# Hybrid heating systems optimization of residential environment to have thermal comfort conditions by numerical simulation

- Nabi Jahantigh
^{1}Email author, - Ali Keshavarz
^{2}and - Masoud Mirzaei
^{2}

**13**:50

https://doi.org/10.1186/s40201-015-0202-2

© Jahantigh et al. 2015

**Received: **29 May 2013

**Accepted: **11 May 2015

**Published: **31 May 2015

## Abstract

The aim of this study is to determine optimum hybrid heating systems parameters, such as temperature, surface area of a radiant heater and vent area to have thermal comfort conditions. DOE, Factorial design method is used to determine the optimum values for input parameters. A 3D model of a virtual standing thermal manikin with real dimensions is considered in this study. Continuity, momentum, energy, species equations for turbulent flow and physiological equation for thermal comfort are numerically solved to study heat, moisture and flow field. *K* − *ɛRNG* Model is used for turbulence modeling and *DO* method is used for radiation effects. Numerical results have a good agreement with the experimental data reported in the literature. The effect of various combinations of inlet parameters on thermal comfort is considered. According to Pareto graph, some of these combinations that have significant effect on the thermal comfort require no more energy can be used as useful tools. A better symmetrical velocity distribution around the manikin is also presented in the hybrid system.

### Keywords

Virtual manikin Thermal comfort Radiant panels Optimal conditions Conventional heating## Introduction

The convectional air conditioning equipment used for heating and cooling environment systems consume a lot of energy. Hybrid heating systems consist of two types of heating systems, namely radiation and convection. They work together to provide an efficient thermal comfort within an environment. This type of system can supply continuous heating energy even when one of them is off. Therefore, this technique is a very promising method which can reduce the energy consumption without lowering the level of comfort conditions.

In general, the thermal comfort is affected by the air temperature, mean radiant temperature; air velocity and relative humidity are included in the environmental parameters whereas the activity level and metabolic rate are categorized as the personal ones. Hence, in the hybrid system, the radiant heater temperature, surfaces, location, the air flow field, and metabolism are the most important factors affecting the level of thermal comfort in an environment [1].

So far, researchers have proposed different models to obtain higher level of thermal comfort in an environment [2, 3]. Thermodynamic analysis of heat and mass of human body and its effects on thermal comfort were studied by Prek [4]. Jeet at el. [5] have evaluated the effect of high-temperature radiant heaters and windows on the thermal comfort. Despite Jeet’s study, Myhern and Holmberg [6] have shown that low radiant panel temperature is more suitable for indoor environment. A combination of flow field around a human body was studied numerically by Murakumi, at el. [7]. A more complex model which includes the real body shape and physiology was considered by Kilic and Sevilgen [8]. They evaluated the heat transfer, mass, air flow and moisture around the human model.

As of now, the effects of flow and geometric parameters on thermal comfort have been studied in several papers individually. However, no detailed combinations of their interaction effects are seen in the literature. Therefore, in this study, the effects of input parameter such as temperature, surface area, and position of the radiant heaters along with their interactions on a hybrid heating system have been investigated. In addition, the air flow parameters of the convection system were also considered. The main objective of this study is to achieve thermal comfort in an indoor environment. In this simulation, a 3D model of a virtual standing thermal manikin with real dimensions is used. A numerical method was used to solve the flow field around the manikin. Also an optimization toward thermal comfort conditions is done.

### Governing equations and solutions

The governing equations, consisting of continuity, momentum, energy, and mass transfer in a room which includes a manikin, are solved here. The radiation and turbulence equations are also considered in this problem. In addition, the Factorial Design Method (FDM) is used to analyze and optimize the variable effective parameters.

*h*is defined as

*Y*

_{ j }is the mass fraction of species j and

Here *T*
_{
ref
} is 298.15 K.

Where, *Sc*
_{
t
} is the turbulent Schmidt number.

By solving the flow field, all terms in equation 11can be calculated.

*S*= 0, the thermal equilibrium will be satisfied [6]. In equation 11

*E*

_{ sk },

*C*

_{ res }and

*E*

_{ res }terms can be calculated as follows

The Factorial Design Method (2^{
k
}) or two level design is used here for optimization [12]. The input and output parameters’ range must also be specified. The input parameters are the area of convection flow, inlet flow rate, temperature, location, and the surface area of radiant heater. The output effective parameters are the radiation flux, convection flux, and PMV index. In this technique, the impact of the factor is defined as the difference between the high and low level of responses.

Range of input parameters

Effect Parameter | Min. | Max. |
---|---|---|

Inlet area of the convection flow(m) | 0.025 | 1 |

Inlet flow velocity(m/s) | 0.05 | 1 |

heater temperature( °C) | 30 | 90 |

The position of heater along vertical direction (m) | 0.0 | 3 |

The position of heater along Horizontal direction(m) | 0.0 | 2 |

The heater area(m | 1 | 3.1 |

A 3D computational code was used to solve the flow field, energy, and mass equation. The PISO algorithm has been used [14]. In this approach, higher-order accuracy is achieved at cell faces. Pressure discretization is done by second order method. The *K* − *εRNG* is also suitable for low-Reynolds numbers and more accurate and reliable for a wider range of indoor environments and flows with heat transfer.

The *DO* radiation model is used to consider the radiation effects of heating surfaces and sources in the flow fluid simulation. It allows the solution of radiation at semi-transparent walls.

### Geometry of the problem

Segment of the manikin and their area

Number | Surface Name | Surface Area(m |
---|---|---|

1 | Head | 0.15898 |

2 | Neck | 0.028926 |

3,23 | Right & Left shoulder | 0.048249 |

4 | Brisket | 0.234812 |

5,22 | Right & Left arm | 0.098026 |

6,20 | Right & Left | 0.021141 |

7,21 | Right & Left forearm | 0.068715 |

8 | Bowl | 0.038951 |

9 | Waist | 0.210502 |

10,19 | Right & Left hand | 0.052163 |

11 | Basin | 0.041288 |

12 | Pelvis | 0.027313 |

13,18 | Right & Left tigh | 0.287548 |

14,17 | Right & Left leg | 0.160346 |

15,16 | Right & Left foot | 0.051366 |

This problem was first modeled using Solid Work and, then, meshed by Hypermesh software. The problem is solved for several different heater locations to optimize its position in the room.

### Computational grid

### Boundary conditions

Boundary condition

zone | T | type | V m/s | Mass flow |
---|---|---|---|---|

inlet | 10 | velocity | 0.15 | 9.5 |

Out let | Pressure outlet | |||

body | 33.1 | covered | 10 | |

33.7 | uncovered | |||

wall | 25 | No slip | 0 |

Physical characteristic of material [15]

Door | Wall | Window | |
---|---|---|---|

width | 50 | 250 | 25 |

ρ( | 700 | 1940 | 840 |

| 2.31 | 0.84 | 0.84 |

| 0.173 | 0.06 | 0.2 |

ε | 0.9 | 0.95 | 0.8 |

### Validation of results

## Results and discussion

### The impact of input parameters on the objective functions

In these Figures, the letter A is the cross section area of the inlet vent, B is the input velocity, C is the heater temperature, D and E are the positions of heaters along the horizontal and vertical directions, and F is the surface area of the heater. The impacts of these parameters as well as their combinations are studied individually.

Hence, by glancing at all Figs. 8 and 9 it can be concluded that:F has the most effect on the object function and requires more energy C has the most effect on the objective function and needs no more energy. The combination of input parameters has different impacts on the objective function in comparison to their individual ones due to their interaction. Some of these combinations which can be used as useful tools have significant effect on thermal comfort and require no more energy

### The optimization

^{2}, radiation flux 40w/m

^{2}, relative humidity 50 % and PMV 0.001. The optimized values are calculated and tabulated in Table 5.

Optimized value for objective parameter

Input parameter | Min. | Max. | Suggested value | Optimized value | Objective parameter | Target value | Computed value along the target |
---|---|---|---|---|---|---|---|

Inlet velocity(m/s) | 0.025 | 1 | 0.2 | 0.1 | PMV | 0.001 | −0.1 |

Inlet area(m | 0.05 | 1 | 0.4 | 0.12 | Total flux | 110 | 107.679 |

Radiation heater temperature( °C) | 30 | 90 | 45 | 30.034 | Radiation flux | 40 | 39.778 |

The vertical position of heater (m) | 0.0 | 3 | .1 | 0.2 | Relative humidity | 50. | 50.001 |

The horizontal position of heater (m) | 0.0 | 2 | 2 | 1.85 | |||

The heater area(m | 1.0 | 3.1 | 1.5 | 1.749 |

### Velocity, temperature and relative humidity distribution around the manikin

### Thermal comfort

Heat losses rate from body

Surface | Case-I | Case- II | ||
---|---|---|---|---|

Con. Flux(w/m | Rad. Flux(w/m | Conv. Flux(w/m | Rad. Flux(w/m | |

Head | 43.14 | 38.61 | 39.65 | 41.53 |

Brisket | 35.82 | 37.44 | 34.45 | 45.37 |

Bowl | 33.73 | 35.90 | 31.92 | 46.03 |

Pelvis | 31.73 | 32.27 | 30.68 | 39.85 |

Waist | 33.32 | 31.76 | 32.57 | 38.32 |

Basin | 33.84 | 34.79 | 31.91 | 40.23 |

Arm | 37.1 | 32.47 | 36.54 | 41.39 |

Forearm | 38.35 | 30.66 | 37.61 | 39.69 |

Shoulder | 35.27 | 38.71 | 34.29 | 54.28 |

Thigh | 34.44 | 31.69 | 33.73 | 48.37 |

Leg | 41.34 | 36.10 | 40.69 | 43.84 |

Neck | 33.36 | 35.23 | 38.62 | 45.78 |

foot | 46.81 | 34.69 | 45.31 | 42.64 |

hand | 41.69 | 29.24 | 40.15 | 38.69 |

Average | 37.1 | 33.7 | 35.68 | 44.35 |

Heat losses rate from body, room and PMV values in two cases

Case 1 | Case 2 | |
---|---|---|

T air | 24.5 | 25.52 |

TMRT | 24.03 | 25.23 |

Relative humidity | 55.36 | 50.46 |

Convection flux | 36.68 | 32.86 |

Radiation flux | 33.61 | 45.23 |

losses | 35.27 | 22.21 |

Total flux of the body | 105.56 | 100.3 |

PMV | −0.89 | 0.0034 |

Total flux of the room | 684.61 | 512.83 |

## Conclusion

In this study, two heating systems, conventional and hybrid, are individually optimized and then compared with each other to have thermal comfort conditions. The Factorial Design Method (2^{K}) or two level designs has been used for optimization. The effect of input parameters and their interaction is investigated on the objective function, such as PMV index, relative humidity and heat fluxes. The effects of the input parameters in normal and Pareto charts are presented. Based on the present study, the individual and the interaction of input parameters effect are significant and different. Heater temperature has the most effect on the object function and requires more energy whereas C has the most effect on the objective function but needs no more energy thus some combination can be used as useful tools in designing heating systems. The thermal comfort can be obtained using less input energy by just increasing the surface area of the heater and its location. A better symmetrical velocity distribution around the manikin is also presented in the hybrid system. The lower velocity makes lower heat losses through the walls and the manikin segments up to 25 %. The heating hybrid systems can provide faster and better human thermal comfort in a residential room.

### Thanksgiving

I would like to thank all those who have helped me in doing the research. Also, I want to thank you for giving us the opportunity to publish our paper in the Journal of Environmental Health Science and Engineering.

## Nomenclature

*C*, Convective heat loss(w/m2)

*C*
_{
res
}, Convection heat loss due to respiration(w/m2)

*D*
_{
i,m
}, Mass diffusion coefficient for species

*D*
_{
T
}, Turbulent diffusivity

*E*
_{
res
}, Evaporative heat loss due to respiration(w/m2)

*E*, Total energy (J)

*E*
_{
sk
}, Evaporative heat loss of skin

\( \overrightarrow{g} \), Gravitational acceleration

*h*, Sensible enthalpy

*I*, Unit tensor

\( {\overrightarrow{J}}_j \), Diffusion flux of species

*k*
_{
eff
}, Effective conductivity

*k*
_{
t
}, Turbulent thermal conductivity

*L*, The heat load of the body

*M*, Metabolic heat production(w/m^{2})

*P*
_{α}, ambient pressure air (kpa)

*PMW*, Predict mean vote

*R*
_{
cl
}, Resistance of clothes

*R*, Radiative heat loss(w/m^{2})

*S*, Heat storage(w\m^{2})

\( \overrightarrow{V} \), Velocity vector

*W*, External work(w/m^{2})

*Y*
_{
j
}, Mass fraction of species

*μ*, Molecular viscosity

*ρ*, Density

\( \overline{\overline{\tau}} \), Stress tensor

## Declarations

## Authors’ Affiliations

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## Copyright

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