We study the problem of double diffusive convective movement of a reacting solute in a viscous incompressible occupying a plane layer in a saturated porous medium and subjected to a vertical magnetic field. The thresholds for linear instability are found and compared to those derived by a global nonlinear energy stability analysis. Then, the accuracy of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. The strong stabilizing effect of gravity field and magnetic field is shown. Moreover, the results support the assertion that the linear theory, in general, is accurate in predicting the onset of convective motion, and thus, regions of stability.

Purpose – The purpose of this paper is to explore a model for thermal convection in a plane layer when the density-temperature relation in the buoyancy term is quadratic. A heat source/sink varying in a linear fashion with a vertical height expressed as z was allowed, functioning as a heat sink in an area of the layer and as a heat source in the remainder. Design/methodology/approach – First, the authors present the governing equations of motion and derive the associated perturbation equations. Second, the authors introduce the linear and nonlinear analysis of the system. Third, the authors transform the system to velocity-vorticity-potential formulation and introduce a numerical study of the problem in three dimensions. Findings – First, the linear instability and nonlinear stability thresholds are derived. Second, the linear instability thresholds accurately predict the onset of instability. Third, the required time to arrive at the steady state increases as Ra tends to RaL . Fourth, the authors find that the convection has three different interesting patterns. Originality/value – With the modernday need for heat transfer or insulation devices in industry, particularly those connected with nanotechnology, the usefulness of a mathematical analysis of such resonance became apparent. Thus, this study is believed to be of value.

In recent years, the summer season in Iraq has become longer and hotter than before, leading to high cooling loads inside buildings and increased demand for electrical energy. The use of sustainable energy and insulation techniques for building envelopes are reasonable solutions for overcoming harsh weather conditions and reaching acceptable thermal comfort levels. In this study, a survey on more than 60 residential buildings in Al-Amarah City, Iraq, was conducted on 21 July 2018 to examine the nature of the most common construction materials used in the building envelopes. Furthermore, the cooling loads of building envelope elements, e.g. roof, external walls and windows, was calculated using the cooling load temperature difference/solar cooling load/cooling load factor method of ASHRAE. The results were tabulated and compared for each combination of elements. The results showed that reflective glass is the optimal choice for exterior windows. The 'clay-insulation-fired clay bricks-cement mortar' and 'cement mortar-thermo-stone bricks-cement mortargypsum mortar' combination layers performed well for roof and external wall installations, respectively. Several recommendations were deduced from this study, which can be used as guidelines for construction authorities in Al-Amarah City and individuals interested in energy-efficient buildings.

Natural convection in a triangular cavity filled with air is investigated numerically. In this paper, the cavity is exposed to air stream cooling exerted on its sides and it is heated by a fixed heat flux from the base. The air inside the cavity is assumed to be laminar and obeying Boussinesq approximation. The governing equations are solved numerically using the finite volume technique with SIMPLE algorithm. The results are achieved with a range of Rayleigh number (104 < Ra < 107), free stream Reynolds number (103 < Re∞ < 1.5 × 104), four aspect ratios (AR = 0.25, 0.5, 0.866, and 1) and five inclination angles (ϕ = 0°, 30°, 45°, 60°, 90°). The influence of these parameters is displayed on the stream function, isotherms lines, local and average Nusselt numbers. The results reveal that the heat transfer rate increases as Rayleigh number, free stream Reynolds number and AR increase. The highest heat transfer rate is obtained at ϕ = 0° while the lowest one is obtained at ϕ = 90°. Furthermore, as the AR augments, the local and average Nusselt numbers are enhanced and the stream function is formed of two symmetric counter‐rotating vortices.

A model for double-diffusive convection in an anisotropic porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source and subjected to a vertical magnetic field and variable gravity effect. The validity of both the linear instability and global nonlinear stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good prediction on the onset of instability in the steady state throughflow. It is known that as R c increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as R c increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated.