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Experimental study of geometric cuboid effect on convective heat transfer

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Abstract

The building energy simulation (BES) models are extensively used to predict heat loads in buildings. Despite its significance, however, the geometric cuboid effect on the convective heat transfer coefficient (CHTC) is yet to be considered in the BES models. In this paper, effects of height, width, length, and angle of attack of a cuboid and also the effect of air speed on the CHTC were experimentally studied to highlight unreliability of the models ignoring the cuboid geometry. For this purpose, a total of 16 experiments were designed using the Taguchi’s design of experiments (DOE), where the considered factors were varied at 4 levels. The percent contribution of each factor to the output variable was determined by the analysis of variance (ANOVA), indicating the significance of all geometric factors when it came to the CHTC. The linear regression analysis was further performed to define a linear correlation for predicting the overall CHTC under different geometric conditions. Accordingly, two nonlinear correlations were developed for the cuboid geometry and one correlation was obtained for building applications, by which one could predict average Nusselt number (Nu).

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Abbreviations

A:

Surface area (m2)

a:

Cuboid width (m)

α :

Angle of attack (°)

\(\overline{{\alpha_{I} }}\) :

Mean effect of α at level Ι

b:

Cuboid height (m)

β :

Unknown parameters

C:

Constant numbers

c:

Cuboid length (m)

CF:

Correction factor

ε :

Error

G:

A function of geometric factors

\({\overline{\text{h}}}\) :

Convective heat transfer coefficient (CHTC) (W/m2K)

K:

Conductivity (W/m.K)

\(\overline{Nu}\) :

Nusselt number

n1, n2 :

Constant numbers

p:

Percent contribution (%)

\(\dot{q}\) :

Heat transfer rate (W)

Q:

Flow (lit/s)

ρ :

Density (kg/m3)

R:

Sum of total experimental results (CHTC)

r:

Correlation coefficient

Reb :

Reynolds number based on dimension b

Rec :

Reynolds number based on dimension c

S (ss):

Total variance or the sum of squares

T:

Temperature (K)

\(\Delta T\) :

Temperature difference (K)

ti:

Turbulence intensity (%)

V:

Air speed (m/s

σ :

Stefan-Boltzmann constant (5.67 × 10–8(W/m2K4))

λ :

Emissivity

w:

Wall or surface

∞:

Free airstream

Ι, ΙΙ, ΙΙΙ, ΙV:

Levels 1 to 4, respectively

in, Out:

Inlet, outlet

1, 2, …, 16:

Experiment number

op:

Optimum conditions

max, Min:

Maximum, minimum

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Authors and Affiliations

  1. Department of Mechanical Engineering, Razi University, Kermanshah, Iran

    Javad Babakhani & Farzad Veysi

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  1. Javad Babakhani
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  2. Farzad Veysi
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Correspondence to Farzad Veysi.

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Babakhani, J., Veysi, F. Experimental study of geometric cuboid effect on convective heat transfer. Eur. Phys. J. Plus 137, 215 (2022). https://doi.org/10.1140/epjp/s13360-022-02430-2

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