Buoyant Convective Thermal Transport in a Discretely Heated–Cooled Porous Parallelogrammic Configuration Saturated with Nanofluids: A Tiwari and Das Approach

Vishwanatha Shivakumar, Vinay C. Veeranna, Mani Sankar (), Sebastian A. Altmeyer and Abdulrahman Al Maqbali
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Vishwanatha Shivakumar: VTU Research Center, Department of Mathematics, JSS Academy of Technical Education, Dr. Vishnuvardhan Road, Bangalore 560060, India
Vinay C. Veeranna: VTU Research Center, Department of Mathematics, JSS Academy of Technical Education, Dr. Vishnuvardhan Road, Bangalore 560060, India
Mani Sankar: Research Center, Visvesvaraya Technological University, Belagavi 590018, India
Sebastian A. Altmeyer: Department of Physics, Aerospace Division, Universitat Politècnica de Catalunya—Barcelona Tech, 08034 Barcelona, Spain
Abdulrahman Al Maqbali: Department of Basic and Applied Sciences, College of Applied and Health Sciences, A’Sharqiyah University, P.O. Box 42, Ibra 400, Oman

Mathematics, 2025, vol. 13, issue 21, 1-25

Abstract: The strategic positioning of heating and cooling segments within complex non-rectangular geometries has emerged as a critical engineering challenge across multiple industries in thermal management systems for electronic components. This analysis presents a numerical inspection of buoyancy-driven convective flow and thermal transport mechnisms of nanofluids in a parallelogrammic porous geometry. A single discrete heating–cooling segment has been placed along the slanting surfaces of the geometry. The mathematical model is formulated utilizing Darcy’s law, incorporating the Tiwari and Das approach to characterize the thermophysical properties of the nanofluid. The governing model equations corresponding to the physical process are solved numerically using finite-difference-based alternating direction implicit (ADI) and successive line over-relaxation (SLOR) techniques. Computational simulations are performed for various parametric conditions, including different nanoparticle volume fractions ( ϕ = 0 – 0.05 ), Rayleigh numbers ( R a = 10 1 – 10 3 ), and parallelogram geometry ( α ) and sidewall ( γ ) tilting angles ( − 45 ° ≤ α ≤ + 45 ° and − 45 ° ≤ γ ≤ + 45 ° ), while examining the effect of discrete thermal locations. The results reveal a significant decrement in thermal transfer rates with an increasing nanoparticle concentration, particularly at higher Rayleigh numbers. The skewness of the parallelogrammic boundaries is found to substantially influence flow patterns and thermal transport characteristics compared to conventional rectangular enclosures. Further, the discrete placement of heating and cooling sources creates unique thermal plumes that modify circulation patterns within the domain. The predictions suggest profound insights for optimizing thermal management systems by employing nanofluids in non-rectangular porous configurations, with potential applications in geothermal energy extraction, electronic cooling systems, and thermal energy storage devices.

Keywords: Tiwari and Das model; buoyancy-driven convection; nanofluid-saturated porous envelope; inclined parallelogram geometry; discrete thermal boundary conditions; porous media; numerical method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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