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

Preview Full PDF 1 693
Export citation
  • 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, Nub , side Nus) and mass transfer (bottom, Shb , side, Shs) 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 = 2×105 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 (Nub , Sub ) 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.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-7-644, author = {Ashok Kumar, Pravez Alam 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, Nub , side Nus) and mass transfer (bottom, Shb , side, Shs) 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 = 2×105 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 (Nub , Sub ) 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 - Ashok Kumar, Pravez Alam & Prachi Fartyal JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 644 EP - 662 PY - 2018 DA - 2018/05 SN - 7 DO - http://dor.org/10.4208/aamm.2014.m632 UR - https://global-sci.org/intro/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, Nub , side Nus) and mass transfer (bottom, Shb , side, Shs) 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 = 2×105 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 (Nub , Sub ) 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
Copy to clipboard
The citation has been copied to your clipboard