heatex-function: Demonstration heatex function In heatex: Heat exchange calculations during physical activity.

Description

The heatex function calculates heat storage in the body and the components of heat exchange (conductive, convective, radiative and evaporative) between the body and the environment during physical activity based on the principles of partitional calorimetry. The function is suitable for walking, running or cycling, and for air velocities up to 4 m.s-1.

Usage

 `1` ```heatex(df) ```

Arguments

 `df` Data frame with example data.

Details

Following is a description of the formulae and their sources which are used for the calculations performed by the heatex function.

1. Environmental Variables

1.1 Calculation of mean radiant temperature, Tr (from Goldman, 1978) Tr (oC) = ((1+(0.222 x (va0.5))) x (Tg - Tdb)) + Tdb where va = air velocity (m.s-1), Tg = black globe temperature (oC) and Tdb = dry bulb temperature (oC).

1.2 Calculation of convective heat transfer coefficient, hc (from Kerslake, 1972) hc (W.m-2.K-1) = 8.3 x (va0.6) where va = air velocity (m.s-1).

1.3 Calculation of radiative heat transfer coefficient, hr (from Parsons, 1993) hr (W.m-2.K-1) = 4.E.sigma.ArAd.((273.2 + ((Tcl + Tr)/2))3) where E = emissivity of the skin surface (0.98: Gonzalez, 1995, p.299), sigma = Stefan-Boltzmann constant (5.67 x 10-8 W.m-2.K-4), ArAd = ratio of the area of the body exposed to radiation versus the total body surface area (0.70 for seated postures, 0.73 for standing postures), Tcl = mean surface temperature of the body (oC), and Tr = mean radiant temperature (oC).

1.4 Calculation of combined heat transfer coefficient, h (from Parsons, 1993) h (W.m-2.K-1) = hc + hr where hc is the convective heat transfer coefficient (W.m-2.K-1) and hr is the convective heat transfer coefficient (W.m-2.K-1).

1.5 Calculation of evaporative heat transfer coefficient, he (from Kerslake, 1972) he (W.m-2.kPa-1) = 16.5 x hc where hc is the convective heat transfer coefficient (W.m-2.K-1).

2. Clothing Variables

2.1 Calculation of the clothing area factor, fcl (adapted from Parsons, 1993) fcl = 1 + (0.31 x (Icl/0.155)) where Icl = intrinsic clothing insulation (m2.oC.W-1).

2.2 Calculation of effective clothing insulation, Icle (from McIntyre, 1980) Icle (clo units) = Icl - ((fcl-1)/(0.155 x fcl x h)) where Icl = intrinsic clothing insulation (m2.oC.W-1), fcl = clothing area factor (ND), h = combined heat transfer coefficient (W.m-2.K-1).

2.3 Calculation of the permeation efficiency factor of clothing, fpcl (adapted from Parsons, 1993) fpcl = 1/(1+(0.344 x hc x Icle)) where hc is the convective heat transfer coefficient (W.m-2.K-1) and Icle is the effective clothing insulation (clo units).

2.4 Calculation of the intrinsic thermal resistance of clothing, Rc (from Holmer, 1985) Rc (m2.K.W-1) = (Tsk - Tdb)/hc where Tsk = mean skin temperature (K), Tdb = dry bulb temperature (K) and hc is the convective heat transfer coefficient (W.m-2.K-1).

2.5 Calculation of the intrinsic evaporative resistance of clothing, Re (from Holmer, 1985) Re (m2.kPa.W-1) = (Ps- Pa)/he where Ps = saturated water vapor pressure at the skin surface (kPa), Pa is the partial water vapor pressure (kPa) and he is the evaporative heat transfer coefficient (W.m-2.KPa-1).

3. Physiological Variables

3.1 Calculation of body surface area, AD AD (m2) = 0.00718 x wt0.425 x H0.725 where wt = body mass (kg) and H = height (cm).

3.2 Calculation of mean body temperature, Tb (from Kerslake, 1972) Tb (oC) = (0.33 x Tsk + 0.67 x Tc) where Tsk = skin temperature (oC) and Tc = body core temperature (oC).

3.3 Calculation of saturated water vapor pressure at the skin surface, Ps (from Fanger, 1970) Ps (mmHg) = 1.92 x Tsk -25.3 (for 27oC < Tsk < 37 oC). where Tsk = skin temperature (oC).

4. Partitional Calorimetry Equations

4.1 Calculation of the energy equivalent of oxygen, EE (modified from Parsons, 1993) EE (J.L O2-1) = (0.23 x RER + 0.77) x 21 166 where RER = respiratory exchange ratio (ND), 21 166 is the energy equivalent of oxygen (J.LO2-1).

4.2 Calculation of metabolic free energy production, M (modified from Parsons,1993) M (W.m-2) = (((EE x VO2 x t)/(t x 60))/AD) where EE = energy equivalent (J.L O2-1), VO2 = oxygen consumption (L.min-1), t = exercise time (min) and AD = body surface area (m2).

4.3 Calculation of mechanical efficiency, n (from Parsons, 1993) n = W/M where W = work rate (W.m-2) and M = metabolic free energy production (W.m-2).

4.4 Calculation of internal heat production, H (from McIntyre, 1980) H (W.m-2) = (M x (1- n)) x 1/AD where M = metabolic free production (W.m-2), n= mechanical efficiency and AD is the body surface area (m2).

4.5 Calculation of body heat storage, S S (W.m-2) = ((3474 x wt x (Tb final - Tb initial))/t)/AD where 3474= average specific heat of body tissue (J.kg-1.oC-1), wt= body mass (kg), Tb = mean body temperature (oC), t = exercise time (s) and AD = body surface area (m2).

4.6 Calculation of heat transfer via conduction, K K (W.m-2) = AD x ((Tsk - Tcl)/Rc) where AD = body surface area (m2), Tsk = mean skin temperature (K), Tcl = mean fabric temperature (K), and Rc = intrinsic thermal resistance of clothing (m2.K.W-1).

4.7 Calculation of heat transfer via radiation, R (adapted from McIntyre, 1980) R (W.m-2) = E.sigma.fcl.feff.(Ts4 - Tr4) where E = emittance from the outer surface of a clothed body (0.97), sigma = Stefan-Boltzmann constant (5.67 x 10-8 W.m-2.K-4), fcl = clothing area factor (ND), feff = effective radiation area of a clothed body (0.71), and Ts = surface temperature of the body (oC) and Tr = mean radiant temperature (oC).

4.8 Calculation of heat transfer via convection, C (from Fanger, 1970) C (W.m-2) = (AD x fcl x hc x (Ts - Tdb))/ AD where AD = body surface area (m2), fcl = clothing area factor (ND), hc = convective heat transfer coefficient (W.m-2.K-1), Ts = surface temperature of the body (oC) and Tdb = dry bulb temperature (oC).

4.9 Calculation of required evaporative heat loss, Ereq (from Gonzalez, 1995) Ereq (W.m-2) = H - K - R - C -S where H = internal heat production (W.m-2), K = heat exchange via conduction (W.m-2), R= heat exchange via radiation (W.m-2), C = heat exchange via convection (W.m-2), and S = body heat storage (W.m-2).

4.10 Calculation of the maximal evaporative capacity of the environment, Emax (from McIntyre, 1980) Emax (W.m-2) = fpcl x he x (Ps - Pa) where fpcl = permeation efficiency factor of clothing, he = evaporative heat transfer coefficient (W.m-2.kPa-1), Ps = partial water vapor pressure at the skin surface (kPa), and Pa = partial water vapor pressure of ambient air (kPa).

4.11 Calculation of skin wettedness, w w = Ereq/ Emax where Ereq = required evaporative heat loss (W.m-2) and Emax= maximal evaporative capacity of the environment (W.m-2).

4.12 Calculation of evaporative heat transfer via skin diffusion, Ed (modified from Fanger, 1970) Ed (W.m-2) = (l.m.(Ps - Pa)) where l = latent heat of evaporation of sweat (2430 J.g-1), m = permeance coefficient of the skin (1.694 x 10-4 g.s-1.m-2.mmHg-1), Ps = partial water vapor pressure at the skin surface (mmHg) and Pa= partial water vapor pressure in ambient air (mmHg)

4.13 Calculation of heat transfer by sweat evaporation from the skin surface, Esw Esw (W.m-2) = ((((wtinitial - wtfinal)-(fluid/food intake+urine/faeces loss)-((0.019 x VO2 x (44-Pa)) x t)))x 2430)/((t x 60) x AD) where wt = body mass (g), fluid/food intake and urine/faeces loss are in grams, the expression 0.019 x VO2 x (44-Pa) accounts for respiratory weight loss in g.min-1 (Mitchell et al., 1972), VO2= oxygen uptake in L.min-1, t = observation time (min), and AD = body surface area (m2).

4.14 Calculation of heat transfer via evaporation from the skin surface, Esk Esk (W.m-2) = Ed + Esw where Ed = heat transfer by skin diffusion (W.m-2) and Esw = heat transfer from sweat evaporation from the skin surface (W.m-2).

4.15 Calculation of heat transfer via the respiratory tract, Eres+Cres (from McIntyre, 1980) Eres+Cres (W.m-2) = (0.0014 x M x (Tex-Tdb))+(0.0017 x M x (58.7-Pa)) where M = metabolic heat production (W.m-2), Tex= expired air temperature (assumed to be 34oC if Tex is not measured directly), Tdb = dry bulb temperature (oC), and Pa= partial water vapor pressure of ambient air (mmHg).

Value

The the heat exchange calculations derived by the heatex function are output to a dataframe named 'results'.The list of items returned in the 'results' dataframe is as follows.

 `tr` Mean radiant temperature. `hc` Convective heat transfer coefficient. `h` Combined heat transfer coefficient. `he` Evaporative heat transfer coefficient. `pa_kpa` Ambient water vapour pressure in kPa. `fcl` Clothing area factor. `icle` Effective clothing insulation. `fpcl` Permeation efficiency factor of clothing. `rc` Intrinsic thermal resistance of clothing. `re` Intrinsic evaporative resistance of clothing. `ad` Body surface area. `tbi` Initial mean body temperature. `tbf` Final mean body temperature. `ps` Saturated water vapor pressure at the skin surface in mmHg. `ps_kpa` Saturated water vapor pressure at the skin surface in kPa. `m` Metabolic free energy production. `n` Mechanical efficiency. `hi` Internal heat production. `s` Body heat storage. `k` Heat transfer via conduction. `r` Heat transfer via radiation. `conv` Heat transfer via convection. `ereq` Required evaporative heat loss. `emax` Maximal evaporative capacity of the environment. `w` Skin wettedness. `ed` Evaporative heat transfer via skin diffusion. `esw` Heat transfer by sweat evaporation from the skin surface. `esk` Heat transfer via evaporation from the skin surface.

Author(s)

Kerry Atkins, email: atkins.kerry04@gmail.com

References

Kerry Atkins and Martin Thompson (2000) A Spreadsheet for Partitional Calorimetry. Sportscience 4(3), sportsci.org/jour/0003/ka.html.

Fanger PO (1970) Thermal Comfort. New York: McGraw-HillGoldman RF (1978) Prediction of human heat tolerance. In: Folinsbee LJ, Wagner JA, Borgia JF, Drinkwater BL, Gliner JA, Bedi JF (editors). Environmental Stress: Individual Human Adaptations. New York: Academic Press.

Gonzalez RR (1995) Biophysics of heat exchange and clothing: applications to sports physiology. Medicine Exercise Nutrition and Health 4, 290-305.

Holmer I (1985) Heat exchange and thermal insulation compared in woolen and nylon garments during wear trials. Textile Research Journal 55, 511-518.

Kerslake DM (1972) The Stress of Hot Environments. Cambridge: University Press.

McIntyre DA (1980) Indoor Climate. London: Applied Science.

Mitchell JW, Nadel ER, Stolwijk JAJ (1972) Respiratory weight losses during exercise. Journal of Applied Physiology 32, 474-476. Parsons KC (1993) Human Thermal Environments. London: Taylor and Francis.

heatex documentation built on May 2, 2019, 2:04 a.m.