Abstract
This paper clearly presents and defines the numerical study on how hollow building block operates to suppress the convectional currents and reduce the amount of heat flux transferred across the petition of the building wall. The configuration and weight of these blocks have made them to fully be utilized in building the facades. The air filled cavities (hollow cells) together with the small cross-sectional area geometry provides an appropriate elevation for the building block. The hollow polythene bars inserted in this bricks also helps to reduce the heat by about 36% depending on the petition number (Mejad 2006).
Varied mass, momentum and energy equations are clearly represented to show the heat flux transported across with varied numbers of partitions used in the building, the air approximation in the hollows using the Bousinesq approximation.
This study of this masonry brick is great importance to areas with relatively high ambient temperatures, such as the tropical zones which clearly requires extensive utilization of air conditioning operations to maintain the thermal experience in the dwellings (Mejad 2006).
The paper also has great analysis on the effect of variations in utilizing a quite number of bricks and insertion of the folded polythene sheets in the voids and their relative effect to temperature change in the bricks.
Introduction
Over year’s hollow building blocks of different shapes and sizes have been employed in the civil engineering sector to build different structures because of its excellent environmental characteristics, decreased cost of building and their ease of use as it does not require scaffolding.
In designating these houses bricks with quite smaller ratio of cross sectional area are always preferred due to their maximum ability transfer lesser heat. The present day building blocks are sophistically build to provide equivalent thermal conductivity of less than 0.1W/ (m-K). This is a situation that can be arrived at by the use lightweight ceramic body with a large number of minute vertical spaces within the void with different angular directions (Mejad 2006).
High ambient temperature zones use reasonably high amount of energy for air conditioning systems in their buildings in order to achieve reasonable thermal conditions to provide comfort in the buildings. Therefore, the utilization of the hollow building blocks in the masonry units in these areas is considered a great necessity. The horizontal direction is always utilized in specifying the equivalent thermal conductivity because of the prevailing heat flow through the walls.
Traditionally the building blocks were modeled by the use of film resistance coefficient to help in the convection-conduction of the ambient heat transfer. These film coefficients also depended upon cavity of the hollow blocks to provide a simple surface temperature and unidirectional heat flux. Overall heat transfer coefficient and parallel path method or isotherm plane was then used to calculate the heat transfer (Zbyneck & Merek 2010)
Heat transfer in this hollow bricks generally involves the use of three-dimension phenomena of conduction, convection and radiation in the voids. This permits the accurate calculation of both the vertical and horizontal air variation in the hollows using the computational fluid dynamics analysis. To provide the solution for the zones the paper aims at developing variant dimensions of conduction, convection and radiation of heat transfer analysis to the hollow building blocks of different patterns and to provide an economical way of enhancing retention of heat and reducing leaks rate in this buildings. Therefore qualitative justification of variant layouts can be justified and applied when necessary (Majed 2006).
Analysis and solution approach
A typical hollow measures dimension of (7*40*19) cm that is (L*w*h) and a wall thickness of 10mm, with three identical square voids of cross-section 5*5cm as shown in below figure. When the bricks are used in construction the hollows turns are to be air filled cavities therefore they are inserted with folded sheets to form inclined petitions and triangular enclose. The number value of these petitions always determines the base lengths and number of triangular enclose produced (Majed, 2010.)
The thermal efficiency of the building block is always showed by means of equivalent thermal conductivity; this is a heat insulating property of the whole order, both vertical and horizontal dimension (Mejad 2010)
).
Fig c Image of the hollow building block with three cavities and variant dimensions
The specific heat capacity of the building block is always 840J/kgK, the thermal conductivity, defined as a ratio is 0.7W/mK and the density is 1890kg/m3. These variations can be used to calculate some important general issues such as the equivalent thermal conductivity in both vertical and horizontal dimensions (Majed, 2010)
. Governing Equations and solution methods on ambient conditions (P1)
The conduction equation (in air, mortar and in the ceramic body of bricks):
Heat transfer in solids wall is always calculated by the Laplace equation which is obtained by the conduction while time and conduction equation is held constant. Grid of known equal number of cells on the x and y direction is for the conventional purposes and analysis (Mohamed and Hasan 2009).
∂2y/2x2 + ∂2y/∂y2 = 0
The boundary conditions denoted below as shown below with the condition of the isotherm state and the motionless fluid assumed.
Where T = T1 at x = 0 T = T0 at X = L
And ∂Y/∂X = 0 at Y = 0 ∂Y/∂Y = 0 at Y= W
At X – direction momentum
∂U/∂X + ∂Y/∂Y =0
At Y- direction momentum
u∂u/∂x + ∂u/∂y=y∂p/p∂x + u∆2u
Convectional equation
u∂u/∂x + u∂v/uy=∂p/p∂y+v∆2+gβ(T-Tc
The boundary equations presented in table format
Energy equation
u∂y/∂x +v∂y/∂y = αa∆2T
In accusations of internal cavity of the brick wall the heat transmission by the long- wave radiation gray body approximation is always used to give the required calculations (Mohamed and Hassan 2009).
Ambient conditions analysis
In analytical conditions to fully predict heat transfer a sinusoidal function may be necessary to be developed to calculate the data provided. In general practical conditions, the value of the temperature is controlled by the number of hours in the variations of solar isolation, orientation and ambient temperature.
The effect of the insertion of the polystyrene cavities on the heat rate is of great analysis on variation as the heat rate reduces i.e. for a common brick it is always 301.57W/m while the filled case it reduces to about 225.81(Mohamed& Hassan 2009).
Solution procedure, mesh generation and validation ( paper2)
The various governing equations with varied relevant boundary conditions were solved using the finite volume method (FLOVET CFD) software. The solution of the software requires validation by performing the required calculations using a three-dimension building block with hollow cavity as the bench mark. The model also dictates the following assumptions that the radiation exchange is independent on the radiation frequency and they are reflected on equal proportions with no relationship to the angle of incident radiation and no substantive amount of heat is lost to the exterior environment from the walls of the block. These equations also are also used to reveal the zero velocities in the interior boundaries and how the buoyancy influences these variations (Zbynek & Marek 2010).
The mesh generation can be fully be used to calculate the natural convection in the air cavities with various dimensions to provide accurate CFD simulation results. In order to make the appropriate mesh size varied test should be carried out with a number of cells to come up with a better grid for the convectional currents and better calculations. The grids of similar number of mesh are selected for convectional purposes and are bounded by a solid of thickness on both top and the bottom. This will provide steady heat throughout the block. The below table shows variation results obtained from hollow building blocks of different cavities (Zbynek & Marek 2010).
Presentation of results of different configurations (Paper 1)
Different material properties used and tabulated in table 1
The CFD analysis always provides an overestimate of the of the heat transfer by the convectional compared to the EN ISO 6946 (2007) in the vertical direction, this proves to be advantage since it provides higher safety margin results. The natural convectional influence in both the upward and downward heat flow is of great significant especially when it approaches the cross- sectional areas and conduction is the main determinant of heat transfer coefficient. The difference in the mesh cross-sectional area in the three dimensional surfaces greatly influences the convection heat transfer and this can be evident in the air flow field (Zbynek & Marek 2010).
The table clearly shows that the dominating effects in the hollow building block are always the convectional currents and they may be eliminated when the air is constant. The standard mortar is use as a control experiment to verify the difference with other cases.
The ratio between vertical and horizontal directions equivalent thermal conductivity
Brick producers always provide equivalent thermal conductivity only with the horizontal direction ignoring the vertical direction an important dimension which should be taken into account. In this section, determination of correlation of the thermal conductivity is made with reference to both the vertical and the horizontal direction in both the forward and downward directions (Zebyneck and Marek 2010).
Equivalent thermal conductivities of the model hollow brick masonry in horizontal and vertical directions (paper 2).
The equivalent thermal conductivity ratio in the downward direction shows a value of less than 1.0 indicating the increased value of the heat flow in the horizontal direction these heat transfer variations are caused by significant convections which occurs naturally in the cavities in the horizontal and upward heat flow directions. The ratio of the equivalent thermal conductivities also varies from horizontal and vertical directions depending on the type of brick used (Zbyneck & Marek 2010).
Graph 2 showing the variations at ambient temperatures.
In order to obtain the temperature variation in ambient conditions, a simple quasi approach which is steady with known time constant, ambient temperature and radiation is used in the analysis together with surface temperature.
The temperature of the surface which is unknown Ts is mathematically obtained by solving the brick model energy equation. The radiation heat flux is always calculated by the Boltzmann law. This will show difference in the flux between the sky and the facade. The ambient temperature is always assumed to be greater than the ambient temperatures. The Newton’s law cooling is then employed to calculate the convectional heat rate between the ambient air and the surface while the Fourier’s law is applied to produce the heat rate into the building (Majed 2010 ).
This repeated equation solutions provide the correspondent heat rate though the brick.
Similar trend is followed as surface temperature and during the night periods the heat rate is nearly negligible because of the steady ambient temperatures of about zero isolation.
The heat rate during the day always follow the trend as shown with assumed heat rate predicted to 25 W/m at maximum points and a minimum of 10W/m neglecting the night variations because of the steady ambient temperatures, this is calculated with repeated equations to obtain the Th=Ts, this provides the heat rate of the building block (Mejad 2010).
The effects of use insulation (Paper3)
It has been observed that walls of ordinary solid slab posses very low equivalence resistance of 0.368mK/W, therefore an improvement using the cross-sectional area of the cavities is necessary since they always increase the wall resistance by approximately 271%. It important also to note that further improvements can be realized through filling the cavities by the insulating materials such as the polystyrene in order to reduce conduction and convection (Mejad 2006).
The variation as a result of the use of insulation such as polystyrene shows that the heat rate is always less in insulated blocks than in the unfilled one. The integral rate of heat in the insulated block is always 225.87W/m while the one for the common block is slightly high of about 301.57W/m, This shows the dictation an insulation has in the design of these blocks to achieve the desired to temperatures(Mejad 2006).
Acceleration the number of inclined petitions decreases the Nusselt average number and the heat flux in the petitioned void is always less than the non petitioned void. This varies with the materials used as paper, cork; plastic sheets therefore economic viability should be a subject of consideration in case of mass utilization of these bricks (Mejad 2006).
The isothermal variation on the one single cellular motion (paper 3)
The above isotherms clearly indicate the isotherm in varied cross-sectional zone of the bricks with (a) showing the rectangular without petitioned cavities, (b) showing squared cavities while (c) shows polystyrene insertion.
When the motion was driven by the by buoyancy and rising flow of 321 at exactly downward current of 297K the above isotherms were obtained, showing the increased gradients at hot and cold zones as the isotherms compact together near the side walls. This shows t he increased convectional heat transfer on the vertical axis (x = w) and the upper cold section of the wall where (x =L + w). The parallel ones dictate the conduction heat transfer domination. This clearly indicates that there is no significant heat transfer on the y- direction (Wakashima & Saiton 2004)
Result analysis on the hollow brick of different grids (Paper 4)
The graph demonstrated above clearly indicates that the convergence of the stretched grid is much advantageous compared to the uniform grid in the similar number of cells. The absolute difference for the stretched grid for 40*40 uniform grids is 0.04 while that of the uniform grid of the same size is 1.8% in this selected case. To select suitable grid for desired accuracy ratio, it is usually recommended that the larger cavities to use finer meshes while the smaller cavities to use rough meshes; this will stabilize the grid by providing the larger number of cells within the cavities (Mejad 2010).
Decreasing the cross-sectional area of these cavities also results to quite less significant R- value, while a significant reduction of the of this value results to reduced convectional heat transfer thereby making the cavities to be dominated by the conduction. Contrary the increase in the smaller –width voids increases the value of R, this suggest the possibility of avoiding the use of insulating materials and redesigning the blocks using the prompt grid capacities to retain the high thermal heat resistance. This sums out that the ratio on both the horizontal direction and vertical direction majorly depends on direction of the heat flow and the cross-sectional area of the cavities employed in designing the bricks and the convection on the downward direction for all the cross-sectional areas is always negligible(Zbynek &Marek).
Conclusion
The effect of intracellular convection Heat transfer in the building blocks is of great importance in calculating the thermal resistance and the blocks with cavities heat transfer is simulated by the conservation system equation and the conduction effect on the surrounding environmental wall.
In designing appropriate air conditioning systems for the buildings, the block thermal inertia which posses the ability to decrease the maximum heat loss or gain is an important consideration. The higher the thermal inertia is inversely proportional to the instantaneous rate of flow to the interior structure providing the hollow blocks greater preference.
These blocks also posse’s a good nature of constant similarity in the layout thereby providing an ease in the repetitive design layout, this helps to accelerate the working operations of the builders Together with elimination on the use of beam and reduced cost of scaffolding advantages, a great potential use of the block can be exhaustedly used it the near future.
In order to come up with variant graphs shown, clear estimation is made using the Fluent software in atypical summer day in the regions preferred and the variations in the ambient heat transfer in the different cavities designed with or without insulation is collected and analyzed exhaustibly.
