FDS Source: Issue #14327. Update Holman refs

Author: mcgratta

Manuals/Bibliography/FDS_general.bib

@@ -2805,6 +2805,15 @@ @BOOK{Holman:1
   year         = {1990},
 }
 
+@BOOK{Holman:2,
+  author       = {Holman, J.P.},
+  title        = {Heat Transfer},
+  edition      = {10th},
+  publisher    = {McGraw-Hill},
+  address      = {New York},
+  year         = {2010}
+}
+
 @TECHREPORT{Hostikka:2008,
   author       = {Hostikka, S.},
   title        = {{Development of fire simulation models for radiative heat transfer and probabilistic risk assessment}},

Manuals/FDS_Technical_Reference_Guide/Solid_Chapter.tex

@@ -113,14 +113,15 @@ \subsubsection{Empirical Natural/Forced Convection Model}
 The following expressions are simplifications of those given in Ref.~\cite{Incropera:1} under the assumption that $\PR=0.7$.
 \be
    \NU_{\rm free} = \left\{ \begin{array}{ll}
-                                                \left( 0.825 +  0.324 \, \hbox{Ra}^{1/6}  \right)^2   &  \hbox{Vertical plate or cylinder} \\
+                                                \left( 0.825 +  0.324 \, \hbox{Ra}^{1/6}  \right)^2   &  \hbox{Vertical plate or cylinder\footnotemark} \\
                                                 0.54 \, \hbox{Ra}^{1/4}                               &  \hbox{Horizontal hot plate facing up or cold plate facing down, Ra}\le 10^7 \\
                                                 0.15 \, \hbox{Ra}^{1/3}                               &  \hbox{Horizontal hot plate facing up or cold plate facing down, Ra} >  10^7 \\
                                                 0.52 \, \hbox{Ra}^{1/5}                               &  \hbox{Horizontal hot plate facing down or cold plate facing up}  \\
                                                 \left( 0.60 +  0.321 \, \hbox{Ra}^{1/6}  \right)^2    &  \hbox{Horizontal cylinder} \\
                                                 2 +  0.454 \, \hbox{Ra}^{1/4}                         &  \hbox{Sphere}
        \end{array} \right.
 \ee
+\footnotetext{The heat transfer coefficient for a vertical plate or cylinder is simplified to $h=1.31 \, (\Delta T)^{1/3}$~\cite{Holman:2} in cases where the back side of a solid obstruction is outside the computational domain and the gas temperature is assumed to be ambient. }
 For forced convection, the Nusselt number takes the form:
 \be
    \NU_{\rm forced} = C_0 + \left( C_1 \, \RE^n - C_2 \right) \, \PR^m  \quad ; \quad \RE = \frac{\rho |\bu| L}{\mu}  \quad ; \quad m=1/3

Manuals/FDS_Verification_Guide/FDS_Verification_Guide.tex

@@ -1884,7 +1884,7 @@ \section{Blasius boundary layer (\texorpdfstring{\ct{blasius}}{blasius})}
 \section{Pohlhausen thermal boundary layer (\texorpdfstring{\ct{Pohlhausen}}{Pohlhausen})}
 \label{sec:Pohlhausen}
 
-This write up follows Appendix B of \cite{Holman:1}.  The nondimensional temperature as a function of the similarity variable $\eta$ is taken to be
+This write up follows Appendix B of \cite{Holman:2}.  The nondimensional temperature as a function of the similarity variable $\eta$ is taken to be
 \begin{equation}
 \label{eq:pohl_theta}
 \theta(\eta) \equiv \frac{T(\eta) - T_w}{T_\infty - T_w}
@@ -1900,7 +1900,7 @@ \section{Pohlhausen thermal boundary layer (\texorpdfstring{\ct{Pohlhausen}}{Poh
 \label{eq:pohl_soln}
 \theta(\eta) = \frac{\displaystyle \int_0^\eta \exp\left( - \frac{\mathrm{Pr}}{2} \int_0^\eta f \d \eta \right) \d \eta}{\displaystyle \int_0^\infty \exp\left( - \frac{\mathrm{Pr}}{2} \int_0^\eta f \d \eta \right)\d \eta}
 \end{equation}
-This solution is plotted in Fig.~\ref{fig:pohlhausen} (left) for different Prandtl numbers (Pr) and may be compared to the plot in Fig.~B-2 of \cite{Holman:1} for verification.
+This solution is plotted in Fig.~\ref{fig:pohlhausen} (left) for different Prandtl numbers (Pr) and may be compared to the plot in Fig.~B-2 of \cite{Holman:2} for verification.
 
 In this test series, the 2-D FDS domain is set 10 m in length and 1 m in height.  The simulation is run as a DNS with the viscosity, conductivity, and specific heat set to provide Prandtl numbers of [0.5, 1, 2].  The grid resolution (after a convergence study) is set to $\delta x=\delta z=1.25$ cm. The inlet velocity is set to 1 m/s with an ambient air temperature of $T_\infty=20$ \si{\degreeCelsius}. The wall boundary is set to a fixed temperature of $T_w=21$ \si{\degreeCelsius}. The outflow is set to \ct{OPEN}.  The top boundary is homogeneous Neumann for velocity and Dirichlet for temperature at $T_\infty=20$ \si{\degreeCelsius}.  The simulation is run to steady state.  The resulting temperature profiles $T(z)$ at $x=5$ m are shown in Fig.~\ref{fig:pohlhausen} (right).
 
@@ -2075,9 +2075,9 @@ \subsection{Horizontal Enclosure (\texorpdfstring{\ct{natconh}}{natconh})}
 
 Consider thermal convection in an enclosure with a hot floor, cold ceiling, and adiabatic walls. Table~\ref{tab:freeconh} lists values for $C$ and $n$, and the length scale, $L$, is taken as the height of the enclosure, $\delta$.
 \begin{table}[h]
-% see table 7.3 in J.P. Holman 7th Ed.
+% see table 7.3 in J.P. Holman 10th Ed.
 \centering
-\caption[Natural convection correlation parameters for a horizontal enclosure]{Natural convection correlation parameters for a horizontal enclosure, $\mathrm{Nu}=C \, \mathrm{Ra}^n$ \cite{Holman:1}.}
+\caption[Natural convection correlation parameters for a horizontal enclosure]{Natural convection correlation parameters for a horizontal enclosure, $\mathrm{Nu}=C \, \mathrm{Ra}^n$ \cite{Holman:2}.}
 \label{tab:freeconh}
 \begin{tabular}{cll}
 Ra                       & $C$    & $n$ \\
@@ -2109,15 +2109,15 @@ \subsection{Horizontal Enclosure (\texorpdfstring{\ct{natconh}}{natconh})}
 \subsection{Vertical Enclosure (\texorpdfstring{\ct{natconv}}{natconv})}
 \label{sec:natconv}
 
-Consider now thermal convection in an enclosure with walls of fixed temperature and insulated floor and ceiling.  The Nusselt number correlation requires an additional factor to account for the ratio of the height, $H$, to the distance between the walls $\delta$ \cite{Holman:1}:
+Consider now thermal convection in an enclosure with walls of fixed temperature and insulated floor and ceiling.  The Nusselt number correlation requires an additional factor to account for the ratio of the height, $H$, to the distance between the walls $\delta$ \cite{Holman:2}:
 \begin{equation}
 \mathrm{Nu} = C \,\mathrm{Ra}^n \,\left(\frac{H}{\delta}\right)^m
 \end{equation}
 The values of $C$, $n$, and $m$ are given below in Tab.~\ref{tab:freeconv}.
 \begin{table}[h]
-% see table 7.3 in J.P. Holman 7th Ed.
+% see table 7.3 in J.P. Holman 10th Ed.
 \centering
-\caption[Free convection correlation parameters for a vertical enclosure]{Free convection correlation parameters for a vertical enclosure, valid for the ranges Pr=[0.5-2] and $L/\delta$=[11-42] \cite{Holman:1}.}
+\caption[Free convection correlation parameters for a vertical enclosure]{Free convection correlation parameters for a vertical enclosure, valid for the ranges Pr=[0.5-2] and $L/\delta$=[11-42] \cite{Holman:2}.}
 \label{tab:freeconv}
 \begin{tabular}{clll}
 Ra                                   & $C$    & $n$ & $m$  \\
@@ -2148,7 +2148,7 @@ \subsection{Vertical Enclosure (\texorpdfstring{\ct{natconv}}{natconv})}
 \subsection{Sphere (\texorpdfstring{\ct{free_conv_sphere}}{free\_conv\_sphere})}
 \label{sec:free_conv_sphere}
 
-Consider a heated sphere in the range $1 < {\rm Ra} < 10^9$.  Yuge~\cite{Yuge:1960} and Amato and Tien~\cite{Amato:1972} propose the following Nusselt number correlations for natural convection from a sphere \cite{Holman:1}.
+Consider a heated sphere in the range $1 < {\rm Ra} < 10^9$.  Yuge~\cite{Yuge:1960} and Amato and Tien~\cite{Amato:1972} propose the following Nusselt number correlations for natural convection from a sphere \cite{Holman:2}.
 \be
 \mathrm{Nu} = \left\{ \begin{array}{ll}  2 + 0.43 \, \mathrm{Ra}^{1/4} & 1 < \mathrm{Ra} < 10^5 \\
                                          2 + 0.50 \, \mathrm{Ra}^{1/4} & 3 \times 10^5 < \mathrm{Ra} < 8 \times 10^8 \end{array} \right.

Source/func.f90

@@ -2045,7 +2045,7 @@ REAL(EB) FUNCTION DRAG(RE,DRAG_LAW,KN)
 
 SELECT CASE(DRAG_LAW)
 
-   ! see J.P. Holman 7th Ed. Fig. 6-10
+   ! see J.P. Holman 10th Ed. Fig. 6-10
    CASE(SPHERE_DRAG)
       IF (RE<1._EB) THEN
          IF (PRESENT(KN)) THEN
@@ -2060,7 +2060,7 @@ REAL(EB) FUNCTION DRAG(RE,DRAG_LAW,KN)
          DRAG = 0.44_EB
       ENDIF
 
-   ! see J.P. Holman 7th Ed. Fig. 6-9
+   ! see J.P. Holman 10th Ed. Fig. 6-9
    CASE(CYLINDER_DRAG)
       IF (RE<=1._EB) THEN
          DRAG = 10._EB/(RE**0.8_EB)

Source/turb.f90

@@ -1379,7 +1379,7 @@ SUBROUTINE RAYLEIGH_HEAT_FLUX_MODEL(H,Z_STAR,REGIME,DZ,TMP_W,TMP_G,K_G,RHO_G,CP_
 ! Rayleigh number scaling in nondimensional thermal wall units
 !
 ! The formulation is based on the discussion of natural convection systems in
-! J.P. Holman, Heat Transfer, 7th Ed., McGraw-Hill, 1990, p. 346.
+! J.P. Holman, Heat Transfer, 10th Ed., McGraw-Hill, 2010, Sec. 7-4.
 
 REAL(EB), INTENT(OUT) :: H,Z_STAR
 REAL(EB), INTENT(IN) :: DZ,TMP_W,TMP_G,K_G,RHO_G,CP_G,MU_G,VEL_G
@@ -1487,7 +1487,7 @@ SUBROUTINE RAYLEIGH_MASS_FLUX_MODEL(H_MASS,Z_STAR,DZ,B_NUMBER,D_FILM,RHO_FILM,MU
 ! Rayleigh number scaling in nondimensional mass transfer wall units
 !
 ! The formulation is based on the discussion of natural convection systems in
-! J.P. Holman, Heat Transfer, 7th Ed., McGraw-Hill, 1990, p. 346.
+! J.P. Holman, Heat Transfer, 10th Ed., McGraw-Hill, 2010, Sec. 7-4.
 
 REAL(EB), INTENT(OUT) :: H_MASS,Z_STAR
 REAL(EB), INTENT(IN) :: DZ,B_NUMBER,D_FILM,RHO_FILM,MU_FILM

Source/wall.f90

@@ -3562,7 +3562,7 @@ REAL(EB) FUNCTION HEAT_TRANSFER_COEFFICIENT(NMX,DELTA_N_TMP,H_FIXED,SFX,WALL_IND
    IF (H_FIXED >= 0._EB) THEN
       HEAT_TRANSFER_COEFFICIENT = H_FIXED
    ELSE
-      HEAT_TRANSFER_COEFFICIENT = 1.31_EB*ABS(DELTA_N_TMP)**ONTH  ! Natural convection for vertical plane
+      HEAT_TRANSFER_COEFFICIENT = 1.31_EB*ABS(DELTA_N_TMP)**ONTH  ! Natural convection for vertical plane, Holman, 10th, Tab. 7.2
    ENDIF
    RETURN
 ENDIF