It is essential and often useful to be aware of the moisture and temperature conditions existing within a building and its construction elements (Scheuneman, 2002).

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Contents
Introduction 3
Discussion: 3
1. Heat transfer Principles: 3
1.1. Conduction principles 4
1.2. Convection concepts 5
1.3. Radiation of heat 5
2. Condensation: 7
2.1. Interstitial condensation: 7
3. Thermal Insulation 8
Wall vapor barriers: 8
4. Structural Gradients 9
4.1. Due point 9
Thermal analysis: 11
1. Conduction: 11
Calculations of U values 12
Ventilation Analysis: 15
Estimating Structural Gradients for the building 17
Due point estimation 21
Conclusion: 22
References 23


Introduction
It is essential and often useful to be aware of the moisture and temperature conditions existing within a building and its construction elements (Scheuneman, 2002). Such information is vital when making new house designs, troubleshooting problems with existing buildings and making plans to renovate a current structure. It is also mandatory to access temperature gradients during hot and cold seasons to determine suitable materials needed for the building structure. Being knowledgeable on temperature and air vapor conditions and their correlation helps when learning a vapor barrier concerning other elements that form the building structure (McMullan, 2012). This paper discusses the principles of heat transfer that apply in building construction. The article also analyzes a structural template and calculates U-values are along with architectural and dew point gradients to determine whether the used construction materials meet comfort and durability thresholds in line with ventilation, heat dissipation, insulation, and condensation.
Discussion:
Heat transfer Principles:
Various heat transfer processes can take place between the interior of a building and the outer surroundings. Heat can be exchanged directly by conduction through wall elements or dissipated from surfaces by radiation or convection. These transfer modes affect the interior temperatures of the structure and subsequently, influences the warm air stability or comfort of its users (Chadderton, 2013). Factors that influence the heat balance and overall thermal performance of a building include:
Design parameters or geometric dimensions of building entities: windows, roofs, orientation and walls
Construction material properties: thermal conductivity, density, transmissivity and specific heat capacity.
Weather constraints: ambient temperature, solar radiation, humidity and wind speed
Building usage: number of occupants, air conditioning, lighting levels and other energy dissipating equipment.
Conduction principles
In this process, heat flow occurs when a body at higher temperature is in contact with another body at lower temperatures. The heat is transferred from the hot body to the cold one with minimal movement of the molecules. Solids, liquids, and gases are good conductors of heat (Steele, 2013). However, some materials can conduct better than others because of their electron mobility. The fundamental equation represents heat conduction:
Q_(cond = (kA (T_h-T_c ))/L)
Whereby;
T_h= warm surface temperature (K)
T_c= cold surface temperature (K).
A= surface area (m2), L= breadth (m)
K = the material’s thermal conductivity (W/m-K)
Q_(cond )= quality of heat flow (W)
Given a certain temperature gradient, a lower thermal conductivity of a component of fixed cross-sectional area and breadth yields a lower transfer rate of heat and vice versa (Hens, 2012).
Convection concepts
Convection is the heat transferred from one part of a liquid or gas at higher temperatures to another area of low temperature via fluid particles. Convection heat transfer takes place through wall surfaces, roofs, and floors. The temperature difference between a fluid (gas) and a surface of contact results to density variations in the fluid leading to buoyancy. Hence heat is exchanged between the fluid and the surface in a process called free convection. However, if external forces like wind force the fluid motion then the process is termed as forced convection (Jain, 2005). Heat transfer by convection can be expressed as:
Q_(conv= Ah (T_s-T_f))
Given:
T_r = the fluid temperature (K).
T_s= the surface temperature (K)
h = the transfer coefficient of heat (W/m2-K)
The transfer coefficient (h) relies on fluid velocity, nature of heat flow, surface orientation and the fluid’s physical characteristics.
Radiation of heat
Radiation is a process of heat transfer from one hot body to another without physical contact. Radiation intensity increase with the temperature difference and propagates without the use of any linking medium. Two bodies separated and at different temperatures emit, absorb and reflect radiant heat on their surfaces (Planck, 2013). If the process takes place across two plane surfaces of uniform area aligned parallel to each other, then the rate of heat transfer can be written as:
Q_12= Aε_eff σ (T_1^4-T_2^4)
ε_eff=〖(1⁄ε_1 + 1⁄ε_2 -1)〗^(-01)
Given:
ε_1 and ε_2= emissivity of surfaces 1 and 2.
A= area of surface (m^2)
T_1 And T_2 = temperatures of cover 1 and 2 (K)
σ = Stefan-Boltzmann constant (5.67×10^(-8) W/m^2 -K^4)
Q_21 = radiative exchange rate between surfaces (W)
But for buildings, the external surfaces like roofs and walls are typically exposed to the atmosphere (Kumar, 2002). Therefore it is vital to consider the radiation exchange for the exposed parts using this fundamental equation.
Q_radiation=A ε(T_s^4- T_sky^4)
Given;
A= the building’s exposed surface
ε= the exposed part’s emissivity
T_s And T_sky= are temperatures of exposed surface and sky respectively.
Radiative and convective heat transfer coefficients are merged to give a uniform heat transfer coefficient for a surface when dealing with building applications (Bergman, 2016).
Condensation:
Water vapor in the air can condense and lead to a state of dampness in a building. This form of humidity can cause mold growth, mist clogging on windows, and beards of water forming on non-absorbent surfaces. Condensation creates unhealthy living conditions for building inhabitants, leads to the destruction of construction materials, fast deterioration of building structures and bring about discomfort to the people (Ching, 2011). In other words, unwanted condensation is a concern for people’s wellbeing and structural stability. However, condensation problems have been increasing in recent years due to poor designs for modern buildings, and inappropriate heating remedies, poor ventilation, and living standards.
Condensation in structures takes place when warm moisture settles on surfaces that are way below a predetermined dew point value of humidity. There are two forms of condensation: interstitial condensation and surface condensation (Charlett, 2013). Interstitial condensation forms in a building’s construction materials while surface condensation takes place on the window or floor surfaces inform of a moisture beards or tiny water droplets.
Interstitial condensation:
When construction materials used are permeable to water to some extent then they can allow air containing moisture to pass through (Laxton, 2009). When the wind meets a fresh surface, it cools as well and loses it moisture carrying capacity. The due-point temperature is adjusted, and the air is forced to shed some humidity. The moisture condenses into liquid form within the building materials and leads to interstitial dampness. Such condensation can destroy construction materials like steel and weaken the insulation capability of the elements.
Proper ventilation helps to prevent condensation inside a building by eradicating moisture content from the air (Seppanen, 2009). Devices like extractor fans are positioned near moisture sources like the kitchen and drive out the moist air efficiently. During construction, it is vital to consider the orientation of windows so that they do not allow vapor into other rooms. It is advisable to close doors of sensitive rooms like Kitchen and bathrooms. Installing ventilators in each room can aid smooth air flow control without loss of comfort at considerably small energy use. Applying exhaust air to houses as a heat recovery measure can curb costs related to heat loss.
Thermal Insulation
Insulation helps to minimize heat loss rates through a structural assembly. Thermal insulation also contributes significantly towards keeping building surfaces warm (Straube, 2011). Heating systems can be installed in a building to catalyze this process. Placing insulation materials inside a structural assembly, for instance, a brick wall bolsters its surface by making temperatures rise or fall in tandem with room values. However, if the insulation is nearer to the interior surface, the exterior surface remains cold hence a moisture barrier is recommended to minimize interstitial condensation.
Wall vapor barriers:
Vapor barriers are typically installed in the insulation layer nearer to the warmer side of the wall. The exterior surface should be allowed water to navigate through so that moisture inside the structure can escape through the outer surface. The outer surface should also be weatherproof. Various construction materials have the weatherproof property but still allow water vapor through since water vapor molecules are smaller compared to liquid water molecules (Zhang, 2011). It is essential and often useful to know the moisture and temperature conditions of any building assembly. Such information is vital when designing new buildings or retrofitting existing ones. The temperature gradient helps one determine the suitable materials required for the building exoskeleton. Information about moisture conditions is crucial when locating vapor barriers concerning other elements in the building envelope.
Structural Gradients
During winter, temperatures of the building’s interior surface are close to room temperatures apart from the surfaces of the windows (Chwieduk, 2014). However, it becomes increasingly colder as one cuts through the walls towards the outside surface. The temperature gradient through the individual wall elements can be calculated put on a chart. During the summer, same analogy applies only that the temperatures keep on increasing when moving towards the exterior surface.
Due point
Relative humidity refers to water vapor content held in the air compared to the maximum amount of vapor the same volume of air could keep at a fixed temperature. For instance, 50% relative humidity means the volume of air is carrying steam amounting to half of its designated capacity. 100% humidity means the air is saturated and the vapor content can condense it temperatures fall below a given value. The temperature at which vapor condenses into liquid is called dew point temperature. Understanding the moisture content of the air and the dew point is vital when analyzing moisture/condensation problems in buildings (Thomas, 2014). A reduction in air temperature results in a considerable decrease in the amount of water vapor it can hold. In other words, as temperatures fall, the airsheds off some steam in the form of liquid and adjusts its carrying capacity.
The psychrometric chart can be used to visualize the relationship between air temperature and relative humidity R.H. Curved contours originating from the vertical scale on the right illustrate the corresponding humidity variations while the straight lines elevating vertically from the baseline horizontal scale towards the saturation curve indicates instantaneous air temperatures. One can use the psychrometric chart to obtain new dew point values given values of relative humidity and air temperature (Wood, 2002).

Figure 1Psychrometric chart
One needs to record air temperature and relative humidity inside the building using a thermometer and a hygrometer respectively.
Identify the measured temperature on the baseline horizontal scale of a psychrometric chart. Trace the vertical projections that emerge from this reading and mark the point where it intersects the R.H curve which represents the measured humidity.
Finally, one shall project a parallel straight line from the point of intersection to the baseline scale to cross the 100 R.H curve. The new intersection point gives a new due point.
Thermal analysis:
Several techniques have been put forward to analyze thermal constraints and estimate building performance. They include Correlation methods, dynamic methods, and steady-state methods. This paper uses simple steady-state techniques that involve calculations and graphical representation using excel.
Conduction:
This equation is used to calculate the heat conduction rate through entities such as walls, roofs, and floors:
Q_ CD = ΔT U A
Given:
A = surface area of the element (m2)
U= temperature transmittance (W/m2-K)
The ΔT= thermal discrepancy of air between surfaces (K).
U is also the reciprocal of total thermal resistance. It depicts the total amount of heat transferred between the indoor and outdoor surfaces of a wall per unit area and time. This parameter is used to classify the insulating properties of building materials. The insulating capabilities of an element decrease as values of U increase and vice versa. One can solve the rate of heat conduction for each construction assembly material individually, for instance, wall, floor or roof. Summing up the results achieves the total flow rate of heat by conduction.
Qc = ∑_(i=1)^Ni▒〖Ai Ui ΔTi〗
Where: I = number of elements and Nc = total components
Note: steady-state calculations do not account for the effects resulting from heat capacities of material elements.
Calculations of U values
Inner wall:
The wall is 190mm thick with 10mm coat of plaster on both sides.

L_1=10mm; k_1=0.721 W/m-K
L_2=10mm; k_2=0.721 W/m-K
L_3=10mm; k_3=0.721 W/m-K

h_o=22.7 W/m^2 -K and h_i=8.3 W/m^2 -K
R_Tt=1⁄8.3+.01⁄.721+ .19⁄.811+ .01⁄.721+1⁄22.7=.4266
U= 1⁄R_T = 1⁄0.4266=2.344 W⁄m^2 -K

Outer wall:
The primary barrier is constructed of two layers of bricks each 90mm thick and a 50mm thick air gap in between the walls. Cement plaster of 10mm thickness is applied on each side.
L_1l=10mm; k_1=.721 W/m-K
L_2l=9mm; k_2=.811 W/m-K

L_4l=9mm; k_4=.811 W/m-K
L_5l=10mm; k_5=.721 W/m-K
L_3l=Enclosed air conductance C=6.22 W/m^2 -K
〖h_o=22.7 W/m^2 -K and h〗_i=8.3 W/m^2 -K
R_Tt=1⁄8.3+.09⁄.811+ .09⁄.811+ .01⁄.721+1⁄22.7+ 1⁄6.22=0.5750
Hence U= 1⁄R_T =1.739 W/m^2 -K
Roof Slab
The RCC roof slab is 150mm thick, and it is insulated with polystyrene. The surface is furnished with brick tiles of 40mm thickness on the top and cement plaster of 10mm thickness at the bottom.

L_1l=10mm; k_1=.721 W/m-K
L_2l=15mm; k_2=1.58 W/m-K
L_3l=5mm; k_3=.035 W/m-K
L_4l=4mm; k_4=.798 W/m-K
h_i=6.1 W/m^2 -K and h_o=22.70 W/m^2 -K
R_Tt=1⁄6.1+.15⁄1.580+ .05⁄.035+ .01⁄.721+1⁄22.7+ .04⁄.798=1.795
Hence U= 1⁄R_T =0.55 W/m^2 -K

Ventilation Analysis:
Ventilation necessitates heat flow between the building and the external air. But the heat flow rate depends on air exchange rates which are calculated as:
Qv = Vr ρ ΔT C
Given;
ΔT = temperature discrepancy (K)
ρ = air density (kg/m3)
C = air’s specific heat (J/kg-K)
Vr = ventilation rate (m3/s)
Vr Can be evaluated if air changes are known by value.
Vr =NV/3600
Given;
V = the room’s volume (m3)
N = total air changes made in per hour
Thus Q_v= ρ C NV/3600 ∆T

The recommended ventilation change rates
Table 1Recommended ventilation change rates
Ventilation space Hourly air changes recommended
Laboratory rooms 6-3
Classrooms 6-3
Kitchen rooms 9-6
Auditorium or Assembly room 6-3
Hospitals 6-3
Living rooms and Bedrooms 6-3
Factories Offices 6-3
Garages 15-12
Restaurants and Cafeterias 15-12
Bathrooms 6-3
Toilets 6-3
Theatres and Cinema rooms 9-6
Bedrooms 6-3

Estimating Structural Gradients for the building
It is necessary to examine how thermal resistance of building materials and temperature change through each material are correlated. One assumption to make is that heat flows across each element in steady state parallel heat flow conditions. Temperature change across each component is obtained as:
ΔT = R/R_T × ∆T_T
Where, ∆T = temperature change across each element, R = the thermal resistance of the element, R_T = total thermal resistance of all elements and ∆T_T= total temperature change from interior to exterior.
The steady-state assumption means that the analysis might be prone to errors when there are rapid alterations of temperature in the outside air. Nevertheless, the results obtained from this study are still applicable. Tables will help with the calculation and graphs aid in visualizing the temperature gradients across the building walls, ceilings, and roofs. Thermal resistance values of various building components are listed in Appendix A; they are used with known interior or exterior temperatures to obtain R,( R)/R_T , ∆T and T values. A graph of temperatures is plotted to give a visual representation of the figures calculated.
NB: Winter T and ∆T columns are filled with data when the Interior temperatures are more than the exterior values while the summer columns are utilized when the surface temperatures are less than the interior readings.
For instance, take a wall assembly with exterior temperatures of -20. 00C and an interior surface with +20. 00C

Figure 5 Wall
All wall components were listed appropriately in the table
The R column was filled using appropriate data from the Appendix x
Total R_T was obtained as 2.55 the by adding all values in the R column
The ratio R⁄R_T was calculated and the amount received was close to 1.00
The interior and exterior temperatures were tabulated appropriately in the Winter column and calculated ∆T
Obtained ∆T_T for each element by multiplying each R⁄R_T with ∆T_T and tabulated the values.
Filled the winter T column by adding ∆Ts to the T values in rows above.
Plotted the graph by altering ∆Tinto percentage form and the air film taken to be a 25mm length.

Table 2 Structural Temperature Gradient
Element Value of R Ratio(R⁄R_T ) Hot Season Cold Season
∆T T ∆T T
Exterior Temperature (T) 35.0 -20
EXTERNAL. FILM OF AIR 1 0.03 0.01 0.15 0.4
34.85 -19.6
Metal siding (13mm) 2 0.12 0.05 0.75 2
34.1 -17.6
13mm plywood 3 0.11 0.04 0.6 1.6
33.5 -16
95 mm batt 4 2.09 0.82 12.3 32.8
21.2 16.8
13 mm gypsum 5 0.08 0.03 0.45 1.2
20.75 18
INT. AIR FILM T 6 0.12 0.05 0.75 2
INTERIOR T 20.0 20
TOTAL 2.55 1.00 15 40

The same procedure is repeated for a summer period whereby interior temperatures are 20oC while the exterior temperatures are 35oC. The information is filled in the summer column.
Structural gradient Graphs
Cold Season

Hot Season

Due point estimation
For instance, the building’s interior temperatures and humidity values are 250c and 60% respectively. The psychrometric chart indicates that the vapor is likely to condense at a temperature of 16.50c

Alternatively, one can estimate new values of relative humidity when temperatures in a building change. The first step is to note the initial R.H and corresponding room temperature values on the psychrometric chart. Then the new R.H value can be obtained by projecting a horizontal line from the old temperature value to the original amount. The intersection point gives the new estimated relative humidity value of the air. For instance, if the building is at 25oC and 50% relative humidity and then it is cooled down to 15oC, new R.H values can be obtained from the psychrometric chart. The horizontal line intersects the humidity curve at 90% hence this is the new R.H value for 15oC.

Conclusion:
Principles of thermodynamics are vital when designing buildings. Knowledge of temperature and moisture parameters is helping architects to create better buildings that meet comfort needs of users and withstand forces of nature. Thermal heat losses, ventilation provisions, insulation and effects of condensation are among many other factors that one should consider when suggesting building materials. The U parameter has been useful when accessing the insulating properties of materials used in the design including walls and roofs. The structure and dew point values calculated are vital when dealing with condensation problems in building assemblies.
References
Bergman, T., 2016. Fundamentals of Heat and Mass Transfer. S .l.: Wiley.
Chadderton, D., 2013. Building Services Engineering. S .l.: Routledge.
Charlett, A., 2013. Fundamental Building Technology. S .l.: Routledge.
Ching, F., 2011. Building Construction Illustrated. S .l.: John Wiley & Sons.
Chwieduk, D., 2014. Thermal Balance for Efficient Heating and Cooling. [Online]
Available at: https://books.google.co.ke
[Accessed 11 January 2018].
Hens, H., 2012. Building Physics – Heat, Air and Moisture. S .l.: John Wiley & Sons.
Jain, K., 2005. Building Construction. S .l.: Firewall Media.
Kumar, S., 2002. Journal of the Indian Institute of Architects. S .l.: Indian Institute of Architects.
Laxton, W., 2009. The Civil Engineer and Architect’s Journal. S .l.: Transport Research Board.
McMullan, R., 2012. Environmental Science in Building. s.l.:Palgrave Macmillan.
Planck, M., 2013. The Theory of Heat Radiation. S .l.:Courier Corporation.
Scheuneman, C., 2002. Estimating temperature gradients and dew point temperatures for. Canada: National Research Council of Canada.
Seppanen, O., 2009. Moisture control and ventilation. [Online]
Available at: https://www.ncbi.nlm.nih.gov/books/NBK143947/
[Accessed 11 January 2016].
Steele, G., 2013. Central Heating: A Design and Installation Manual. S .l.:Technology & Engineering.
Straube, J., 2011. Thermal Control in Buildings. [Online]
Available at: https://buildingscience.com/documents/digests/bsd-011-thermal-control-in-buildings
[Accessed 11 January 2018].
Thomas, K., 2014. Condensation in Buildings, s.l.: Australian Government and States and Territories of Australia.
Wood, L., 2002. The Use of Dew-Point Temperature in Humidity Calculations, Washington: Institute for Materials Research.
Zhang, H., 2011. Building Materials in Civil Engineering. [Online]
Available at: https://www.sciencedirect.com/science/book/9781845699550
[Accessed 11 January 2018].

APPENDIX A
PROPERTIES OF CONSTRUCTION MATERIALS
Material Density
(kg/m3) Specific heat
(kJ/kg-K) Thermal conductivity
(W/m-K) Material Density
(kg/m3) Specific heat
(kJ/kg-K) Thermal conductivity
(W/m-K)
Brick (burnt) 1821 0.880 0.8110 Cement mortar 1648 0.920 0.720
Mud brick 1731 0.88 0.750 Plaster Cement 1762 0.84 0.721
Concrete (Dense) 2410 0.89 1.740 Cinder concrete 1406 0.84 0.686
RCC 2288 0.88 1.580 Gypsum plaster 1120 0.96 0.512
Limestone 2420 0.84 1.800 Sheet AC 1520 0.84 0.245
Slate 2750 0.84 1.720 GI sheet 7520 0.50 61.060
Reinforced concrete 1920 0.840 1.100 Face bricks* 2083 1.004 1.30
Brick tile 1892 0.88 0.798 Polycarbonate sheet* 1350 1.17 0.21
Lime concrete 1646 0.88 0.730 Timber 480 1.68 0.072
Mud phuska 1622 0.88 0.519 Plywood 640 1.76 0.174
Glass 2350 0.88 0.814
Hard board 979 1.42 0.279 Sand 2240 0.84 1.740
Wall board 262 1.26 0.047 Expanded polystyrene 34 1.34 0.035
Chip board 432 1.26 0.067 Foam glass 160 0.75 0.055
Particle board 750 1.30 0.098 Foam concrete 704 0.92 0.149
Jute fibre 329 1.09 0.067 Polyurethane foam (PUF)* 30 1.570 0.026
Wood wool board 674 1.13 0.108 Cork 540 1.00 0.085
Coir 97 1.00 0.038 Plastic tile* 1050 1.07 0.50
Saw dust 188 1.00 0.051 Gypsum plasterboard 950 0.82 0.16
Rice husk 120 1.00 0.051 Thatch (reed)* 270 1.00 0.09

APPENDIX B
BUILDING MATERIAL RESISTANCE
Insulation Structural
Material Resistance/mm Material Resistance/mm
Batt 0.022 Softwood Lumber 0.0087
Polystyrene 0.020 Cedar Logs 0.0092
Wood Fibre 0.023 Concrete 2400kg/m3 0.00045
Wood Shavings 0.017 Concrete 1760kg/m3 0.0013
Cork 0.026 Concrete 480kg/m3 0.0069
Glass Fibre 0.028 Lime/Sandstone 0.00060
Straw Board 0.028 Steel 0.000022
Air Aluminum 0.0000049
Air surface films 0.03 Glass 0.01