%% 
%%  This file is asmejour-template.tex, a template to format papers in the style of ASME journal papers 
%%  as they are being published in early 2019.
%%
%%  This file is version 1.02 dated 2019/05/22
%%
%%  Author: John H. Lienhard V
%%          Department of Mechanical Engineering
%%          Massachusetts Institute of Technology
%%          Cambridge, MA 02139-4307 USA
%%
%%  Class options are set up in the asmejour.cls file. These include:
%%
%%          * Option to color the vertical bar in the title block [barcolor = colorname] 
%%               where colorname is any name def'd by xcolor package; omit barcolor option to get black
%%
%%          * Option to include line numbers [lineno]. The lineno package does not number equation 
%%          *    lines, captions, etc. You must run twice for proper placement. 
%%          *    If you have been using lineno and then disable it, you may see errors about \@LN@col 
%%          *    undefined. To resolve this, delete your aux file.
%%
%%          * Math options from M. Sharpe's newtxmath package: upright integrals [upint]; and
%%          *    varvw for a v and w that are better distinguished from greek nu; and also 
%%          *    smallerops, varg, slantedGreek, frenchmath, varbb, cmbraces. Version 1.5 or higher
%%          *    is recommended.
%%
%%          * Many options for calligraphic, script, and fraktur fonts from the mathalfa package; the
%%          *    example value used is: mathalfa=cal=euler (use Euler font for \mathcal)
%%          *    some other options for cal are: dutchcal, zapfc, cm (default), boondox,...
%%          *    frak (fraktur), bb (blackboard bold), scr (script) may also be controlled.
%%
%%          * An option to omit all the ASME text fields from the footer: nofoot
%%          * An option to omit only the ASME copyright field from the footer: nocopyright
%%
%%          * An optional to use newtxtext's superiors font for footnotes [nodefaultsups] and an option
%%          *    for slightly larger small capitals, largesc
%%
%%  For details of newtxmath and mathalfa, refer to their documentation (available on CTAN: http://ctan.org).
%%
%%  The use of commands defined or modified by the asmejour class is illustrated below. In particular, 
%%  some care is needed when using complicated math and macros in section headings, 
%%  to avoid problems with pdf bookmarks, which is facilitated by the optional argument of \section, 
%%  as also illustrated below.
%%
 %=========================================================
%% 
%% LICENSE:
%%
%% Copyright (c) 2019 John Lienhard
%%
%% Permission is hereby granted, free of charge, to any person obtaining a copy of this software and 
%% associated documentation files (the "Software"), to deal in the Software without restriction, 
%% including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, 
%% and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, 
%% subject to the following conditions:
%%
%% The above copyright notice and this permission notice shall be included in all copies or 
%% substantial portions of the Software.
%%
%% The software is provided "as is", without warranty of any kind, express or implied, including but 
%% not limited to the warranties of merchantability, fitness for a particular purpose and noninfringement. 
%% In no event shall the authors or copyright holders be liable for any claim, damages or other liability, 
%% whether in an action of contract, tort or otherwise, arising from, out of or in connection with the 
%% software or the use or other dealings in the software.
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Class options are described above.
\documentclass[largesc,upint,varvw,barcolor=Red4,nocopyright]{asmejour}

\usepackage{balance}  % issue balance command near the end to nearly balance heights of final page short columns

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% The following two packages can be deleted if not being used

\usepackage{lipsum}   % Generates paragraphs of gibberish latin for checking layout ... e.g. \lipsum[2-4] produces
                      % paragraphs 2 through 4 of the text.
\usepackage{metalogo,hologo} % Access various LaTeX logos


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%  Fields to be completed   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%  pdf metadata, the user should edit %%%%%%%%%%%%%%%%%%
\hypersetup{%
	pdftitle={ASME Journal Paper Template},                % <=== change to YOUR pdf file title
	pdfkeywords={ASME, Paper, Template, LaTeX, BibTeX},    % <=== change to YOUR pdf keywords
	pdfauthor={John H. Lienhard},                          % <=== change to YOUR name[s]!!!
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Omit "Journal of"
%% If Journal Name is quite long, use \\ to insert linebreak
\JourName{Heat Transfer} %<=== change to name of your journal

\PaperYear % defaults to current year if no argument; \PaperYear{} omits year; \PaperYear{2018} sets 2018.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{document}

% Change to your name[s] and addresses, in the desired order of authors.
% First name, middle initial, last name
% Use title case (upper and lower case letters)
% Note usage below for corresponding author.

\SetAuthorBlock{Author Name[s]}{Department of Mechanical Engineering,\\
   Institution or Company Name,\\
   Street address,\\
   City, State, Country \\
   email: xxx@yyy.zzz} 

% To label one or more corresponding authors put "Name\CorrespondingAuthor". No space after "Name".
% An optional argument can be added if email is not in address block as
%      "Name\CorrespondingAuthor{write@to.me}"
% Can also include multiple emails and use the command more than once for multiple corresponding authors,
%      "Name\CorrespondingAuthor{write@to.him, write@to.her}"

\SetAuthorBlock{John H.\ Lienhard V\CorrespondingAuthor}{%
Rohsenow Kendall Heat Transfer Laboratory, \\
Department of Mechanical Engineering,\\
Massachusetts Institute of Technology, \\
Cambridge, MA 02139 USA \\
email: lienhard@mit.edu
}

%%% Change to your title. Can insert line breaks if you wish, otherwise selected automatically.
\SetTitle{Preprint Template for ASME\\ Journal Papers:  asmejour.cls}


%%% Change these to your keywords.  Keywords are automatically printed at the end of the abstract.
%%% This command must come BEFORE the end of the abstract.
%%% If you don't want keywords, delete the command.

\keywords{ASME, Paper, Template, \LaTeX, \hologo{BibTeX}}
 
   
%% Abstract should be no more than 250 words
\SetAbstract{%
This paper is an example and template for the {\upshape\texttt{asmejour}} class. Papers typeset in this class will follow ASME journal style for margins, fonts, headings, captions, and reference formats. Standard \LaTeX\ commands are used. The class will lay out the author, title, and abstract in ASME style. The class will produce a pdf file that that includes hyperlinks, bookmarks, and pdf metadata. The class is intended to be used with the {\upshape\texttt{asmejour.bst}} \hologo{BibTeX} style for typesetting references, which is part of this distribution.  This style supports hyperlinks and modern reference formats, following current ASME practice. The class may be invoked with several options, most of which address math fonts. The class calls a number of packages, all of which are in \TeX\textsc{live}\ and on CTAN (\href{http://ctan.org}{ctan.org}). The class is compatible with \hologo{pdfLaTeX} or \LuaLaTeX.
}

\MakeTitlePage

%%%%%%%%%%%%%%%%%%%%%  End of fields to be completed. Now write! %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section*{Introduction}
The \texttt{asmejour} class file will typeset papers with margins, fonts, headings, captions, and reference formats that follow those used in journals published by the American Society of Mechanical Engineers (ASME). Internal and external hyperlinks will be set automatically, and the pdf file will contain bookmarks and metadata.

This class is not a publication of ASME. The intended use of this package is to allow authors to format their papers in ASME style prior to submission to an ASME journal for peer review. 

The \texttt{.tex} file may be written using standard \LaTeX\ commands, although some specific initial commands are needed to format the block containing the author[s], title, and abstract.

\subsection*{Essential Initial Commands}
To begin, fill in the fields to be completed at top of the \texttt{asmejour-template.tex} file. The pdf metadata will be placed into the pdf file itself. 

For each author, put author names and affiliation (with line breaks) into a separate \verb|\SetAuthorBlock{name}{affiliation}| command; follow the syntax illustrated \texttt{asmejour-template.tex} file.  One author (or more) may be designated as the \verb|\CorrespondingAuthor| by placing the command at the end of the name.  

The title should be placed into \verb|\SetTitle{..}|, and line breaks may be included if desired. Keywords may optionally be including using the \verb|\keywords{..}| command; this command \textit{must} be issued before the abstract. The abstract text must be placed into \verb|\SetAbstract{..}|. The abstract will automatically be italized. 

After setting up the authors, title, and abstract, issue the \verb|\MakeTitlePage| command. 

\subsection*{Optional to the Color Title Bar}
The vertical bar in the title block is black in all ASME journals. Since the \texttt{asmejour} class is only for preprints, we include the [fun] option to have the bar in color. Any color \texttt{name} recognized by the \texttt{xcolor} package may be invoked by including the option \texttt{barcolor=name} in the \verb|\documentclass[..]{asmejour}| command. The color name is \texttt{Red4} by default. (To have a black bar, either omit the option entirely or use the name \texttt{black}.)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{References to Figures, Equations, and Citations}
For ASME papers, the labels Figure and Equation should be abbreviated when they do not start a sentence, as in Fig.~\ref{fig:1} and Eq.~\eqref{eqn:1}. Figure~\ref{fig:1} is spelled out when it starts a sentence. Equation~\eqref{eqn:1} is spelled out when it starts a sentence. 

Citations will be numbered automatically \cite{DKE1969}. They should be inserted at the appropriate point using a \verb|\cite{ref}| command~\cite{toohey2007,gibson2008}. The citations will be automatically sorted and compressed, as well, if they are given in a set \cite{stevens1999, DKE1969, wions2005, oligaria2011,mollen2014,smith2014,apple2019}. See the \texttt{asmeconf-sample.bib} file for examples of how to enter your references.

Equations are typeset in the usual way.  The class file loads the \texttt{amsmath} and \texttt{mathtools} packages. Further, the \texttt{newtxmath} package used for the math fonts includes many additional features.
\begin{equation}\label{eqn:1}
\mathbf{q} = -k\nabla T
\end{equation}
Be sure to put your symbols into the nomenclature list, including SI units.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Section Headings and Captions}
ASME requires that section headings and captions be set in bold face. In addition, the captions must be in sans serif type. The \texttt{asmejour} class will do this automatically.  You can place \verb|\cite{..}|, \verb|\ref{..}|, \verb|\label{..}|, and into headings and captions directly, as you would in the main text.  You can place \verb|\footnote{..}| into headings, but not into captions.\footnote{See \texttt{tex-stackexchange} for various approaches to footnotes in captions, if they seem necessary. For footnotes in tables, use the \texttt{tablefootnote} package.}

Sections may either be numbered or left unnumbered. ASME publishes papers in either style.

Math can be used in either captions or section headings, and an appropriate math font will be automatically selected. For a section heading that includes complicated math (and macros), you may use the optional argument of \verb|\section[..]{..}| to create a pdf bookmark without losing characters or producing warnings or errors. See the \texttt{asmejour-template.tex} source file for examples of this. These bookmarks should usually be text expressions, although some math is supported.  

If you wish to override the default math format in a heading or caption, put \verb|\mathversion{normal}| in the heading or caption. (The \texttt{newtxmath} package \cite{sharpe1} includes a complete set of bold math fonts, however, so the need to override should be rare.)

\subsection*{Subsection Headings}
Section and subsection headings should be in title case (first letter of primary words capitalized). ASME does not use \verb|\subsubsection| or \verb|\paragraph|, so the class file treats these commands like \verb|\subsection|. 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{More on Math}
To get bold math outside of the captions, you can use the \verb|\bm{..}| macro from the \texttt{bm} package, which is loaded by the class.

\begin{equation}
\bm{ S = k \ln w}
\end{equation}

Math italics are used for roman and greek letters by default.  If you want an upright letter in math, you can use the relevant math alphabet, e.g., \verb|\mathrm, \mathbf, \mathsf|:
\begin{equation}\label{eqn:newton2}
\vec{F} = m \vec{a} \quad\textrm{or}\quad \vec{\mathrm{F}} = m \vec{\mathrm{a}} \quad\textrm{or}\quad \mathbf{F} = m \mathbf{a} \quad\textrm{or}\quad \vec{\mathsf{F}} = m \vec{\mathsf{a}}
\end{equation}
ASME typesets vectors in upright bold, like the third instance in Eq.\ \eqref{eqn:newton2}, and sets matrices in bold italic.

The \texttt{newtxmath} package includes a large number of options for mathematics, most of which can be called using options to the documentclass. For example, the \texttt{upint} option of \texttt{newtxmath} selects upright integral signs (rather than slanted integral signs):
\begin{quote}
\verb|\documentclass[upint]{asmejour}|. 
\end{quote}  
Options are discussed further in the \texttt{asmejour-template.tex} file. 

In addition, many options for calligraphic, script, and fraktur fonts are available as options to the \texttt{mathalfa} package, which is also loaded. These may be invoked, for example, as 
\begin{quote}
\verb|\documentclass[mathalfa=cal=euler]{asmejour}| 
\end{quote}
which selects the Euler font for \verb|\mathcal| (this is our default). To find all the font options, refer to the \texttt{mathalfa} package documentation \cite{sharpe2}.

The typewriter font loaded is \texttt{inconsolata} (which is sans serif), as suggested by the \texttt{newtx} package documentation. The class is not set up for use with the \texttt{fontspec} or \texttt{unicode-math} packages.

%%%%%%%%%%%%% begin figure %%%%%%%%%%%%%%%%%

%% captions go below figures
\begin{figure}
\centering\includegraphics[width=0.7\linewidth]{sample-figure-1.pdf}
\caption{A figure caption with math, $z = (r,\phi)$ \cite{Lienhard2019b}\label{fig:1}}
\end{figure}
 
%%%%%%%%%%%%% end figure %%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Tables}
Table \ref{tab:1} is an example of a simple table. Table captions should be placed above tables.
The class loads the \texttt{array} and \texttt{dcolumn} packages which provide extended capabilities for columns in the \texttt{tabular} environment (used in Tables \ref{tab:2} and \ref{tab:3}). Table~\ref{tab:3} is designed to have exactly the width of a text column. Table~\ref{tab:4} shows a table that spans both text columns. 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Reference Formatting with \texttt{asmejour.bst}}
The {\upshape\texttt{asmejour.bst}} \hologo{BibTeX} style follows the reference styles observed in ASME journals in 2019. The vast majority of published references are to journal papers and books. Examples for these and many other cases are given in the \texttt{asmejour-sample.bib} file, which is part of this distribution.  Nevertheless, a few comments are necessary. 

\subsection*{Hyperlinked Titles} If an \verb|@article{..| or \verb|@book{..| includes \verb|doi={..}|, the journal title will be hyperlinked to that doi number. If no doi is included, but a url is included, then the title will be hyperlinked to that url. To display the doi (or the url when no doi is given), put it into the \verb|note={..}| field:
\begin{quote}
\verb|note = {\doi{10.1115/1.4042912}}|
\end{quote}

Elementary support for \texttt{eprint} numbers is also included, generating a url at the end of the citation. The \texttt{archive} type may be specified using the macros \texttt{arxiv, googlebooks, hndl, jstore}, or \texttt{pubmed} (e.g., \texttt{archive=hndl},  \textit{without} braces). Both fields \textit{must} be given. Other root urls may be invoked using \verb|archive = {http://another.url.org/}|.

\subsection*{Online Sources} A bibliography field \verb|@online{..| is included for citation of online sources, such as web pages. See the examples of use in the \texttt{asmejour-sample.bib} file. 

\subsection*{Date Accessed} The \verb|urldate={..}| field may be used to provide the date on which a given url was accessed. By default, the text printed will be \texttt{accessed `date',}. The word ``accessed'' may be changed using the \verb|urltype={..}| field.

\subsection*{Location and Date of Conference} For \verb|@inproceeedings{..| and \verb|@proceeedings{..|, you may include \verb|venue={..}| and \verb|eventdate={..}| to specify the city and the date of a conference. 

\subsection*{Version Number\footnote{Another longer footnote to show the leading and line breaking, and how it will sit at the bottom of a column. Another longer footnote to show the leading and line breaking, and how it will sit at the bottom of a column.}} The \verb|version={..}| field may be used with \verb|@book|, \verb|@online|, and \verb|@manual|. By default, the text will read \texttt{Version `number'} as in \cite{sharpe1,sharpe2},  but different wording may be selected using the \verb|versiontype={..}| field, to have ``Revision''  or something similar, as in \cite{GSL}. ASME often puts the version in the title, as in \cite{dlmf, texshop}, so I've left the final decision for discussion between the authors and the copy editor.

%% Dealing with complicated math in a section heading: optional argument of \section provides the pdfbookmark
%%   without losing characters or producing warnings/errors. Note that bookmark can include simple math.
%%
%% Newtxmath provides the option for upright Greek letters as \upomega (vs. \omega), etc.
%%
\section*[Math in a Section Heading: \omega\cdot U=0]{Math in a Section Heading: $\hat{\upomega}\cdot\hat{\mathrm{U}}=0$}

The rest of this is fake Latin text to demonstrate formats.
\lipsum[6] % <=== This command generates paragraphs of fake Latin.  Delete it here and elsewhere!


%%%%%%%%%%%%%%% begin simple table %%%%%%%%%%%%%%%%%%%%%%%%%% 

%% captions go above tables

\begin{table}[t]
\caption{A simple table\label{tab:1}}
\centering{%
\begin{tabular}{l l r}
\hline\hline
Experiment & $u$ [m/s] & $T$ [\textdegree C] \rule{0pt}{10pt} \\[2pt]
\hline
Run 11 & 12.5 & 103.4 \rule{0pt}{10pt} \\
Run 12 & 24   & 68.3 \\[1pt]
\hline\hline
\end{tabular}
}
\end{table}

%%%%%%%%%%%%%%%% end table  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%% begin more complicated table %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{table}[t]
\caption{Table with more complicated columns}\label{tab:2}%
\centering{%
\begin{tabular}{!{\hspace*{0.5cm}} >{\raggedright\hangindent=1em} p{3cm} d{3} @{\hspace*{1cm}} d{3} !{\hspace*{0.5cm}}}
\hline\hline
\rule{0pt}{10pt} Experiment & \multicolumn{1}{c@{\hspace*{1cm}}}{$u$ [m/s]} & \multicolumn{1}{c!{\hspace*{0.5cm}}}{$T$ [\textdegree C]} \\[1pt]
\hline
The first experiment we ran this morning   & 124.3     &   68.3   \rule{0pt}{10pt} \\
The second experiment we ran this morning  &  82.50    &  103.46  \\
Our competitor's data                      &  72.321   &  141.384 \\[1pt]
\hline\hline
\end{tabular}
}
\end{table}

%%%%%%%%%%%%%%%% end table  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 


%%%%%%%%%%%%%%%%%%%  begin linewidth table  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{table}[b]
\newcolumntype{C}{>{$}c<{$}} % math-mode version of "c" column type, from array package
\caption{\label{tab:3}Table at full column width with columns in math mode}
\centering{%
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}CCCC@{\extracolsep{\fill}}}
\hline\hline
X_{z} & X_{c} & X_{c,m} & X_{c,2}\rule{0pt}{11pt}\\
 3.92069  & 5.70943 & 6.32429 & 7.08757\\[2pt]
\varepsilon (T_1)  & \varepsilon^i (T_1) & \varepsilon^i (T_m) & \alpha (T_1, T_2)\\
0.7258 & 0.6237 & 0.6807 & 0.7964 \\[2pt]
q_\textrm{gray}  & q_\textrm{int, $T_1$} & q_\textrm{int, $T_m$} & q_\textrm{exact}\\
400.2 & 462.1 & 371.0 & 371.8 \\[1pt]
\hline\hline
\end{tabular*}
}
\end{table}

%%%%%%%%%%%%%%%%%%%%  end linewidth table %%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%  begin wide figure  %%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure*}[t]
\begin{minipage}[c]{0.5\textwidth}
\centering{
  \includegraphics{sample-figure-2a.pdf}
\subcaption{Interior region\label{fig:interior-region}}
}\end{minipage}
%%%%%%%% don't leave a break here
\begin{minipage}[c]{0.5\textwidth}
\centering{
\includegraphics{sample-figure-2b.pdf}
\subcaption{Exterior region\label{fig:exterior-region}}
}\end{minipage}
\caption{A figure with two subfigures  \cite{Lienhard2019b}}
\end{figure*}

%%%%%%%%%%%%%%%%%%%  end wide figure  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\subsection*{Subsection Heading}

\lipsum[12-13] % <=== This command generates paragraphs of fake Latin.  Delete it here and elsewhere!
\begin{equation}\label{eqn:dw}
d\mathbf{w} =
   \begin{pmatrix}
 	du \\ dv
   \end{pmatrix} = 
   \underbrace{\begin{pmatrix}
	 \partial u/\partial x &  \partial u/\partial y \\
	 \partial v/\partial x &  \partial v/\partial y
   \end{pmatrix}}_{=\,\bm{J}_1}  \begin{pmatrix}
 	dx \\ dy
   \end{pmatrix} 
\end{equation}
Note ASME style for vectors, $\mathbf{w}$, and matrices, $\bm{J}_1$.

\subsubsection*{Third Level Heading}
\lipsum[13]

%%%%%%%%%%%%%%% begin table %%%%%%%%%%%%%%%%%% 
\begin{table*}[t]
\caption{A table spanning two columns}\label{tab:4}%
\centering{%
\begin{tabular*}{0.8\textwidth}{@{\hspace*{1.5em}}@{\extracolsep{\fill}}ccc!{\hspace*{3.em}}ccc@{\hspace*{1.5em}}}
\hline\hline
\multicolumn{1}{@{\hspace*{1.5em}}c}{$x$\rule{0pt}{11pt}} &
\multicolumn{1}{c}{$\textrm{erf}(x)$} &
\multicolumn{1}{c!{\hspace*{3.em}}}{$\textrm{erfc}(x)$} &
\multicolumn{1}{c}{$x$} &
\multicolumn{1}{c}{$\textrm{erf}(x)$} &
\multicolumn{1}{c@{\hspace*{1.5em}}}{$\textrm{erfc}(x)$} \\ \hline
0.00 & 0.00000 & 1.00000 & 1.10 & 0.88021 & 0.11980\rule{0pt}{11pt} \\
0.05 & 0.05637 & 0.94363 & 1.20 & 0.91031 & 0.08969 \\
0.10 & 0.11246 & 0.88754 & 1.30 & 0.93401 & 0.06599 \\
0.15 & 0.16800 & 0.83200 & 1.40 & 0.95229 & 0.04771 \\
0.20 & 0.22270 & 0.77730 & 1.50 & 0.96611 & 0.03389 \\
0.30 & 0.32863 & 0.67137 & 1.60 & 0.97635 & 0.02365 \\
0.40 & 0.42839 & 0.57161 & 1.70 & 0.98379 & 0.01621 \\
0.50 & 0.52050 & 0.47950 & 1.80 & 0.98909 & 0.01091 \\
0.60 & 0.60386 & 0.39614 & 1.82\makebox[0pt][l]{14} & 0.99000 & 0.01000 \\
0.70 & 0.67780 & 0.32220 & 1.90 & 0.99279 & 0.00721 \\
0.80 & 0.74210 & 0.25790 & 2.00 & 0.99532 & 0.00468 \\
0.90 & 0.79691 & 0.20309 & 2.50 & 0.99959 & 0.00041 \\
1.00 & 0.84270 & 0.15730 & 3.00 & 0.99998 & 0.00002 \\[2pt]
\hline\hline
\end{tabular*}
}
\end{table*}
%%%%%%%%%%%%%%%% end table %%%%%%%%%%%%%%%%%%% 


\section*{Summary}
\lipsum[17] % <=== This command generates paragraphs of fake Latin.  Delete it here and elsewhere!

\begin{enumerate}
\item First conclusion 
\item Second conclusion
\item Third conclusion
\item Fourth conclusion

\end{enumerate}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Acknowledgement}
\lipsum[17] % <=== This command generates paragraphs of fake Latin.  Delete it here and elsewhere!

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Funding Data}
\begin{itemize}
\item U.S.\ Department of Heat Transfer, Office of Important Ideas (DOHT Award No.\ 3.14159265)
\end{itemize}


%%%%%%%%%  NOMENCLATURE  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% Leave off second argument of \entry to produce a subheading (e.g., \entry{Greek letters}  )
%% Must run latex twice to align the columns.

\begin{nomenclature}
\entry{$\overline{h}$}{average heat transfer coefficient (W m$^{-2}$ K$^{-1}$)}
\entry{$k$}{thermal conductivity (W m$^{-1}$ K$^{-1}$)}
\entry{$\mathbf{q}$}{heat flux vector (W m$^{-2}$)}

\entry{Greek Letters}
\entry{$\alpha$}{thermal diffusivity (m$^2$ s$^{-1}$)}
\entry{$\nu$}{kinematic viscosity (m$^2$ s$^{-1}$)}

\entry{Dimensionless Groups}
\entry{Pr}{Prandtl number, $\nu/\alpha$}

\entry{Superscripts and Subscripts}
\entry{b}{bulk value}
\entry{$\infty$}{free stream value}

\end{nomenclature}


%%%%%%%%%%%%%%%  Appendices  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Note that appendices will be "numbered" A, B, C, ... etc. Use \section, not \section*
%% Subsections need not be numbered, use \subsection*
%% The equation counter is reset for each appendix
%% Figures will be numbered consecutively


\appendix       %%% starting appendices

\section{Incomplete Zeta Function~\cite{Lienhard2019c}\label{app:zetafunction}}

The radiation fractional function may be written in terms of the incomplete zeta function for convenience:
\begin{align}
f(\lambda T)  = {}&  \frac{1}{\sigma T^4} \int_0^\lambda\frac{2\pi h c_o^2}{\lambda^5 \left[ \exp (h c_o/k_B T \lambda) - 1\right] } \, d\lambda \\
 = {}&  \frac{1}{\sigma T^4}\frac{2\pi k_B^4 T^4}{h^3c_o^2}\int^\infty_{c_2/\lambda T}\frac{t^3}{e^t -1}\, dt\label{eqn:zeta}
\end{align}
When $\lambda T \rightarrow \infty$, $f = 1$ and the last equation yields the well-known result
\begin{equation}
 {\sigma T^4} =\frac{2\pi k_B^4 T^4}{h^3c_o^2} \underbrace{\int_0^\infty \frac{t^3}{e^t - 1} \, dt}_{\equiv \zetaup(4)\Gamma(4)} 
\end{equation}
where the Gamma function $\Gamma(4) = 3!$ and the Riemann zeta function, $\zetaup(4)$, has the indicated integral representation \cite[\S13.12]{ww1927}.  A classical result due to Euler \cite{euler1740} gives $\zetaup(4) = \pi^4/90$ (see also \cite[\S167]{euler1748}), from which we recover the usual definition of the  Stefan-Boltzmann constant, $\sigma$.  

%%%%%%%%%%%%%  Bibliography  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\balance %<=== this command, from the balance package, attempts to balance column heights on last page.
         %     performance is a bit variable, however...

\nocite{*} %% <=== delete this line unless you want to typeset the entire contents of your .bib file.
\bibliographystyle{asmejour}   %% .bst file following ASME journal format. Do not change.
\bibliography{asmejour-sample} %% <=== change this to name of your bib file


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\clearpage

%% ASME requires these lists for production
\twocolumn[
  \begin{@twocolumnfalse}
\listoffigures
\listoftables
  \end{@twocolumnfalse} 
]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
 