Numerical simulation of thermal radiation influence on natural convection in a trapezoidal enclosure : heat flow visualization through energy flux vectors

A theoretical and numerical study of natural convection intwo-dimensional laminarincompressible flow in a trapezoidal enclosurein the presence of thermal radiation is conducted,motivated by energy systems applications. Heat flow visualization via the method of energy fluxvectors (EFVs) is also included. The trapezoidal cavity has an inclined top wall which in addition to the bottom wall is maintained at constant temperature, whereas the remaining (vertical side)walls are adiabatic. The governing partial differential conservation equations are transformedusing a vorticity-stream function formulation and non-dimensional variables and the resultingnonlinear boundary value problem is solved using a finite difference method with incremental timesteps. EFVs provide abundant details of the heat flow at the core of the enclosure. The largerenergy flux vectors indicate high temperature gradient zones and the sparse EFVs correspond tolow temperature gradient zone. Heat flow distribution in the trapezoidal enclosure can be clearlyelaborated via energy flux vectors and provides a deeper insight into thermal characteristics. Acomprehensive parametric study is performed to evaluate the impact of Rayleigh number(buoyancy parameter) and radiation parameter on transport phenomena. The computations indicatethat local Nusselt number and velocity are increasing functions of the Rayleigh number andradiation parameter. Significant changes in streamlines, temperature contours and energystreamlines for high Rayleigh number are observed. The energy flux vectors show that a large eddyis formed within the enclosure which migrates towards the cold wall. Greater thermal buoyancyforce accelerates the primary flow whereas it decelerates the secondary flow. The simulations arerelevant to solar collector systems, enclosure fire dynamics, electronic cooling and fuel cellsystems. Furthermore, the computations furnish a good benchmark for more general computationalfluid dynamics (CFD) analysis with commercial software e.g. ANSYS FLUENT