Comparative Analysis of the Mesh Treating Methods in the Numerical Heat Transfer Calculation of Nonhomogeneous Building Components

Abstract

Two two-dimensional numerical models for solving the heat transfer problems within no-homogeneous building components, choosing the interfaces between two layers (Method A) or the thermal property step surfaces (TPSSs) (Method B) as the nodes of computational meshes, were compared, A typical hollow building block wall was selected and multiple heat transfer experiments with constant and dynamic temperature conditions have been conducted. The calculation results of the two models both show a reasonable agreement with the experimental data. Furthermore, this demonstrates that there is lower calculation error for Method B than that for Method A, and the factors causing errors for Method A have been analyzed. The calculation error of the Method A decreases with the thermal resistance of the whole structure and the thickness of each layer, but increases with the thermal conductivity difference between the two materials adjacent to TPSS, the thermal capacities of materials, and the number of TPSSs. In addition, for both the two mesh treating methods, small enough mesh step size (≤0.005 m) guarantees high calculation accuracy.

NOMENCLATURE

c	=	specific heat, kJ kg−1 K−1
f(τ)	=	heat flow function as a function of τ, W/m2
ha	=	convective heat transfer coefficient when x = 1, W m−2 K−1
hb	=	convective heat transfer coefficient when x = Nx, W m−2 K−1
i	=	sequence number of data
n	=	amount of data
Ni	=	ith datum
Nsta,i	=	ith standard datum
Nx	=	total number of the meshes in the x direction
Ny	=	total number of the meshes in the y direction
T	=	temperature, °C
Tfa	=	boundary air temperature when x = 1, °C
Tfb	=	boundary air temperature when x = Nx, °C
Tinit	=	initial temperature, °C
Tx,y,τ	=	temperature of the point (x, y) at time point τ, C
Tx,y,τ+1	=	temperature of the point (x, y) at the time of τ + 1, C
x	=	direction of thickness, mm
y	=	direction of width, mm

Greek Symbols

ρ	=	density, kg m−3
λ	=	thermal conductivity, W m−1 K−1
τ	=	time, s
σ	=	standard error, °C
σ′	=	maximum absolute error, °C

Subscripts

E	=	point right of the point p
init	=	initial
N	=	point above the point p
N′	=	point above the point p′
p	=	boundary meshes when x = 1
p′	=	boundary meshes when x = Nx
S	=	point under the point p
S′	=	point under the point p′
sta	=	standard
W′	=	point left of the point p′

Additional information

Notes on contributors

Yuan Zhang

Yuan Zhang is a lecturer at the School of Energy and Power Engineering of Jiangsu University in Jiangsu Province, China. He received his Ph.D. degree in 2014 from Southeast University, Nanjing, China, in heating, ventilation, and air conditioning. He is currently working on energy conservation in the building envelope, phase transition heat transfer, and the indoor thermal environment.

Geng Wang

Geng Wang is a lecturer at Anhui Jianzhu University in Anhui province, China. He received his Ph.D. degree in 2013 from Southeast University, Nanjing, China, in heating, ventilation, and air conditioning. He is currently working on heat and moisture transfer phenomena in the building envelope.

Kai Du

Kai Du is a professor at Southeast University, Nanjing, China. He received his B.Sc. degree in 1982 from the Power Department of the Southeast University, Nanjing, China. He is currently working on energy-saving buildings, refrigeration, and air-conditioning devices.

Jiapeng He

Jiapeng He is a professor at Nanjing Tech University, Nanjing, China. He received his M.Sc. degree in 1996 from the College of Aerospace Engineering of the Nanjing University of Aeronautics and Astronautics, Nanjing, China. He is currently working on energy-saving buildings, and fire smoke control in high-rise buildings.