Perturbation and MAPLE quadrature computation of thermo-solutal dissipative reactive convective flow in a geothermal duct with Robin boundary conditions

Umavathi, JC; Beg, OA; Vasu, B; Gorla, RSR

Abstract

Buoyancy-driven reactive flows feature extensively in geophysics, materials processing and energy systems. In respect to the latter, geothermal energy holds great promise in India and other Asian geographical locations and offers immense resources in the 21st century. Motivated by such applications, in the current study a mathematical model is developed for thermo-solutal convection flow in an open two-dimensional vertical channel containing a porous medium saturated with reactive Newtonian fluid is studied. Robin boundary conditions are prescribed and a first order homogenous chemical reaction is considered. The Darcy-Forchheimer model is used to simulate both first and second order porous medium drag effects. The reference temperatures are taken as symmetric or asymmetric. Viscous heating is also included in the model. The conservation equations are written in dimensionless form taking into account the effects of viscous dissipation. For the case of small Brinkman number (i.e.viscous heating parameter) and neglecting the Forchheimer quadratic drag effect, perturbation solution of the simpler Darcian boundary value problem is developed. For the general non-Darcy-case, a numerical solution is presented with the Runge-Kutta quadrature and a shooting method. Good correlation between analytical and numerical solutions is demonstrated. The influence of thermal and solute Grahsof numbers, Biot numbers, Brinkman number, first order chemical reaction parameter, porous medium parameter and Forchheimer (inertial drag) parameter on velocity, temperature and concentration (species) distributions is visualized graphically. Nusselt number and skin friction at the walls are computed for selected parameters relevant to real geothermics.
Increasing porous media parameter (decreasing medium permeability) reduces temperatures for both equal and unequal Biot numbers. Increasing thermal Grashof number accelerates the flow and elevates temperatures for both equal and unequal Biot numbers. With higher values of solutal Grashof number velocity and temperature near the cold plate (wall) are reduced whereas the converse behaviour is induced at the hot wall. Increasing chemical reaction parameter elevates the species concentration in the left half space of the channel whereas it suppresses concentration in the right half space and in both scenarios a parabolic distribution is observed. In the absence of chemical reaction, a linear growth in concentration is computed from the left plate to the right plate. With increasing porous medium parameter and Forchheimer inertial parameter the flow is strongly decelerated across the channel span whereas there is a much weaker reduction in temperatures. Skin friction is consistently lowered at both plates with increasing thermal Grashof number for equal Biot numbers. However, with unequal Biot numbers, skin friction at the left plate is increased whereas it is still reduced at the right plate. With increasing solutal Grashof number, skin friction is always reduced at both plates for both equal and unequal Biot numbers. There is also a consistent decrease in Nusselt numbers at both plates with increasing solutal Grashof number.

Citation

Umavathi, J., Beg, O., Vasu, B., & Gorla, R. (2022). Perturbation and MAPLE quadrature computation of thermo-solutal dissipative reactive convective flow in a geothermal duct with Robin boundary conditions. In P. Mahanta, P. Kalita, A. Paul, & A. Banerjee (Eds.), Advances in thermofluids and renewable energy : select proceedings of TFRE 2020 (3-21). Singapore: Springer. https://doi.org/10.1007/978-981-16-3497-0_1

• End Date: Nov 28, 2020
• Acceptance Date: Aug 13, 2021
• Online Publication Date: Oct 22, 2021
• Publication Date: Jan 1, 2022
• Deposit Date: Aug 16, 2021
• Publicly Available Date: Oct 22, 2022
• Pages: 3-21
• Series Title: Lecture Notes in Mechanical Engineering
• Book Title: Advances in thermofluids and renewable energy : select proceedings of TFRE 2020
• ISBN: 9789811634963-(hardcover);-9789811634994-(softcover);-9789811634970-(ebook)
• DOI: https://doi.org/10.1007/978-981-16-3497-0_1
• Publisher URL: https://doi.org/10.1007/978-981-16-3497-0_1
• Related Public URLs: https://doi.org/10.1007/978-981-16-3497-0
• Additional Information: Access Information : This document is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/978-981-16-3497-0_1; Event Type : Conference