Nonlinear buoyancy-driven thermal energy transport on a moving vertical plate with boundary slips and non-uniform heat source/sink

Astick Banerjee; Sohita Rajput; Krishnendu Bhattacharyya; Mitu Dular; Dimpal Sharma; Sanat Kumar Mahato

doi:10.65112/tcmis.10087

Authors

Astick Banerjee Department of Mathematics and Computing, Biswa Bangla Biswabidyalay, Bolpur, Birbhum-723104, West Bengal, India https://orcid.org/0000-0001-6466-8171
Sohita Rajput Mathematics Section, Department of Science and Humanity, Sershah Engineering College, Sasaram-821113, Bihar, India https://orcid.org/0000-0001-7102-303X
Krishnendu Bhattacharyya Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India https://orcid.org/0000-0001-7975-0709
Mitu Dular Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India https://orcid.org/0009-0000-6341-1294
Dimpal Sharma Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India https://orcid.org/0009-0005-3653-4076
Sanat Kumar Mahato Department of Mathematics, Sidho-Kanho-Birsha University, Purulia-723104, West Bengal, India https://orcid.org/0000-0001-5455-5173

DOI:

https://doi.org/10.65112/tcmis.10087

Keywords:

Thermal energy transport, nonlinear buoyancy, moving vertical plate, partial slip, non-uniform heat source/sink

Abstract

This work investigates the key controlling mechanisms of two-dimensional buoyancy-driven nonlinear mixed convection and thermal energy transport in the flow generated by a vertically moving plate with partial slip and variable heat source/sink effects. The problem is motivated by applications in nuclear power systems, polymer processing, and other industrial operations where nonlinear heat convection and controllable heat generation are essential. By employing suitable similarity transformations, the governing nonlinear partial differential equations are reduced to coupled ordinary differential equations, which are solved using the MATLAB bvp4c solver. A combination of graphical and tabulated results is used to illustrate the influence of key controlling parameters. The analysis uncovers several notable physical trends. Nonlinear mixed convection significantly lowers fluid temperature while enhancing near-wall velocity. Both temperature-dependent and space-dependent heat sources or sinks intensify or reduce the velocity and temperature distributions and simultaneously cause the thickening or thinning of the associated boundary layers. Velocity slip and thermal jump at the surface reduce the near-wall momentum, which causes a reduction in velocity inside the boundary layer. Heat sources, whether spatially-dependent or temperature-dependent, consistently reduce surface drag force and cooling rate, whereas heat sinks boost both drag force and heat removal. Most importantly, temperature-dependent and space-dependent heat source/sink mechanisms exhibit a stronger influence on heat transport regulation, making them an important mode of thermal control. Overall, the results demonstrate that mixed convection flow is highly sensitive to nonlinear buoyancy and non-uniform heat generation/absorption. These findings provide useful insights for the design and optimization of thermal management systems across a wide range of engineering applications.

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