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Journal of Thermal Analysis and Calorimetry

, Volume 137, Issue 6, pp 2029–2043 | Cite as

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

  • Alireza ZendehboudiEmail author
  • S. H. Hosseini
Article
  • 34 Downloads

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.

Keywords

Frost layer thickness Ultra-low-temperature surface Genetic algorithm Variable sequencing Modeling Leverage approach 

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

List of symbols

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, χi)

Kernel function

L

Lagrangian function

N

Total number of data

Oi, j

Output of the ith node in ANFIS

P

Predicted output

R2

Coefficient of determination

Greek symbols

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

Subscripts

a

Air

w

Wall

Notes

Supplementary material

10973_2019_8087_MOESM1_ESM.xlsx (25 kb)
Supplementary material 1 (XLSX 24 kb)

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Building ScienceTsinghua UniversityBeijingChina
  2. 2.Department of Chemical EngineeringIlam UniversityIlamIran

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