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Modeling of the frost deposition by natural convection on horizontal ultra-low-temperature surfaces

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Abstract

The present work develops a reliable predictive model for precise estimation of the frost layer thickness by free convection on horizontal ultra-low-temperature surfaces. Wall temperature, relative humidity, time, and air temperature are considered as the input variables, and six well-known heuristic models are developed to estimate the desired output. The comparative results demonstrate that the least square support vector machine incorporating the genetic algorithm (GA-LSSVM) outperforms the other approaches. The coefficient of determination of 0.9998 and 0.9976, average absolute relative deviation of 0.8536% and 9.4002%, root mean squared error of 0.0115 and 0.0486, and relative root mean square error of 1.4479 and 5.8989 are the results of training and testing stages of the suggested model, respectively. A new test condition is studied to verify applicability of the proposed approach in computing the values that have not been evaluated in the experiments. It is observed that a decrease in the wall temperature causes a decrease in the frost layer thickness on horizontal surfaces under ultra-low-temperature conditions. The non-dominated sorted genetic algorithm II is also employed and combined with LSSVM model to study a sensitivity analysis. According to the Pareto optimal solutions, the time, wall temperature, air temperature, and relative humidity are, respectively, the most influential parameters on the frost layer thickness.

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Abbreviations

AARD:

Average absolute relative deviation

ANFIS:

Adaptive neuro-fuzzy inference system

ANN:

Artificial neural network

GA:

Genetic algorithms

GMDH:

Group method of data handling

LSSVM:

Least square support vector machine

MLP:

Multilayer perceptron

NSGA II:

Non-dominated sorted genetic algorithm II

PSO:

Particle swarm optimization

RMSE:

Root mean squared error

RRMSE:

Relative root mean square error

SR:

Standardized residual

SVM:

Support vector machine

b :

Bias

e :

Error

T :

Temperature (°C)

t :

Time (min)

\(\bar{A}\) :

Average of actual output

A :

Actual output

h :

Diagonal element of the hat matrix

H :

Hat matrix

H*:

Warming leverage

K(χ, χ i):

Kernel function

L :

Lagrangian function

N :

Total number of data

O i, j :

Output of the ith node in ANFIS

P :

Predicted output

R 2 :

Coefficient of determination

φ :

Relative humidity (%)

δ :

Frost layer thickness (mm)

χ :

Input variable

α :

Mass

μ :

Membership function

ψ :

Firing strength

Ω :

Normalized firing strength

θ :

Feature map

ρ :

Lagrange multiplier

γ :

Regularization parameter

a:

Air

w:

Wall

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Authors and Affiliations

  1. Department of Building Science, Tsinghua University, Beijing, 100084, China

    Alireza Zendehboudi

  2. Department of Chemical Engineering, Ilam University, Ilam, 69315–516, Iran

    S. H. Hosseini

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  1. Alireza Zendehboudi
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  2. S. H. Hosseini
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Correspondence to Alireza Zendehboudi.

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Zendehboudi, A., Hosseini, S.H. Modeling of the frost deposition by natural convection on horizontal ultra-low-temperature surfaces. J Therm Anal Calorim 137, 2029–2043 (2019). https://doi.org/10.1007/s10973-019-08087-x

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