@article{10.11648/j.ijtam.20261201.13,
  author = {Sridhar Kulkarni and Nagappa Kallappa Enagi},
  title = {A Review on Visco-Elastic Fluid Heat Transfer in Porous Media
},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {12},
  number = {1},
  pages = {24-30},
  doi = {10.11648/j.ijtam.20261201.13},
  url = {https://doi.org/10.11648/j.ijtam.20261201.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20261201.13},
  abstract = {This review presents a stimulating discussion in which, in a systematic and coherent way, the governing equations and the different mathematical models used in the characterization of the heat transfer properties of viscoelastic fluids flowing through porous structures are illuminated. Particular attention is paid to the dissection of the role played by several key parameters that control the flow and thermal regime. These are the basic porosity effects, which govern the available pathways for flow and interfacial area; the form of the drag forces experienced, normally modelled via extensions of Darcy’s Law, such as the Darcy-Brinkman-Forchheimer formulation, accounting for the effects of viscous diffusion and inertial resistance; and the influence of the boundary effects, which often introduce nonlinear velocity and temperature gradients near the confining walls. Moreover, a significant portion of the research is devoted to the details of fluid rheology, studying how various viscoelastic constitutive models, such as Oldroyd-B, Maxwell, or generalized power-law models, interact with the geometric constraints imposed by the porous matrix to modify momentum and energy transport. Important research findings indicate ways in which non-Newtonian behavior and non-equilibrium conditions can profoundly impact the more traditional predictions of heat transfer. For example, the elasticity of the fluid may either stabilize or destabilize the onset of thermal convection and lead to novel flow patterns and heat transport mechanisms absent in simpler Newtonian-fluid systems. These important findings are synthesized within the review to provide the researcher and engineer with a consolidated view of acquired knowledge and quantitative insight. Beyond its consolidation of current knowledge, this comprehensive review undertakes a critical review of the current state-of-the-art. It painstakingly identifies persistent gaps in existing literature, highlighting outstanding areas where understanding at either the theoretical or experimental level remains incomplete. The result is the formulation of specific high-priority, potential future research directions. The suggested avenues for investigation are often novel rheological models, micro-scale pore-level heat transfer mechanisms, or coupled phenomena in non-idealized porous structures, opening new avenues for further development of the fundamental knowledge base and practical uses of heat transport phenomena in complex viscoelastic-porous systems.
},
 year = {2026}
}

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TY  - JOUR
T1  - A Review on Visco-Elastic Fluid Heat Transfer in Porous Media

AU  - Sridhar Kulkarni
AU  - Nagappa Kallappa Enagi
Y1  - 2026/02/04
PY  - 2026
N1  - https://doi.org/10.11648/j.ijtam.20261201.13
DO  - 10.11648/j.ijtam.20261201.13
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 24
EP  - 30
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20261201.13
AB  - This review presents a stimulating discussion in which, in a systematic and coherent way, the governing equations and the different mathematical models used in the characterization of the heat transfer properties of viscoelastic fluids flowing through porous structures are illuminated. Particular attention is paid to the dissection of the role played by several key parameters that control the flow and thermal regime. These are the basic porosity effects, which govern the available pathways for flow and interfacial area; the form of the drag forces experienced, normally modelled via extensions of Darcy’s Law, such as the Darcy-Brinkman-Forchheimer formulation, accounting for the effects of viscous diffusion and inertial resistance; and the influence of the boundary effects, which often introduce nonlinear velocity and temperature gradients near the confining walls. Moreover, a significant portion of the research is devoted to the details of fluid rheology, studying how various viscoelastic constitutive models, such as Oldroyd-B, Maxwell, or generalized power-law models, interact with the geometric constraints imposed by the porous matrix to modify momentum and energy transport. Important research findings indicate ways in which non-Newtonian behavior and non-equilibrium conditions can profoundly impact the more traditional predictions of heat transfer. For example, the elasticity of the fluid may either stabilize or destabilize the onset of thermal convection and lead to novel flow patterns and heat transport mechanisms absent in simpler Newtonian-fluid systems. These important findings are synthesized within the review to provide the researcher and engineer with a consolidated view of acquired knowledge and quantitative insight. Beyond its consolidation of current knowledge, this comprehensive review undertakes a critical review of the current state-of-the-art. It painstakingly identifies persistent gaps in existing literature, highlighting outstanding areas where understanding at either the theoretical or experimental level remains incomplete. The result is the formulation of specific high-priority, potential future research directions. The suggested avenues for investigation are often novel rheological models, micro-scale pore-level heat transfer mechanisms, or coupled phenomena in non-idealized porous structures, opening new avenues for further development of the fundamental knowledge base and practical uses of heat transport phenomena in complex viscoelastic-porous systems.

VL  - 12
IS  - 1
ER  - 

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