**Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions**

Numerical simulations are undertaken for the benchmark drawback of natural convection flow during a sq. cavity. The management volume methodology is employed to unravel the conservation equations for bedded and turbulent flows for a series of Rayleigh numbers (Ra) reaching values up to 1010. The k‐ϵ model has been used for turbulence modelling with and while not power wall functions. Uniform and non‐uniform (stretched) grids are utilized with increasing density to ensure correct solutions, particularly close to the walls for prime Ra‐values. ADI and SIP solvers square measure enforced to accelerate convergence. glorious agreement is obtained with previous numerical solutions, whereas some discrepancies with others for prime Ra‐values is also because of a presumably totally different implementation of the wall functions. Comparisons with experimental information for warmth transfer (Nusselt number) clearly demonstrates the restrictions of the quality k‐ϵ model with power wall functions, which supplies important overpredictions. **[1]**

**Longitudinal vortices in natural convection flow on inclined plates**

Experiments are performed to demonstrate the prevalence associate degreed explore the characteristics of a secondary flow superposed upon the natural convection main flow on an inclined plate. A flow visualisation technique is used whereby the flow pattern is formed visible by native changes of color of the fluid itself, the color modification being led to by a change in pH scale. The secondary flow consists of longitudinal vortices or rolls distributed additional or less sporadically across the dimension of the plate. the amount of such vortices will increase with the temperature distinction between the surface and therefore the close fluid, however seems to be comparatively insensitive to the inclination angle of the plate. The secondary flow results from the destabilizing impact of the buoyancy force part, that acts traditional to the plate surface. The longitudinal vortices are the primary stage of the laminarturbulent transition method. this is often in distinction to the case of natural convection on a vertical plate, wherever the primary stage of transition is Tollmien-Schlichting waves. **[2]**

**Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field**

In the gift paper, the result of viscous dissipation and dependent consistence on free convection flow over a sphere has been investigated. Joule heating and warmth conductivity over a sphere area unit thought of additionally during this investigation. With a goal to achieve similarity solutions of the matter being posed , the developed equations area unit created dimensionless by mistreatment appropriate transformations. The non-dimensional equations area unit then remodeled into non-linear equations introducing a non- similarity transformation. The ensuing non-linear similar equations along with their corresponding boundary conditions supported conductivity and convection area unit resolved numerically by mistreatment the finite distinction technique along side Newton’s linearization approximation. The numerical results description the speed profiles, temperature profiles, skin friction constant and therefore the native heat transfer constant area unit shown each in graph and tabular forms for the various values of the parameters related to the matter.** [3]**

**Natural Convection Flow of a Nanofluid in an Inclined Square Enclosure Partially Filled with a Porous Medium**

This work Associate in Nursingalyses free convection flow of a nanofluid in an inclined sq. enclosure consisting of a porous layer and a nanofluid layer exploitation the finite distinction methodology. curved temperature boundary conditions are obligatory on the 2 opposing vertical walls. Nanofluids with water as base and Ag or Cu or Al2O3 or TiO2 nanoparticles are thought-about for the matter. The connected parameters of this study are the Darcy range, nanoparticle volume fraction, section deviation, amplitude quantitative relation, porous layer thickness and therefore the inclination angle of the cavity. A comparison with antecedently printed work is performed and therefore the results are in smart agreement. elaborated numerical knowledge for the fluid flow and thermal distributions within the sq. enclosure, and therefore the Nusselt numbers are conferred.** [4]**

**Conjugate Effects of Viscous Dissipation and Dependent Viscosity on Natural Convection Flow over a Sphere with Joule Heating and Heat Conduction**

In the present paper, the effect of viscous dissipation and dependent viscosity on free convection flow over a sphere has been investigated. Joule heating and heat conduction over a sphere are considered as well in this investigation. With a goal to attain similarity solutions of the problem being posed, the developed equations are made dimensionless by using suitable transformations. The non-dimensional equations are then transformed into non-linear equations introducing a non- similarity transformation. The resulting non-linear similar equations together with their corresponding boundary conditions based on conduction and convection are solved numerically by using the finite difference method along with Newton’s linearization approximation. The numerical results detailing the velocity profiles, temperature profiles, skin friction coefficient and the local heat transfer coefficient are shown both in graph and tabular forms for the different values of the parameters associated with the problem. **[5]**

**Reference**

**[1]** Barakos, G., Mitsoulis, E. and Assimacopoulos, D., 1994. Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions. International Journal for Numerical Methods in Fluids, 18(7), (Web Link)

**[2]** Sparrow, E.M. and Husar, R.B., 1969. Longitudinal vortices in natural convection flow on inclined plates. Journal of Fluid Mechanics, 37(2), (Web Link)

**[3]** Hamad, M.A.A., 2011. Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field. International communications in heat and mass transfer, 38(4), (Web Link)

**[4]** Natural Convection Flow of a Nanofluid in an Inclined Square Enclosure Partially Filled with a Porous Medium

A. I. Alsabery, A. J. Chamkha, H. Saleh & I. Hashim

Scientific Reports volume 7, (Web Link)

**[5]** Alam, M. M., Imran, R., Ghosh, S. and Haque, R. (2018) “Conjugate Effects of Viscous Dissipation and Dependent Viscosity on Natural Convection Flow over a Sphere with Joule Heating and Heat Conduction”, Journal of Advances in Mathematics and Computer Science, 26(4), (Web Link)