Perturbation and MAPLE Quadrature Computation of Thermosolutal Dissipative Reactive Convective Flow in a Geothermal Duct with Robin Boundary Conditions

Abstract

AbstractBuoyancy-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 twenty-first century. Motivated by such applications, in the current study, a mathematical model is developed for thermosolutal convection flow in an open two-dimensional vertical channel containing a non-Darcy porous medium saturated with reactive Newtonian viscous heating fluid is studied with Robin boundary conditions. The non-dimensional conservation equations are derived for the case of small Brinkman number, and neglecting the Forchheimer quadratic drag effect, a 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 (MAPLE). Good correlation between analytical and numerical solutions is demonstrated. The influence of thermophysical parameters 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 chemical reaction parameter elevates the species concentration in the left half space of the channel (duct), whereas it suppresses concentration in the right half space, and in both scenarios, a parabolic distribution is observed. With increasing 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.KeywordsGeothermal reactive systemsNon-Darcy porous mediumRobin boundary conditionsPerturbation methodThermosolutal buoyancyNusselt number