Nikita Gibanov and Mikhail A. Sheremet
The purpose of this paper is to investigate natural convective heat transfer in a cubical cavity with the heat source of a trapezoidal form having a constant temperature.
Abstract
Purpose
The purpose of this paper is to investigate natural convective heat transfer in a cubical cavity with the heat source of a trapezoidal form having a constant temperature.
Design/methodology/approach
The domain of interest is a cubical cavity with two isothermal opposite vertical walls, while other walls are adiabatic. A discrete heater of a trapezoidal shape is located at the bottom wall of the cavity. Governing equations formulated in dimensionless vector potential functions, vorticity vector and temperature with corresponding initial and boundary conditions have been solved numerically using a developed computational code based on the finite difference method.
Findings
The results show that the variation of geometric parameters, such as height, length and size of the local heater, significantly influences the evolution of a temperature field and fluid flow inside the enclosure. The effects of Rayleigh number and time on streamlines, isotherms and average Nusselt number have been studied.
Originality/value
The originality of this work is to explore three-dimensional (3D) natural convection in a cubical cavity with a local heat source of trapezoidal shape, to analyze the effects of heater geometric parameters and to compare obtained 3D data with two-dimensional results.
Details
Keywords
Nikita Sergeevich Gibanov, Mohammad Mehdi Rashidi and Mikhail Sheremet
The purpose of this paper is to investigate numerically thermal convection heat transfer in closed square and cubical cavities with local energy sources of various geometric…
Abstract
Purpose
The purpose of this paper is to investigate numerically thermal convection heat transfer in closed square and cubical cavities with local energy sources of various geometric shapes.
Design/methodology/approach
The analyzed regions are square and cubical cavities with two isothermally cold opposite vertical walls, whereas other walls are adiabatic. A local energy element of rectangular, trapezoidal or triangular shape is placed on the lower surface of the cabinet. The lattice Boltzmann technique has been used as the main method for the problem solution in two-dimensional (2D) and three-dimensional (3D) formulations, whereas the finite difference technique with non-primitive parameters such as stream function and vorticity has been also used.
Findings
The velocity and temperature fields for a huge range of Rayleigh number 104–106, as well as for various geometry shapes of the heater have been studied. A comparative analysis of the results obtained on the basis of two numerical techniques for 2D and 3D formulations has been performed. The dependences of the energy transfer strength in the region on the shape of energy source and Rayleigh number have been established. It has been revealed that the triangular shape of the energy source corresponds to the maximum values of the velocity vector and temperature within the cavity, and the rectangular shape corresponds to the minimum values of these mentioned variables. With the growth of the Rayleigh number, the difference in the values of these mentioned variables for rectangular and triangular shapes of heaters also increases.
Originality/value
The originality of this work is to scrutinize the lattice Boltzmann method and finite difference method for the problem of natural convection in 2D and 3D closed chambers with a local heated element.
Details
Keywords
Nikita Gibanov and Mikhail Sheremet
The purpose of this paper is to study natural convective fluid flow and heat transfer inside a cubical cavity having a local heat source of constant temperature.
Abstract
Purpose
The purpose of this paper is to study natural convective fluid flow and heat transfer inside a cubical cavity having a local heat source of constant temperature.
Design/methodology/approach
The cubical cavity is cooled from two vertical opposite walls and heated from the local heater mounted on the bottom wall, while the rest walls are adiabatic. The governing equations formulated in dimensionless vector potential functions and vorticity vector have been solved using implicit finite difference method of the second-order accuracy. The effects of the Rayleigh number (Ra = 1e+04 – 1e+06), heat source position (l/L = 0.05 – 0.35) and dimensionless time (0 < tau < 100) on velocity and temperature fields, streamlines, isotherms and average Nusselt number at the heat source surface have been analyzed.
Findings
It is found that the extreme left position of the heater (l/L = 0.05) illustrates more essential cooling of the cavity where the thermal plume over the heat source is suppressed by low temperature waves from the cold vertical walls.
Originality/value
The originality of this work is to analyze transient 3D natural convection in a cubical cavity with a heater of triangular shape and compare obtained 3D data with 2D results. It should be noted that for numerical simulation, the authors used vector potential function and vorticity vector that for transient problems allows to reduce the computational time. The results would benefit scientists and engineers to become familiar with the analysis of transient convective heat and mass transfer in 3D domains with local heaters, and the way to predict the properties of convective flow in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.