R/CONV_ecto.R
In mrke/NicheMapR: R implementation of Niche Mapper software for biophysical modelling
Defines functions
CONV_ecto
Documented in
CONV_ecto
#' CONV_ecto
#'
#' R version of Fortran CONV.f (ectotherm model) for calculating convective exchange and heat and mass transfer coefficients.
#'
#' @encoding UTF-8
#' @param GEOMETRY organism shape, 0-5, 0=plate, 1=cyl, 2=ellips, 3=lizard (desert iguana), 4=frog (leopard frog), 5=custom
#' @param ATOT total body surface area (m2)
#' @param AV ventral surface area (m2)
#' @param AL animal characteristic dimension (length) (m)
#' @param AT body surface area contacting another organism of same temperature (m2)
#' @param BP air pressure (Pa)
#' @param ALT elevation (m)
#' @param TA air temperature (°C)
#' @param VEL wind speed (m/s)
#' @param FLTYPE fluid type, air (0) or water (1)
#' @param TSKIN skin temperature (°C)
#' @param CONV_ENHANCE convective enhancement factor (-)
#' @export
CONV_ecto <- function(
GEOMETRY = 3,
ATOT = 0.01325006,
AV = 0.001325006,
AL = 0.03419952,
AT = 0,
BP = 101325,
ALT = 0,
TA = 20,
VEL = 1,
FLTYPE = 0,
TSKIN = 25,
CONV_ENHANCE = 1){
# C NICHEMAPR: SOFTWARE FOR BIOPHYSICAL MECHANISTIC NICHE MODELLING
#
# C COPYRIGHT (C) 2018 MICHAEL R. KEARNEY AND WARREN P. PORTER
#
# C THIS PROGRAM IS FREE SOFTWARE: YOU CAN REDISTRIBUTE IT AND/OR MODIFY
# C IT UNDER THE TERMS OF THE GNU GENERAL PUBLIC LICENSE AS PUBLISHED BY
# C THE FREE SOFTWARE FOUNDATION, EITHER VERSION 3 OF THE LICENSE, OR (AT
# C YOUR OPTION) ANY LATER VERSION.
#
# C THIS PROGRAM IS DISTRIBUTED IN THE HOPE THAT IT WILL BE USEFUL, BUT
# C WITHOUT ANY WARRANTY; WITHOUT EVEN THE IMPLIED WARRANTY OF
# C MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. SEE THE GNU
# C GENERAL PUBLIC LICENSE FOR MORE DETAILS.
#
# C YOU SHOULD HAVE RECEIVED A COPY OF THE GNU GENERAL PUBLIC LICENSE
# C ALONG WITH THIS PROGRAM. IF NOT, SEE HTTP://WWW.GNU.ORG/LICENSES/.
#
# C COMPUTES CONVECTIVE HEAT EXCHANGE
# C ALL UNITS SI (M,KG,S,C,K,J,PA)
# C ALT = ALTITUDE
# C ANU = NUSSELT NUMBER
# C ATOT = TOTAL AREA
# C BETA = COEFFICIENT OF THERMAL EXPANSION AT CONSTANT DENSITY (1/K)
# C (USED IN GRASHOF NUMBER (1/FLUID TEMP (C), I.E. AIR OR WATER)
# C BP = BAROMETRIC PRESSURE
# C CP = SPECIFIC HEAT OF DRY AIR (J/KG-C)
# C D = CHARACTERISTIC DIMENSION FOR CONVECTION
# C DB = DRY BULB TEMPERATURE (C)
# C DELTAT = TEMPERATURE DIFFERENCE
# C DENSTY = DENSITY OF AIR
# C DIFVPR = DIFFUSIVITY OF WATER VAPOR
# C FLTYPE = FLUID TYPE (0.0 = AIR; 1.0 = WATER)
# C G = ACCELERATION DUE TO GRAVITY
# C GGROUP = GROUP OF GRASHOF VARIABLES
# C GR = GRASHOF NUMBER
# C GRRE2 = GRASHOF/REYNOLDS NUMBER SQUARED
# C HC = HEAT TRANSFER COEFFICIENT
# C HCFREE = HEAT TRANSFER COEFFICIENT, FREE CONVECTION
# C HCFORC = HEAT TRANSFER COEFFICIENT, FORCED CONVECTION
# C HD = MASS TRANSFER COEFFICIENT
# C HDFREE = MASS TRANSFER COEFFICIENT, FREE CONVECTION
# C HDFORC = MASS TRANSFER COEFFICIENT, FORCED CONVECTION
# C HTOVPR = WATER VAPOR PRESSURE
# C IGEOM = CHOOSER FOR CONVECTION EQUATIONS ACTUALLY USED
# C GEOMETRY = NUMBER SPECIFYING GEOMETRY TO BE USED:
# C 0 = PLATE, 1 = CYLINDER, 2 = ELLIPSOID, 3 = LIZARD
# C 4 = FROG, 5 = USER SUPPLIED
# C PATMOS = ATMOSPHERIC PRESSURE
# C PR = PRANDTL NUMBER
# C QCONV = HEAT LOSS BY CONVECTION
# C RE = REYNOLD'S NUMBER
# C SC = SCHMIDT NUMBER
# C SH = SHERWOOD NUMBER
# C TA = AIR TEMPERATURE (C)
# C TCOEFF = TEMPERATURE COEFFICIENT OF EXPANSION OF AIR
# C RAYLEI = RAYLEIGH NUMBER = GRASHOF-PRANDTL PRODUCT
# C THCOND = THERMAL CONDUCTIVITY OF AIR
# C VEL = AIR VELOCITY
# C VISDYN = DYNAMIC VISCOSITY OF AIR
# C VISKIN = KINEMATIC VISCOSITY OF AIR
# C TSKIN = CURRENT GUESS OF OBJECT SURFACE TEMPERATURE
# C CONV_ENHANCE = CONVECTIVE ENHANCEMENT FACTOR (SEE MITCHELL 1979 https://doi.org/10.1016/S0006-3495(76)85711-6)
#PI <- 3.14159265
ANUFRE <- 0
ANU <- 0
#C SETTING THE CHARACTERISTIC DIMENSION FOR NUSSELT-REYNOLDS CORRELATIONS
D <- AL
BETA <- 1 /(TA + 273)
CP <- 1.0057E+3
G <- 9.80665
#C CONVECTIVE AREA CALCULATION = TOTAL AREA - VENTRAL AREA IN CONTACT WITH SUBSTRATE
CONVAR <- ATOT - AV - AT
#C USING ALTITUDE TO COMPUTE BP (SEE DRYAIR LISTING)
#C BP=0.0
DB <- TA
#C GET THERMAL PROPERTIES OF DRY AIR AT CURRENT TEMP AND PRESSURE
dryair.out <- DRYAIR(DB, BP, ALT)
#PATMOS <- dryair.out$patmos
DENSTY <- dryair.out$densty
VISDYN <- dryair.out$visdyn
#VISKIN <- dryair.out$viskin
DIFVPR <- dryair.out$difvpr
THCOND <- dryair.out$thcond
#HTOVPR <- dryair.out$htovpr
#TCOEFF <- dryair.out$tcoeff
#GGROUP <- dryair.out$ggroup
#C CHECKING TO SEE IF THE FLUID IS WATER, NOT AIR
if(FLTYPE == 1){
WATERPROP.out <- WATERPROP(TA)
CP <- WATERPROP.out$CP
DENSTY <- WATERPROP.out$DENSTY
THCOND <- WATERPROP.out$THCOND
VISDYN <- WATERPROP.out$VISDYN
BETA <- WATERPROP.out$BETA
}
#C COMPUTING PRANDTL AND SCHMIDT NUMBERS
PR <- CP * VISDYN / THCOND
if(FLTYPE == 0){
#C AIR
SC <- VISDYN / (DENSTY * DIFVPR)
}else{
#C WATER; NO MEANING
SC <- 1
}
#C SKIN/AIR TEMPERATURE DIFFERENCE
DELTAT <- TSKIN - TA
if(DELTAT == 0){
DELTAT <- 0.01
}
#C COMPUTING GRASHOF NUMBER
GR <- ((DENSTY ^ 2) * BETA * G * (D ^ 3) * DELTAT) / (VISDYN ^ 2)
#C CORRECTING IF NEGATIVE DELTAT
GR <- abs(GR)
#C AVOIDING DIVIDE BY ZERO IN FREE VS FORCED RAYLEI
if(VEL <= 0){
VEL <- 0.0001
}
#C REYNOLDS NUMBER
RE <- DENSTY * VEL * D / VISDYN
#C CHOOSING FREE OR FORCED CONVECTION
#C SIGNIFICANT FREE CONVECTION IF GR/RE ^ 2 .GE. 20.0
#C KREITH (1965) P. 358
# GRRE2 <- GR / (RE ^ 2)
#C ********************* FREE CONVECTION ********************
if(GEOMETRY == 0){
RAYLEI <- GR * PR
ANUFRE <- 0.55 * RAYLEI ^ 0.25
}
if((GEOMETRY == 1) | (GEOMETRY == 3) | (GEOMETRY == 5)){
#C FREE CONVECTION OF A CYLINDER
#C FROM P.334 KREITH (1965): MC ADAM'S 1954 RECOMMENDED COORDINATES
RAYLEI <- GR * PR
if(RAYLEI < 1.0E-05){
ANUFRE <- 0.4
}else{
if(RAYLEI < 0.1){
ANUFRE <- 0.976 * RAYLEI ^ 0.0784
}else{
if(RAYLEI <= 100){
ANUFRE <- 1.1173 * RAYLEI ^ 0.1344
}else{
if(RAYLEI < 10000.){
ANUFRE <- 0.7455 * RAYLEI ^ 0.2167
}else{
if(RAYLEI < 1.0E+09){
ANUFRE <- 0.5168 * RAYLEI ^ 0.2501
}else{
if(RAYLEI < 1.0E+12){
ANUFRE <- 0.5168 * RAYLEI ^ 0.2501
}}}}}}
}
if((GEOMETRY == 2) | (GEOMETRY == 4)){
#C SPHERE FREE CONVECTION
#C FROM P.413 BIRD ET AL (1960) TRANSPORT PHENOMENA)
RAYLEI <- (GR ^ (1 /4)) * (PR ^ (1 / 3))
ANUFRE <- 2 + 0.60 * RAYLEI
if(RAYLEI < 200){
#GO TO 20
}else{
message(paste0(RAYLEI, '(GR ^ 0.25) * (PR ^ 0.333) IS TOO LARGE FOR CORREL.'))
}
}
#C CALCULATING THE FREE CONVECTION HEAT TRANSFER COEFFICIENT, HC (NU=HC*D/KAIR)
HCFREE <- (ANUFRE * THCOND) / D
#C CALCULATING THE SHERWOOD NUMBER FROM THE COLBURN ANALOGY
#C (BIRD, STEWART & LIGHTFOOT, 1960. TRANSPORT PHENOMENA. WILEY.
SHFREE <- ANUFRE * (SC / PR) ^ (1 / 3)
#C CALCULATING THE MASS TRANSFER COEFFICIENT FROM THE SHERWOOD NUMBER
HDFREE <- SHFREE * DIFVPR / D
#C CALCULATING THE CONVECTIVE HEAT LOSS AT THE SKIN
QFREE <- HCFREE * CONVAR * (TSKIN - TA)
#C ******************* FORCED CONVECTION *********************
if(GEOMETRY == 0){
ANU <- 0.102 * RE ^ 0.675 * PR ^ (1 / 3)
}
if(GEOMETRY == 1){
#C FORCED CONVECTION OF A CYLINDER
#C ADJUSTING NU - RE CORRELATION FOR RE NUMBER (P. 260 MCADAMS,1954)
if(RE < 4){
ANU <- 0.891 * RE ^ 0.33
}else{
if(RE < 40){
ANU <- 0.821 * RE ^ 0.385
}else{
if(RE < 4000.){
ANU <- 0.615 * RE ^ 0.466
}else{
if(RE < 40000.){
ANU <- 0.174 * RE ^ 0.618
}else{
if(RE < 400000.){
ANU <- 0.0239 * RE ^ 0.805
}}}}}
}
if(GEOMETRY > 1){
#C FORCED CONVECTION IN SPHERE
#C ANU=0.34 * RE ^ 0.24 ! ORIGINAL RELATION
ANU <- 0.35 * RE ^ 0.6 # FROM McAdams, W.H. 1954. Heat Transmission. McGraw-Hill, New York, p.532
}
#C FORCED CONVECTION FOR ANIMAL
# if(GEOMETRY == 4){
# #C ***********************FROG******************************
# #C C.R. TRACY'S LEOPARD FROGS - ECOL. MONOG. 1976 V. 46(3)
# #C CHECKING FOR OUT OF BOUNDS VALUES
# if(RE < 80){
# message(paste0(' RE, ',RE,',TOO SMALL FOR FROG ANCORR'))
# }else{
# if (RE > 40000){
# message(paste0(' RE, ',RE,',TOO LARGE FOR FROG ANCORR'))
# }
# }
# #C COMPUTING NUSSELT AND SHERWOOD NUMBERS
# if(RE <= 2000){
# ANU <- 0.88 * RE ^ 0.5
# }else{
# ANU <- 0.258 * RE ^ 0.667
# }
# }
#C FORCED CONVECTION FOR ANIMAL
HCFORC <- CONV_ENHANCE * ANU * THCOND / D # HEAT TRANFER COEFFICIENT
SHFORC <- CONV_ENHANCE * ANU * (SC / PR) ^ (1 / 3) # SHERWOOD NUMBER
HDFORC <- SHFORC * DIFVPR / D # MASS TRANSFER COEFFICIENT
#C USING BIRD, STEWART, & LIGHTFOOT'S MIXED CONVECTION FORMULA (P. 445, TRANSPORT PHENOMENA, 2002)
NUTOTAL <- (ANUFRE ^ 3 + CONV_ENHANCE * ANU ^ 3) ^ (1 / 3)
HC <- NUTOTAL * (THCOND / D) # MIXED CONVECTION HEAT TRANSFER
QCONV <- HC * CONVAR * (TSKIN - TA) # TOTAL CONVECTIVE TRANSFER
#C CALCULATING THE SHERWOOD NUMBERs FROM THE COLBURN ANALOGY
#C (BIRD, STEWART & LIGHTFOOT, 1960. TRANSPORT PHENOMENA. WILEY.
SH <- NUTOTAL * (SC / PR) ^ (1 / 3) # SHERWOOD NUMBER
HD <- SH * DIFVPR / D # MASS TRANSFER COEFFICIENT
return(list(CONVAR = CONVAR, QCONV = QCONV, HC = HC, HD = HD, SH = SH, QFREE = QFREE, HCFREE = HCFREE, HCFORC = HCFORC, SHFREE = SHFREE, SHFORC = SHFORC, HDFREE = HDFREE, HDFORC = HDFORC))
}
mrke/NicheMapR documentation built on April 3, 2024, 10:05 a.m.
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Defines functions CONV_ecto
Documented in CONV_ecto
#' CONV_ecto
#'
#' R version of Fortran CONV.f (ectotherm model) for calculating convective exchange and heat and mass transfer coefficients.
#'
#' @encoding UTF-8
#' @param GEOMETRY organism shape, 0-5, 0=plate, 1=cyl, 2=ellips, 3=lizard (desert iguana), 4=frog (leopard frog), 5=custom
#' @param ATOT total body surface area (m2)
#' @param AV ventral surface area (m2)
#' @param AL animal characteristic dimension (length) (m)
#' @param AT body surface area contacting another organism of same temperature (m2)
#' @param BP air pressure (Pa)
#' @param ALT elevation (m)
#' @param TA air temperature (°C)
#' @param VEL wind speed (m/s)
#' @param FLTYPE fluid type, air (0) or water (1)
#' @param TSKIN skin temperature (°C)
#' @param CONV_ENHANCE convective enhancement factor (-)
#' @export
CONV_ecto <- function(
GEOMETRY = 3,
ATOT = 0.01325006,
AV = 0.001325006,
AL = 0.03419952,
AT = 0,
BP = 101325,
ALT = 0,
TA = 20,
VEL = 1,
FLTYPE = 0,
TSKIN = 25,
CONV_ENHANCE = 1){
# C NICHEMAPR: SOFTWARE FOR BIOPHYSICAL MECHANISTIC NICHE MODELLING
#
# C COPYRIGHT (C) 2018 MICHAEL R. KEARNEY AND WARREN P. PORTER
#
# C THIS PROGRAM IS FREE SOFTWARE: YOU CAN REDISTRIBUTE IT AND/OR MODIFY
# C IT UNDER THE TERMS OF THE GNU GENERAL PUBLIC LICENSE AS PUBLISHED BY
# C THE FREE SOFTWARE FOUNDATION, EITHER VERSION 3 OF THE LICENSE, OR (AT
# C YOUR OPTION) ANY LATER VERSION.
#
# C THIS PROGRAM IS DISTRIBUTED IN THE HOPE THAT IT WILL BE USEFUL, BUT
# C WITHOUT ANY WARRANTY; WITHOUT EVEN THE IMPLIED WARRANTY OF
# C MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. SEE THE GNU
# C GENERAL PUBLIC LICENSE FOR MORE DETAILS.
#
# C YOU SHOULD HAVE RECEIVED A COPY OF THE GNU GENERAL PUBLIC LICENSE
# C ALONG WITH THIS PROGRAM. IF NOT, SEE HTTP://WWW.GNU.ORG/LICENSES/.
#
# C COMPUTES CONVECTIVE HEAT EXCHANGE
# C ALL UNITS SI (M,KG,S,C,K,J,PA)
# C ALT = ALTITUDE
# C ANU = NUSSELT NUMBER
# C ATOT = TOTAL AREA
# C BETA = COEFFICIENT OF THERMAL EXPANSION AT CONSTANT DENSITY (1/K)
# C (USED IN GRASHOF NUMBER (1/FLUID TEMP (C), I.E. AIR OR WATER)
# C BP = BAROMETRIC PRESSURE
# C CP = SPECIFIC HEAT OF DRY AIR (J/KG-C)
# C D = CHARACTERISTIC DIMENSION FOR CONVECTION
# C DB = DRY BULB TEMPERATURE (C)
# C DELTAT = TEMPERATURE DIFFERENCE
# C DENSTY = DENSITY OF AIR
# C DIFVPR = DIFFUSIVITY OF WATER VAPOR
# C FLTYPE = FLUID TYPE (0.0 = AIR; 1.0 = WATER)
# C G = ACCELERATION DUE TO GRAVITY
# C GGROUP = GROUP OF GRASHOF VARIABLES
# C GR = GRASHOF NUMBER
# C GRRE2 = GRASHOF/REYNOLDS NUMBER SQUARED
# C HC = HEAT TRANSFER COEFFICIENT
# C HCFREE = HEAT TRANSFER COEFFICIENT, FREE CONVECTION
# C HCFORC = HEAT TRANSFER COEFFICIENT, FORCED CONVECTION
# C HD = MASS TRANSFER COEFFICIENT
# C HDFREE = MASS TRANSFER COEFFICIENT, FREE CONVECTION
# C HDFORC = MASS TRANSFER COEFFICIENT, FORCED CONVECTION
# C HTOVPR = WATER VAPOR PRESSURE
# C IGEOM = CHOOSER FOR CONVECTION EQUATIONS ACTUALLY USED
# C GEOMETRY = NUMBER SPECIFYING GEOMETRY TO BE USED:
# C 0 = PLATE, 1 = CYLINDER, 2 = ELLIPSOID, 3 = LIZARD
# C 4 = FROG, 5 = USER SUPPLIED
# C PATMOS = ATMOSPHERIC PRESSURE
# C PR = PRANDTL NUMBER
# C QCONV = HEAT LOSS BY CONVECTION
# C RE = REYNOLD'S NUMBER
# C SC = SCHMIDT NUMBER
# C SH = SHERWOOD NUMBER
# C TA = AIR TEMPERATURE (C)
# C TCOEFF = TEMPERATURE COEFFICIENT OF EXPANSION OF AIR
# C RAYLEI = RAYLEIGH NUMBER = GRASHOF-PRANDTL PRODUCT
# C THCOND = THERMAL CONDUCTIVITY OF AIR
# C VEL = AIR VELOCITY
# C VISDYN = DYNAMIC VISCOSITY OF AIR
# C VISKIN = KINEMATIC VISCOSITY OF AIR
# C TSKIN = CURRENT GUESS OF OBJECT SURFACE TEMPERATURE
# C CONV_ENHANCE = CONVECTIVE ENHANCEMENT FACTOR (SEE MITCHELL 1979 https://doi.org/10.1016/S0006-3495(76)85711-6)
#PI <- 3.14159265
ANUFRE <- 0
ANU <- 0
#C SETTING THE CHARACTERISTIC DIMENSION FOR NUSSELT-REYNOLDS CORRELATIONS
D <- AL
BETA <- 1 /(TA + 273)
CP <- 1.0057E+3
G <- 9.80665
#C CONVECTIVE AREA CALCULATION = TOTAL AREA - VENTRAL AREA IN CONTACT WITH SUBSTRATE
CONVAR <- ATOT - AV - AT
#C USING ALTITUDE TO COMPUTE BP (SEE DRYAIR LISTING)
#C BP=0.0
DB <- TA
#C GET THERMAL PROPERTIES OF DRY AIR AT CURRENT TEMP AND PRESSURE
dryair.out <- DRYAIR(DB, BP, ALT)
#PATMOS <- dryair.out$patmos
DENSTY <- dryair.out$densty
VISDYN <- dryair.out$visdyn
#VISKIN <- dryair.out$viskin
DIFVPR <- dryair.out$difvpr
THCOND <- dryair.out$thcond
#HTOVPR <- dryair.out$htovpr
#TCOEFF <- dryair.out$tcoeff
#GGROUP <- dryair.out$ggroup
#C CHECKING TO SEE IF THE FLUID IS WATER, NOT AIR
if(FLTYPE == 1){
WATERPROP.out <- WATERPROP(TA)
CP <- WATERPROP.out$CP
DENSTY <- WATERPROP.out$DENSTY
THCOND <- WATERPROP.out$THCOND
VISDYN <- WATERPROP.out$VISDYN
BETA <- WATERPROP.out$BETA
}
#C COMPUTING PRANDTL AND SCHMIDT NUMBERS
PR <- CP * VISDYN / THCOND
if(FLTYPE == 0){
#C AIR
SC <- VISDYN / (DENSTY * DIFVPR)
}else{
#C WATER; NO MEANING
SC <- 1
}
#C SKIN/AIR TEMPERATURE DIFFERENCE
DELTAT <- TSKIN - TA
if(DELTAT == 0){
DELTAT <- 0.01
}
#C COMPUTING GRASHOF NUMBER
GR <- ((DENSTY ^ 2) * BETA * G * (D ^ 3) * DELTAT) / (VISDYN ^ 2)
#C CORRECTING IF NEGATIVE DELTAT
GR <- abs(GR)
#C AVOIDING DIVIDE BY ZERO IN FREE VS FORCED RAYLEI
if(VEL <= 0){
VEL <- 0.0001
}
#C REYNOLDS NUMBER
RE <- DENSTY * VEL * D / VISDYN
#C CHOOSING FREE OR FORCED CONVECTION
#C SIGNIFICANT FREE CONVECTION IF GR/RE ^ 2 .GE. 20.0
#C KREITH (1965) P. 358
# GRRE2 <- GR / (RE ^ 2)
#C ********************* FREE CONVECTION ********************
if(GEOMETRY == 0){
RAYLEI <- GR * PR
ANUFRE <- 0.55 * RAYLEI ^ 0.25
}
if((GEOMETRY == 1) | (GEOMETRY == 3) | (GEOMETRY == 5)){
#C FREE CONVECTION OF A CYLINDER
#C FROM P.334 KREITH (1965): MC ADAM'S 1954 RECOMMENDED COORDINATES
RAYLEI <- GR * PR
if(RAYLEI < 1.0E-05){
ANUFRE <- 0.4
}else{
if(RAYLEI < 0.1){
ANUFRE <- 0.976 * RAYLEI ^ 0.0784
}else{
if(RAYLEI <= 100){
ANUFRE <- 1.1173 * RAYLEI ^ 0.1344
}else{
if(RAYLEI < 10000.){
ANUFRE <- 0.7455 * RAYLEI ^ 0.2167
}else{
if(RAYLEI < 1.0E+09){
ANUFRE <- 0.5168 * RAYLEI ^ 0.2501
}else{
if(RAYLEI < 1.0E+12){
ANUFRE <- 0.5168 * RAYLEI ^ 0.2501
}}}}}}
}
if((GEOMETRY == 2) | (GEOMETRY == 4)){
#C SPHERE FREE CONVECTION
#C FROM P.413 BIRD ET AL (1960) TRANSPORT PHENOMENA)
RAYLEI <- (GR ^ (1 /4)) * (PR ^ (1 / 3))
ANUFRE <- 2 + 0.60 * RAYLEI
if(RAYLEI < 200){
#GO TO 20
}else{
message(paste0(RAYLEI, '(GR ^ 0.25) * (PR ^ 0.333) IS TOO LARGE FOR CORREL.'))
}
}
#C CALCULATING THE FREE CONVECTION HEAT TRANSFER COEFFICIENT, HC (NU=HC*D/KAIR)
HCFREE <- (ANUFRE * THCOND) / D
#C CALCULATING THE SHERWOOD NUMBER FROM THE COLBURN ANALOGY
#C (BIRD, STEWART & LIGHTFOOT, 1960. TRANSPORT PHENOMENA. WILEY.
SHFREE <- ANUFRE * (SC / PR) ^ (1 / 3)
#C CALCULATING THE MASS TRANSFER COEFFICIENT FROM THE SHERWOOD NUMBER
HDFREE <- SHFREE * DIFVPR / D
#C CALCULATING THE CONVECTIVE HEAT LOSS AT THE SKIN
QFREE <- HCFREE * CONVAR * (TSKIN - TA)
#C ******************* FORCED CONVECTION *********************
if(GEOMETRY == 0){
ANU <- 0.102 * RE ^ 0.675 * PR ^ (1 / 3)
}
if(GEOMETRY == 1){
#C FORCED CONVECTION OF A CYLINDER
#C ADJUSTING NU - RE CORRELATION FOR RE NUMBER (P. 260 MCADAMS,1954)
if(RE < 4){
ANU <- 0.891 * RE ^ 0.33
}else{
if(RE < 40){
ANU <- 0.821 * RE ^ 0.385
}else{
if(RE < 4000.){
ANU <- 0.615 * RE ^ 0.466
}else{
if(RE < 40000.){
ANU <- 0.174 * RE ^ 0.618
}else{
if(RE < 400000.){
ANU <- 0.0239 * RE ^ 0.805
}}}}}
}
if(GEOMETRY > 1){
#C FORCED CONVECTION IN SPHERE
#C ANU=0.34 * RE ^ 0.24 ! ORIGINAL RELATION
ANU <- 0.35 * RE ^ 0.6 # FROM McAdams, W.H. 1954. Heat Transmission. McGraw-Hill, New York, p.532
}
#C FORCED CONVECTION FOR ANIMAL
# if(GEOMETRY == 4){
# #C ***********************FROG******************************
# #C C.R. TRACY'S LEOPARD FROGS - ECOL. MONOG. 1976 V. 46(3)
# #C CHECKING FOR OUT OF BOUNDS VALUES
# if(RE < 80){
# message(paste0(' RE, ',RE,',TOO SMALL FOR FROG ANCORR'))
# }else{
# if (RE > 40000){
# message(paste0(' RE, ',RE,',TOO LARGE FOR FROG ANCORR'))
# }
# }
# #C COMPUTING NUSSELT AND SHERWOOD NUMBERS
# if(RE <= 2000){
# ANU <- 0.88 * RE ^ 0.5
# }else{
# ANU <- 0.258 * RE ^ 0.667
# }
# }
#C FORCED CONVECTION FOR ANIMAL
HCFORC <- CONV_ENHANCE * ANU * THCOND / D # HEAT TRANFER COEFFICIENT
SHFORC <- CONV_ENHANCE * ANU * (SC / PR) ^ (1 / 3) # SHERWOOD NUMBER
HDFORC <- SHFORC * DIFVPR / D # MASS TRANSFER COEFFICIENT
#C USING BIRD, STEWART, & LIGHTFOOT'S MIXED CONVECTION FORMULA (P. 445, TRANSPORT PHENOMENA, 2002)
NUTOTAL <- (ANUFRE ^ 3 + CONV_ENHANCE * ANU ^ 3) ^ (1 / 3)
HC <- NUTOTAL * (THCOND / D) # MIXED CONVECTION HEAT TRANSFER
QCONV <- HC * CONVAR * (TSKIN - TA) # TOTAL CONVECTIVE TRANSFER
#C CALCULATING THE SHERWOOD NUMBERs FROM THE COLBURN ANALOGY
#C (BIRD, STEWART & LIGHTFOOT, 1960. TRANSPORT PHENOMENA. WILEY.
SH <- NUTOTAL * (SC / PR) ^ (1 / 3) # SHERWOOD NUMBER
HD <- SH * DIFVPR / D # MASS TRANSFER COEFFICIENT
return(list(CONVAR = CONVAR, QCONV = QCONV, HC = HC, HD = HD, SH = SH, QFREE = QFREE, HCFREE = HCFREE, HCFORC = HCFORC, SHFREE = SHFREE, SHFORC = SHFORC, HDFREE = HDFREE, HDFORC = HDFORC))
}
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