saidur, R.; Mekhilef, S.; Al-Salem, K.: Finite element solution of MHD mixed convection in a channel with a fully or partially heated cavity. Comput. Fluids 79, 53–64 (2013). https://doi.org/10.1016/j.compfluid.2013.03.003

    Article  MathSciNet  MATH  Google Scholar 

  35. Abhinav, R.; Sunder, P.B.S.; Gowrishankar, A.; Vignesh, S.; Vivek, M.; Kishore, V.R.: Numerical study on effect of vent locations on natural convection in an enclosure with an internal heat source. Int. Commun. Heat Mass Transf. 49, 69–77 (2013). https://doi.org/10.1016/j.icheatmasstransfer.2013.09.001

    Article  Google Scholar 

  36. Selimefendigil, F.; Öztop, H.F.: Influence of inclination angle of magnetic field on mixed convection of nanofluid flow over a backward facing step and entropy generation. Adv. Powder Technol. 26(6), 1663–1675 (2015). https://doi.org/10.1016/j.apt.2015.10.002

    Article  Google Scholar 

  37. Koufi, L.; Younsi, Z.; Cherif, Y.; Naji, H.: Numerical investigation of turbulent mixed convection in an open cavity: effect of inlet and outlet openings. Int. J. Therm. Sci. 116, 103–117 (2017). https://doi.org/10.1016/j.ijthermalsci.2017.02.007

    Article  Google Scholar 

  38. Sivasankaran, S.; Cheong, H.T.; Bhuvaneswari, M.; Ganesan, P.: Effect of moving wall direction on mixed convection in an inclined lid-driven square cavity with sinusoidal heating. Numer. Heat Transf. Part A Appl. 69, 630–642 (2016). https://doi.org/10.1080/10407782.2015.1069669

    Article  Google Scholar 

  39. Chattopadhyay, A.; Pandit, S.K.; Sen Sarma, S.; Pop, I.: Mixed convection in a double lid-driven sinusoidally heated porous cavity. Int. J. Heat Mass Transf. 93, 361–378 (2016). https://doi.org/10.1016/j.ijheatmasstransfer.2015.10.010

    Article  Google Scholar 

  40. Boulahia, Z.; Wakif, A.; Sehaqui, R.: Numerical study of mixed convection of the nanofluids in two-sided lid-driven square cavity with a pair of triangular heating cylinders. J. Eng. (2016). https://doi.org/10.1155/2016/8962091

    Article  Google Scholar 

  41. Sharif, M.A.R.: Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom. Appl. Therm. Eng. 27, 1036–1042 (2007). https://doi.org/10.1016/j.applthermaleng.2006.07.035

    Article  Google Scholar 

  42. Sivasankaran, S.; Sivakumar, V.; Hussein, A.K.: Numerical study on mixed convection in an inclined lid-driven cavity with discrete heating. Int. Commun. Heat Mass Transf. 46, 112–125 (2013). https://doi.org/10.1016/j.icheatmasstransfer.2013.05.022

    Article  Google Scholar 

  43. Cheng, T.S.; Liu, W.H.: Effects of cavity inclination on mixed convection heat transfer in lid-driven cavity flows. Comput. Fluids 100, 108–122 (2014). https://doi.org/10.1016/j.compfluid.2014.05.004

    Article  MathSciNet  MATH  Google Scholar 

  44. Mamun, M.A.H.; Rahman, M.M.; Billah, M.M.; Saidur, R.: A numerical study on the effect of a heated hollow cylinder on mixed convection in a ventilated cavity. Int. Commun. Heat Mass Transf. 37, 1326–1334 (2010). https://doi.org/10.1016/j.icheatmasstransfer.2010.07.019

    Article  Google Scholar 

  45. Billah, M.M.; Rahman, M.M.; Sharif, U.M.; Rahim, N.A.; Saidur, R.; Hasanuzzaman, M.: Numerical analysis of fluid flow due to mixed convection in a lid-driven cavity having a heated circular hollow cylinder. Int. Commun. Heat Mass Transf. 38, 1093–1103 (2011). https://doi.org/10.1016/j.icheatmasstransfer.2011.05.018

    Article  Google Scholar 

  46. Karimi, F.; Xu, H.T.; Wang, Z.; Yang, M.; Zhang, Y.: Numerical simulation of steady mixed convection around two heated circular cylinders in a square enclosure. Numer. Heat Transf. Part A Appl. 37, 64–75 (2015). https://doi.org/10.1080/10407782.2013.846607

    Article  Google Scholar 

  47. Khanafer, K.; Aithal, S.M.: Laminar mixed convection flow and heat transfer characteristics in a lid driven cavity with a circular cylinder. Int. J. Heat Mass Transf. 66, 200–209 (2013). https://doi.org/10.1016/j.ijheatmasstransfer.2013.07.023

    Article  Google Scholar 

  48. Islam, A.W.; Sharif, M.A.R.; Carlson, E.S.: Mixed convection in a lid driven square cavity with an isothermally heated square blockage inside. Int. J. Heat Mass Transf. 55, 5244–5255 (2012). https://doi.org/10.1016/j.ijheatmasstransfer.2012.05.032

    Article  Google Scholar 

  49. Radhakrishnan, T.V.; Verma, A.K.; Balaji, C.; Venkateshan, S.P.: An experimental and numerical investigation of mixed convection from a heat generating element in a ventilated cavity. Exp. Therm. Fluid Sci. 32, 502–520 (2007). https://doi.org/10.1016/j.expthermflusci.2007.06.001

    Article  Google Scholar 

  50. Selimefendigil, F.; Öztop, H.F.: Fuzzy-based estimation of mixed convection heat transfer in a square cavity in the presence of an adiabatic inclined fin. Int. Commun. Heat Mass Transf. 39, 1639–1646 (2012). https://doi.org/10.1016/j.icheatmasstransfer.2012.10.006

    Article  Google Scholar 

  51. Promvonge, P.; Koolnapadol, N.; Pimsarn, M.; Thianpong, C.: Thermal performance enhancement in a heat exchanger tube fitted with inclined vortex rings. Appl. Therm. Eng. 62, 285–292 (2014). https://doi.org/10.1016/j.applthermaleng.2013.09.031

    Article  Google Scholar 

  52. Mokhtari, M.; Gerdroodbary, M.B.; Yeganeh, R.; Fallah, K.: Numerical study of mixed convection heat transfer of various fin arrangements in a horizontal channel. Eng. Sci. Technol. Int. J. (2016). https://doi.org/10.1016/j.jestch.2016.12.007

    Article  Google Scholar 

  53. Gururaja Rao, C.; Balaji, C.; Venkateshan, S.P.: Effect of surface radiation on conjugate mixed convection in a vertical channel with a discrete heat source in each wall. Int. J. Heat Mass Transf. 45, 3331–3347 (2002). https://doi.org/10.1016/S0017-9310(02)00061-3

    Article  MATH  Google Scholar 

  54. Premachandran, B.; Balaji, C.: Conjugate mixed convection with surface radiation from a horizontal channel with protruding heat sources. Int. J. Heat Mass Transf. 49, 3568–3582 (2006). https://doi.org/10.1016/j.ijheatmasstransfer.2006.02.044

    Article  MATH  Google Scholar 

  55. Belmiloud, M.A.; Eddine, N.; Chemloul, S.: Numerical study of mixed convection coupled to radiation in a square cavity with a lid-driven. Int. J. Mech. Aerosp. Ind. Mechatron. Manuf. Eng. 9, 1690–1696 (2016)

    Google Scholar 

  56. Bahlaoui, A.; Raji, A.; Hasnaoui, M.; Naïmi, M.; Makayssi, T.; Lamsaadi, M.: Mixed convection cooling combined with surface radiation in a partitioned rectangular cavity. Energy Convers. Manag. 50, 626–635 (2009). https://doi.org/10.1016/j.enconman.2008.10.001

    Article  Google Scholar 

  57. Mohammadi, M.; Gandjalikhan-Nassab, S.A.: The combined heat transfer of radiation and mixed convection analysis in a lid-driven trapezoidal cavity. J. Theor. Appl. Mech. 53, 643 (2015). https://doi.org/10.15632/jtam-pl.53.3.643

    Article  Google Scholar 

  58. Mahapatra, S.K.; Nanda, P.; Sarkar, A.: Interaction of mixed convection in two-sided lid driven differentially heated square enclosure with radiation in presence of participating medium. Heat Mass Transf. Stoffuebertragung. 42, 739–757 (2006). https://doi.org/10.1007/s00231-005-0034-1

    Article  Google Scholar 

  59. Mahapatra, S.K.: Mixed convection inside a differentially heated enclosure and its interaction with radiation-an exhaustive study. Heat Transf. Eng. 35, 74–93 (2014). https://doi.org/10.1080/01457632.2013.730912

    Article  Google Scholar 

  60. Mohammadi, M.; Nassab, S.A.G.: Effect of radiation on mixed convection inside a lid-driven square cavity with various optical thicknesses and Richardson numbers. Heat Transf. Eng. 38, 653–665 (2017). https://doi.org/10.1080/01457632.2016.1200386

    Article  Google Scholar 

  61. Modest, M.F.: Radiative Heat Transfer, 2nd edn, pp. 1–822. Academic Press, San Diego (2003)

    Book  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Mécanique, Matériaux et Energétique (L2ME), Faculté de Technologie, Université A. Mira de Bejaia, 06000, Bejaia, Algérie

    N. Hamici & D. Sadaoui

  2. Laboratoire de Physique Théorique (LPT), Faculté de Technologie, Université A. Mira de Bejaia, 06000, Bejaia, Algérie

    A. Sahi

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Hamici, N., Sahi, A. & Sadaoui, D. Combined Mixed Convection and Radiation Heat Transfer in the Presence of Participating Medium in a Square Cavity with an Inside Heated Plate. Arab J Sci Eng 45, 7305–7319 (2020). https://doi.org/10.1007/s13369-020-04485-8

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