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Volume 7, Issue 5
Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall

Ashok Kumar, Pravez Alam & Prachi Fartyal

Adv. Appl. Math. Mech., 7 (2015), pp. 644-662.

Published online: 2018-05

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This article summaries a numerical study of thermo-solutal natural convection in a square cavity filled with anisotropic porous medium. The side walls of the cavity are maintained at constant temperatures and concentrations, whereas bottom wall is a function of non-uniform (sinusoidal) temperature and concentration. The non-Darcy Brinkmann model is considered. The governing equations are solved numerically by spectral element method using the vorticity-stream-function approach. The controlling parameters for present study are Darcy number $(Da)$, heat source intensity i.e., thermal Rayleigh number $(Ra)$, permeability ratio $(K^∗)$, orientation angle $(ϕ)$. The main attention is given to understand the impact of anisotropy parameters on average rates of heat transfer (bottom, $Nu_b$, side $Nu_s$) and mass transfer (bottom, $Sh_b$, side, $Sh_s$) as well as on streamlines, isotherms and iso-concentration. Numerical results show that, for irrespective value of $K^∗$, the heat and mass transfer rates are negligible for $10^{-7}≤Da≤10^{−5}, Ra=2×10^5$ and $ϕ=45^◦$. However, a significant impact appears on Nusselt and Sherwood numbers when Da lies between $10^{−5}$ to $10^{−4}$. The maximum bottom heat and mass transfer rates ($Nu_b, Su_b$) is attained at $ϕ=45^◦$, when $K^∗= $0.5 and 2.0. Furthermore, both heat and mass transfer rates increase on increasing Rayleigh number ($Ra$) for all the values of $K^∗$. Overall, It is concluded from the above study that due to anisotropic permeability the flow dynamics becomes complex.

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@Article{AAMM-7-644, author = {Ashok and Kumar and and 19797 and and Ashok Kumar and Pravez and Alam and and 19798 and and Pravez Alam and Prachi and Fartyal and and 19799 and and Prachi Fartyal}, title = {Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {5}, pages = {644--662}, abstract = {

This article summaries a numerical study of thermo-solutal natural convection in a square cavity filled with anisotropic porous medium. The side walls of the cavity are maintained at constant temperatures and concentrations, whereas bottom wall is a function of non-uniform (sinusoidal) temperature and concentration. The non-Darcy Brinkmann model is considered. The governing equations are solved numerically by spectral element method using the vorticity-stream-function approach. The controlling parameters for present study are Darcy number $(Da)$, heat source intensity i.e., thermal Rayleigh number $(Ra)$, permeability ratio $(K^∗)$, orientation angle $(ϕ)$. The main attention is given to understand the impact of anisotropy parameters on average rates of heat transfer (bottom, $Nu_b$, side $Nu_s$) and mass transfer (bottom, $Sh_b$, side, $Sh_s$) as well as on streamlines, isotherms and iso-concentration. Numerical results show that, for irrespective value of $K^∗$, the heat and mass transfer rates are negligible for $10^{-7}≤Da≤10^{−5}, Ra=2×10^5$ and $ϕ=45^◦$. However, a significant impact appears on Nusselt and Sherwood numbers when Da lies between $10^{−5}$ to $10^{−4}$. The maximum bottom heat and mass transfer rates ($Nu_b, Su_b$) is attained at $ϕ=45^◦$, when $K^∗= $0.5 and 2.0. Furthermore, both heat and mass transfer rates increase on increasing Rayleigh number ($Ra$) for all the values of $K^∗$. Overall, It is concluded from the above study that due to anisotropic permeability the flow dynamics becomes complex.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m632}, url = {http://global-sci.org/intro/article_detail/aamm/12068.html} }
TY - JOUR T1 - Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall AU - Kumar , Ashok AU - Alam , Pravez AU - Fartyal , Prachi JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 644 EP - 662 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2014.m632 UR - https://global-sci.org/intro/article_detail/aamm/12068.html KW - AB -

This article summaries a numerical study of thermo-solutal natural convection in a square cavity filled with anisotropic porous medium. The side walls of the cavity are maintained at constant temperatures and concentrations, whereas bottom wall is a function of non-uniform (sinusoidal) temperature and concentration. The non-Darcy Brinkmann model is considered. The governing equations are solved numerically by spectral element method using the vorticity-stream-function approach. The controlling parameters for present study are Darcy number $(Da)$, heat source intensity i.e., thermal Rayleigh number $(Ra)$, permeability ratio $(K^∗)$, orientation angle $(ϕ)$. The main attention is given to understand the impact of anisotropy parameters on average rates of heat transfer (bottom, $Nu_b$, side $Nu_s$) and mass transfer (bottom, $Sh_b$, side, $Sh_s$) as well as on streamlines, isotherms and iso-concentration. Numerical results show that, for irrespective value of $K^∗$, the heat and mass transfer rates are negligible for $10^{-7}≤Da≤10^{−5}, Ra=2×10^5$ and $ϕ=45^◦$. However, a significant impact appears on Nusselt and Sherwood numbers when Da lies between $10^{−5}$ to $10^{−4}$. The maximum bottom heat and mass transfer rates ($Nu_b, Su_b$) is attained at $ϕ=45^◦$, when $K^∗= $0.5 and 2.0. Furthermore, both heat and mass transfer rates increase on increasing Rayleigh number ($Ra$) for all the values of $K^∗$. Overall, It is concluded from the above study that due to anisotropic permeability the flow dynamics becomes complex.

Ashok Kumar, Pravez Alam & Prachi Fartyal. (1970). Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall. Advances in Applied Mathematics and Mechanics. 7 (5). 644-662. doi:10.4208/aamm.2014.m632
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