**9. The heat load on the cooling system of the WBC zone**

When designing cooling systems of the WBC zone, it is necessary to adequately estimate the power of the heat fluxes that need to be compensated. It was shown above that during the WBC procedure, 440 kJ/m<sup>2</sup> of the heat is released from the patient's body surface, and the mean heat flux from the body to the cryogenic heat carrier varies from 3.5 to 2.3 kW/m<sup>2</sup> (**Table 2**). Taking into account the surface area of the body (1.6 m<sup>2</sup> [7]), the heat input from one patient will be 700 kJ; the mean power of the heat input is 4.6 kW. It is necessary to spend at least 2.7 kg of liquid nitrogen only to remove the heat released from a patient's body surface with a gas with the temperature of *Tg* = 140 K:

$$\mathbf{G}\_{LN} = \frac{\mathbf{Q}\_{HC}}{\left[r\_{LN} + c\_{LN}\left(T\_{\mathbf{g}} - T\_{LN}^{'}\right)\right]'} \tag{25}$$

where *rLN* means the heat of vaporization of nitrogen, *rLN* = 199 kJ/kg;*сLN* means the heat capacity of nitrogen vapor, *cLN* = 1.002 kJ/kg; and *T*″ *LN* means the boiling point of liquid nitrogen at atmospheric pressure,*T*″ *LN* = 78 K.

Estimated nitrogen flowrate for removal of the heat from the body surface is 2.7 times higher than in modern nitrogen-cooled WBC installations [13]. To restore the WBC effectiveness, it is necessary to provide cryotherapy installations with sufficiently powerful cooling systems.

The heat input from the patients *Q HC* is only the useful part of the heat load on the cooling system. In addition, it is necessary to compensate for the heat input from the walls of the thermal fencing of the WBC zone and *QTI* the heat that the warm gas fluxes bring from the adjacent volumes (lock chamber or environment) to the volume of the treatment cab *QGC*. The total heat load is defined as the sum of heat received from different sources:

**8. Algorithm for changing the cooling gas temperature during the**

*The dependence of the cooling phase duration and safe exposure WBC on the gas temperature.*

Installations for GWBC consist of two or three heat-insulated rooms with different air temperatures [7]. Patients pass from the treatment room to the chamber with the minimum temperature (main chamber, MC) and back through the lock chambers (LC). In most modern installations, the temperature in the main chamber is maintained at 160 K and in the lock chamber means at 210 K. At the time of entry (exit) of patients into the LC or MC, warmer air enters from adjacent volumes. Because of this, the air temperature in the MC volume increases by at least 25 K. From the body surface of each patient, 3.5 to 4.5 kW of heat is released into the MC volume. Taking into account these factors, the actual GWBC temperature regime depends not only on the choice of the nominal temperatures in MC and LC but also on the power of the cooling system. Another uncertainty factor is the duration of stay of patients in the main cab. There are different opinions about the advisability of pre-cooling the body surface at an intermediate temperature of 210 K. Some researchers believe that a gradual decrease in temperature increases subjective comfort and safety [7]. In other works it is proposed to reduce the time of stay of patients in LC to a minimum [13]. Given all the reasons presented, it is obvious that it is extremely difficult to simulate the GWBC process. The temperature of the cooling gas varies according to a complex schedule, which consists of at least eight

The algorithm of changing the gas temperature in IWBC is much simpler (**Figure 11**). The patient enters the cab filled with atmospheric air, which is quickly replaced by vapors of liquid nitrogen with a temperature not higher than 140 K. The time to reduce the gas temperature in the IWBC cab to the optimum level depends

Taking into account the results of simulating the WBC process under conditions of a constant gas temperature, it can be argued that the GWBC procedures using the algorithm shown in **Figure 11** do not provide significant therapeutic outcomes. To restore the effectiveness of GWBC, it is necessary to significantly reduce the minimum air temperature in the main treatment cab. Experiments on a mathematical model of the body shell showed that the effectiveness of GWBC reaches the optimal level when the air temperature in the main cab drops to 130 K. However, modern installations for GWBC cannot maintain the temperature at this level, since they use

on the power of the cooling system and is at least 20 sec.

**individual and group WBC procedures**

stages (**Figure 11**).

**148**

**Figure 10.**

*Low-temperature Technologies*

$$Q\_{\Sigma} = Q\_{HC} + Q\_{TI} + Q\_{GC} \,. \tag{26}$$

where *F*<sup>3</sup> means the total area of the internal surface of the cab's thermal fencing,

where α3–<sup>2</sup> and α1–<sup>2</sup> means the heat transfer coefficients from the thermal fenc-

Specific characteristics of devices designed for the implementation of GWBC and IWBC technologies have large differences. In multi-seat installations, the

; the thermal fencing area of the WBC zone is 2.4–3.0 m<sup>2</sup>

compactness of accommodation of patients in multi-seat installations is necessary so

In single-seat cryosaunas, the patient accommodation density reaches 2.0

/m<sup>3</sup>

The heat input with gas fluxes is determined by the intensity of convective mass

84% [7]. High compactness of the patient accommodation is ensured by the fact that the patient does not move during the procedure; therefore, the cab size is

transfer of warm gas to the volume of the WBC zone. The heat input by gas convection across the boundary of the WBC zone is determined from the

*qGS* ¼ *cpgG Tg* � *T*<sup>2</sup>

Large heat flows with gas fluxes are supplied into the WBC zone as patients enter and exit. For example, a multi-seat lock chamber and a cab of a single-seat cryosauna are filled with atmospheric air at the moment patients enter. 93 kJ/m<sup>3</sup> of heat enters the lock cab with atmospheric air. When the temperature recovers to the nominal level, the air density in the lock cab increases by 40%; this is accompanied by supplying additional air from the atmosphere, which contributes another 27 kJ/m<sup>3</sup> of heat. In one procedure, 120 kJ/m3 of heat transferred by gas convection

The basis of the mathematical model of the WBC zone is a one-dimensional

*ρ ∂h <sup>∂</sup><sup>τ</sup>* <sup>¼</sup> *<sup>∂</sup>qx ∂x*

where *qv* means the heat from internal sources:

where *gG* means the specific transfer of the gas mass into the volume of the WBC zone, kg/(m3 sec); *cp* means the heat capacity of the gas, kJ/(kg K); and *Tg* means

, the specific surface area of the patient's body is 3.2 m2

*qTI* ¼ *α*3�<sup>2</sup> *f* <sup>3</sup>ð Þ *T*<sup>3</sup> � *T*<sup>2</sup> *; qHC* ¼ *α*1�<sup>2</sup> *f* <sup>1</sup>ð Þ *T*<sup>1</sup> � *T*<sup>2</sup> *,* (29)

, and the specific volume of

/m<sup>3</sup>

, and the specific free space volume is

*,* (30)

þ *qv,* (31)

*qv* ¼ *q*<sup>Σ</sup> þ *qHC* þ *qTI* þ *qGC:* (32)

/m<sup>3</sup> . Low

, the thermal

*n* means the number of patients in the cab, and *F*<sup>1</sup> means the surface area of a

ing and the patient's body, respectively; *T*<sup>1</sup> and *T*<sup>3</sup> means the temperatures of surfaces of the body and the fencing; and *T*<sup>2</sup> means the temperature of the heat

free space *V0* is at least 98%. The specific surface area of the patient's body is

that they can move from one low-temperature chamber to another.

calculated considering the temperatures of their surfaces:

*Technique and Technology of Whole-Body Cryotherapy (WBC)*

*DOI: http://dx.doi.org/10.5772/intechopen.83680*

patient accommodation density is 0.4–0.7 person/m<sup>3</sup>

The specific heat input from the patient's body and the thermal fencing is

patient's body.

carrier gas.

0.6–1.0 m2

persons/m<sup>3</sup>

expression:

enters the lock chamber.

energy equation:

**151**

/m<sup>3</sup>

fencing area of the WBC zone is 6.4 m<sup>2</sup>

comparable to the size of the patient's body.

the temperature of the gas entering the WBC zone.

The energy efficiency of the installation design for WBC can be estimated by the share of the useful load on the cryostatting system, the coefficient of thermal efficiency:

$$
\eta\_H = \mathbf{Q}\_{HC} / \mathbf{Q}\_{\Sigma}. \tag{27}
$$

To estimate the expenditure of energy and select the optimal technology for WBC procedures, it is necessary to conduct a numerical experiment on a mathematical model of a cryotherapeutic device.
