% !TEX encoding = UTF-8 Unicode
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%
%%  This file is asmeconf-template.tex, a LaTeX template to format ASME Conference papers according to
%%  the requirements on ASME's conference web pages, and including hypertext support for the pdf.
%%
%%  This file is version 1.44 dated 2025/11/07
%%  
%%  As of version 1.11, this template defaults to ASME's newer conference guidelines first posted July 2019.
%% 			Those guidelines changed the author block formatting to be inline. 
%%			If you need the traditional grid format, use the class option [grid].
%%			Nomenclature now follows the abstract, and abstract text is set in italics.
%%
%%  Author: John H. Lienhard, V
%%          Department of Mechanical Engineering
%%          Massachusetts Institute of Technology
%%          Cambridge, MA 02139-4307 USA
%%
%%  Class options include:
%%
%%          * An option to use the traditional grid arrangement of author names, [grid].  
%%			*	 With this option, line breaks (\\) may be inserted into the address as needed. 
%%			*	 Author names that include commas should be enclosed in braces, e.g., {Joseph L. Smith, Jr.}.  
%%			*	 Authors may be grouped above a single affiliation using braces, e.g., {Henry Tudor, Catherine Parr}.
%%
%%          * An option to balance the heights of columns on the last page [balance]. 
%%
%%          * An option to include line numbers, [lineno]. You must *run twice* for proper placement of the line numbers. 
%%			*	 The lineno package does not number titles, footnotes, captions, or tables.
%%          *    This option will disable balancing column height on final page if that option has been invoked.
%%          *    The lineno package won't always number the lines preceding displayed math in a paragraph because
%%          *    paragraph has not ended.  See that package's documentation for macros to address this problem, or
%%          *    just leave a blank line above the displayed equation while you are editing and then remove the 
%%          *    blank line with [lineno] option when you move to your final version.
%%
%%			* An option not to use a boldface font for caption text, [unboldcaption]
%%
%%          * Options to: 	omit the ASME copyright footer, [nofoot]; 
%%			*				use government employee copyright notice, [govt];
%%			*				use government contractor copyright notice, [contractor];
%%			*				use copyright notice for some gov't employees, [somegovt];
%%			*				omit the conference headers on the titlepage, [nohead]
%%
%%			* Option to use LuaLaTeX ** without ** unicode-math and fontspec, [nofontspec]
%%
%%          * Math options from M. Sharpe's newtxmath package: upright integrals [upint]; 
%%          *    [varvw] for a v and w that are better distinguished from Greek nu; and also 
%%          *    [subscriptcorrection, smallerops, varg, frenchmath, varbb, cmbraces, slantedGreek,...] 
%%			* 	 See newtx documentation for descriptions (at CTAN: https://www.ctan.org/pkg/newtx, v1.6 or higher is best).
%%			*	 newtx is not loaded with lualatex unless the [nofontspec] option is used.
%%
%%          * An option to allow hyphenation of the typewriter font [hyphenate], from the inconsolata package.
%%          *    Hyphenation is normally suppressed for typewriter mode because it is often used for code.
%%			*	 To replace the default variable word spacing by monospacing, use the option [mono].
%%			*	 To get a zero without a slash, use [var0]
%%
%%			* PDF/A compliance:  Since 2022, LaTeX has included integrated support for pdf-a, through the \DocumentMetadata{..}
%%			*    command. This approach works with both pdfTeX and LuaLaTeX.
%%
%%          * Options (used by the babel package) to include passages in languages other than English (e.g., a translation 
%%			*    of the abstract).  See Appendix C for details.
%%			*    	pdftex: Appropriate scripts will be loaded if you call the class options [greek], [russian], or [vietnamese].
%%			*    
%%			*    	lualatex: Language support is most extensive when running LuaLaTeX, which automatically loads fontspec.
%%			*		Non-Latin scripts require the [loadscripts] option, see Appendix C. 
%%			*	 	Be aware that you might need to install additional fonts for some languages.
%%			 
%%  The use of commands defined or modified by the asmeconf class is illustrated throughout this file. In particular, 
%%  ASME requires capitalized section headings, and as a result some care is needed when using macros in section headings,
%%  as also illustrated below.
%%
%%  Be sure to use **up-to-date and complete** installation of LaTeX, such as TeX Live 2023 or later. Errors often occur with old set-ups.
%%
 %=========================================================
%% 
%% LICENSE: 
%%
%% Copyright (c) 2025 John H. Lienhard
%%
%% Offered under the MIT license: https://ctan.org/license/mit 
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%  RECOMMENDED pdf management code.
%%  This code was added to the LaTeX kernel in June 2022.
%% 		See https://www.latex-project.org/news/latex2e-news/ltnews35.pdf
%%  If you have problems with these lines, your LaTeX format may be out of date. You can comment them out.

\DocumentMetadata{%
	lang=en-US, % default
	pdfstandard=A-3u,% A-2b, A-2u, A-3b, A-3u. Check that your figures also meet the standard you choose.
	pdfversion=1.7,% 2.0 (Version 2.0 supports pdfstandard=A-4f with pdftex or UA-2 with LuaLaTeX)
%	pdfversion  = 2.0, % default
%	pdfstandard = { ua-2 , a-4f },
%	tagging = on, % for producing tagged pdf
}

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

%% CLASS OPTIONS are described above. Change the options given below to meet your needs.
%% 
%%	 	NB: Remove the [colorlinks] option before *final* submission to ASME, to get black text for printing,
%%			but keep that option for electronic use.
%%
%%		NB: If you are not using the language options, remove them (together with Appendices C and D)
%%			Vietnamese, greek, and cyrillic languages, if used, must be named in \documentclass under pdftex, but not under lualatex.
%%			Spanish, german, and many others, if used, do not need to be named when the babel package is dated 2024 or later.
%%
%%		NB: the mathalfa option was dropped in v1.41; load the mathalpha package in your preamble instead.

\documentclass[grid,colorlinks,upint,subscriptcorrection,varvw,hyphenate,balance,german]{asmeconf}

%%%%%  pdf metadata  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\hypersetup{%
	pdfauthor={John H. Lienhard},									  % <=== change to YOUR name
	pdftitle={ASME Conference Paper LaTeX Template},                  % <=== change to YOUR pdf file title
	pdfkeywords={ASME conference paper, LaTeX template, BibTeX style},% <=== change to YOUR pdf keywords
	pdfsubject = {Describes the asmeconf LaTeX template},			  % <=== change to YOUR subject
%	pdfurl={https://ctan.org/pkg/asmeconf},% may delete
%	pdflicenseurl={https://ctan.org/pkg/asmeconf},% may delete
}
% If an author name or the title include a comma, enclosed it in braces, e.g., pdfauthor{John Forbes Nash{,} Jr.}


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

\allowdisplaybreaks % from amsmath package, allows multiline equations to break across pages (delete if not wanted)
					% using \\* instead of \\ will prevent specific lines from being pagebreaks.

% logos used in this document
\newcommand*\pdfTeX{pdf\TeX}    
\newcommand*\LuaLaTeX{Lua\LaTeX}
\newcommand*\BibTeX{Bib\TeX}

\begin{document}

% Change these fields to the right content for your conference.
% You can comment these out if for some reason you don't want a header.
% Use title case for the conference name (first letters capitalized), not all capitals

\ConfName{Proceedings of the ASME 2025\linebreak International Mechanical Engineering Congress and Exposition}
\ConfAcronym{IMECE2025}
\ConfDate{November 16--20, 2025} 
\ConfCity{Memphis, TN}
\PaperNo{IMECE2025-XXXX}

% Units of measure (e.g., cm) and other specialty lowercase terms in the title should be 
%   enclosed in \NoCaseChange{...} to maintain lower case type.
%   The rest of the title will automatically be set in all capital letters.
%
%	\title{Place Title Here: Place Subtitle After Colon} 

\title{A LATEX Template for ASME Conference Papers: \NoCaseChange{\texttt{asmeconf.cls}}} % <=== replace with YOUR title
 
%   Put author names into the order you want. Use the same order for affiliations.
%   \affil{#} tags the author's affiliation to the address in \SetAffiliation{#}.
%   No space between last name and \affil{#}, separate names with commas.
%
%	For a sole author or a single affiliation for all authors, {#} may be left empty, i.e. \affil{} and \SetAffiliation{} (but not with [grid] option!)
%
%   \CorrespondingAuthor{email} follows that author's affiliation, no spaces before or after 
%   If multiple corresponding authors, put both email addresses in the same command and place after both authors.
%
%   \JointFirstAuthor, if applicable, follows the affiliation of the relevant authors, no spaces.

%    Most of the names below are not real people, just very common names.
\SetAuthors{%
	Luis Hern\'{a}ndez\affil{1}\JointFirstAuthor, 
	Maria Silva\affil{2}\JointFirstAuthor, 
	{Henry Tudor,  Catherine~Parr\CorrespondingAuthor{}}\affil{3}, 
	Jinsoo Kim\affil{1}, 
	Yusuf Yilmaz\affil{1}, 
	Amelia Smith\affil{1}, 
	Aadhya Acharya\affil{1}, 
	Omar Abu Bakr\affil{1}, 
	John H.\ Lienhard\affil{4}\CorrespondingAuthor{lienhard@mit.edu, kate@thepalace.gov}
}

\SetAffiliation{1}{Institution or Company Name\\ City, State}
\SetAffiliation{2}{Institution or Company Name\\ City, Province, Canada}
\SetAffiliation{3}{Hampton Court Palace\\ Richmond, England}
\SetAffiliation{4}{Massachusetts Institute of Technology\\ Cambridge, MA }

% be sure to issue [grid] option

\maketitle

%%% Use this footnote for tracking various versions of your draft. Change text to suit your own needs. 
%%% \date{..} calls the same command. 
\versionfootnote{Documentation for \texttt{asmeconf.cls}: Version~\versionno, \today.}% <=== Delete before final submission.

%%% Change the following 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, leave the argument of \keywords{} empty (or use the abstract* environment)

\keywords{ASME conference paper, \LaTeX\ Template, \BibTeX}

%%%%%  End of fields to be completed. Now write your paper. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%  ABSTRACT  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% Abstract should be 200 words or less
\begin{abstract}
This paper is an example of and a {\upshape\LaTeX} template for typesetting ASME conference papers using the {\upshape\texttt{asmeconf}} class. This  {\upshape\LaTeX} template follows ASME guidelines for margins, fonts, headings, captions, and reference formats as of 2025. The class should be used with the {\upshape\texttt{asmeconf.bst} \BibTeX} style for reference formatting, which is part of this distribution. The template produces pdfs that contain hyperlinks, bookmarks, and metadata; and references can include the DOI and URL fields. Links may be colored, for online use, or black, for publication. The class enables inline author names, following ASME's current style, but can also produce the traditional grid style. Options include line numbering, final column balancing, various math options, government copyright, and archivability (PDF/A). In addition, section headers may contain mathematics, references, citations, and footnotes. The class is compatible with {\upshape\pdfTeX} or {\upshape\LuaLaTeX}.
\end{abstract}

%%%%%%%%%  NOMENCLATURE (OPTIONAL) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% To change space between the symbols and  definitions, use \begin{nomenclature}[Xcm] where X is a number 
%% The unit cm can be replaced by any LaTeX unit of dimension: pt, in, ex, em, pc, etc.
%% Default is 2em.
%%
%% \EntryHeading{..} produces an italicized subheading in the nomenclature list, e.g., \EntryHeading{Greek letters}

\begin{nomenclature}
\EntryHeading{Roman letters}
\entry{$k$}{Thermal conductivity [W m$^{-1}$ K$^{-1}$]}
\entry{$\vec{q}$}{Heat flux vector [W m$^{-2}$]}

\EntryHeading{Greek letters}
\entry{$\alpha$}{Thermal diffusivity [m$^2$ s$^{-1}$]}
\entry{$\nu$}{Kinematic viscosity [m$^2$ s$^{-1}$]}

\EntryHeading{Dimensionless groups}
\entry{Pr}{Prandtl number, $\nu/\alpha$}
\entry{Sc}{Schmidt number, $\nu/\mathcal{D}_{1,2}$}

\EntryHeading{Superscripts and subscripts}
\entry{b}{bulk value}
\entry{$\infty$}{free stream value}
\end{nomenclature}

%%%%%%%%%  BODY OF PAPER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Introduction}
The \texttt{\hrefurl{https://ctan.org/pkg/asmeconf}{asmeconf}} class typesets papers with margins, fonts, headings, captions, and reference formats that follow the specifications for conference papers of the American Society of Mechanical Engineers (ASME). The \texttt{asmeconf} class will set internal and external hyperlinks, and the pdf file will contain bookmarks and metadata. Many other useful features have been incorporated. This class is not a publication of ASME, but the author has published in ASME conferences since 1983. 

The \texttt{.tex} file may be written using standard \LaTeX\ commands, although some class-specific initial commands are needed to format the blocks containing the author[s], title, and abstract.  This class loads a number of other packages, all of which are contained in up-to-date versions of \hrefurl{https://www.tug.org/texlive/}{\TeX\ Live}, \hrefurl{http://www.tug.org/mactex/}{Mac\TeX}, and similar platforms. If you get an error message about a missing package, you can download that package at no cost from CTAN (\hrefurl{https://ctan.org}{ctan.org}). 

\subsection{Essential Initial Commands}

To begin, fill in the fields to be completed at top of the \texttt{asmeconf-template.tex} file. These fields include the headers for your conference and your paper number. The metadata you provide will be placed into the pdf file itself. 
The title should be placed into \verb|\title{..}|. 

Put author names into the \verb|\SetAuthors{name, name,...}| command in the desired order; follow the syntax illustrated \texttt{asmeconf-template.tex} file. Put each distinct address sequentially into a separate \verb|\SetAffiliation{n}{address}|, where $n = 1,2,\ldots$ Tag each author with an affiliation by putting \verb|\affil{n}| after that author's name inside the \verb|\SetAuthors{..| command. 

Keep author addresses short.  List the author institution, and the City, State (US authors), City, Province, Canada (Canadian authors), or City, Country (other international authors). 

One author (or more) may be designated as the corresponding author by placing \verb|\CorrespondingAuthor{email}|  after \verb|\affil{n}|. Two or more authors may be joint first authors by putting \verb|\JointFirstAuthor| after \verb|\affil{n}|.

After setting up the headers, authors,  and title, issue the \verb|\maketitle| command. 

The abstract text must be placed into \verb|\begin{abstract}| \ldots \verb|\end{abstract}|. The abstract will automatically be italicized. Keywords may be included using the \verb|\keywords{..}| command. The \texttt{keyword} command \emph{must} be issued before the abstract environment. 

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

\section{Referring to Citations, Figures, and Equations}

Citations are automatically numbered \cite{ning2002}. They should be inserted in the text using a \verb|\cite{ref}| command~\cite{gibson2008,stevens1999}. The citations will be automatically sorted and compressed if they are given in a set \cite{stevens1999,ning2002,gibson2008,wions2005,smith2002,watson1982}. 
A specific reference may be named with an abbreviation, as in Ref.~\cite{watson1982}.
See the \texttt{asmeconf-sample.bib} file and Sect.~\ref{sec:references} for examples of entering references.

For ASME conference papers, the labels Equation and Figure should be abbreviated when they do not start a sentence, as in  Eq.~\eqref{eqn:dw} and Fig.~\ref{fig:1}. Figure~\ref{fig:1} is spelled out when it starts a sentence. Equation~\eqref{eqn:dw} is spelled out when it starts a sentence. 

Equations are typeset in the usual way and will be automatically numbered.  The class file loads the \texttt{amsmath} and \texttt{mathtools} packages. Further, the \texttt{newtxmath} package used for the math fonts includes many additional math features (see Sect.~\ref{sec:moremath}).
\begin{equation}\label{eqn:fourier}
\vec{q} = -k\nabla T
\end{equation}

ASME prefers SI units. (U.S.\ style units may follow in parentheses.) Be sure to put all symbols into the nomenclature list, including their units.


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

%% captions go below figures

\begin{figure}
\centering\includegraphics[width=\linewidth, alt = {Linearization error in radiant flux}]{sample-figure-1.pdf}
\caption{Caption with math, eqn.~\eqref{eqn:fourier}: $\Delta T/T_m$ vs.\ $\Delta T/T_1$~\cite{Lienhard2019}}\label{fig:1}
\end{figure}
 
%%%%%%%%%%%%% end figure %%%%%%%%%%%%%%%%%%%


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

%% Use title case for subsections and subsubsections (first letter of words capitalized)

\section{Section Headings and Captions}

ASME requires that section headings and captions be set in an uppercase, sans serif font.  The class will do this automatically.  You can place \verb|\cite{..}|, \verb|\ref{..}|, \verb|\label{..}|, and mathematics into headings and captions directly, as you would in the main text. Do not enclose them braces, e.g.\ \verb|{\cite{..}}|, which will cause errors. 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.}\footnote{Sequential footnotes are automatically separated by a comma.}

Text in section headings and captions will not be capitalized if enclosed in a \verb|\NoCaseChange{..}| command.

Sections may either be numbered or left unnumbered.

Simple mathematical expressions can be used in either captions or section headings. For a section heading that includes more 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{asmeconf-template.tex} source file for examples of this procedure. These bookmarks should usually be text expressions, although some math is supported.  

To eliminate boldface type in caption text and math, use the class option \texttt{[unboldcaption]}.  To prevent sans-serif math, put \verb|\NoCaseChange{\mathversion{normal}}| in the caption.

\subsection{Subsection and Sub-subsection Headings}

Subsections and sub-subsection headings should be entered in title case, with the first letter of primary words capitalized. Sub-subsections (i.e., paragraphs) are never numbered.


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

%% Captions go above tables
%%
%% Note that placement of figures and tables can managed with the [!tbhp] options. See: https://latexref.xyz/Floats.html

\begin{table}[t]
\caption[Table]{A simple table}\label{tab:1}
\centering{%
\tagpdfsetup{table/header-rows={1}}%
\begin{tabular}{llr}
\toprule
Experiment & $u$ [m/s] & $T$ [\textdegree C] \\
\midrule
Run 11 & 12.5 & 103.4 \\
Run 12 & 24   & 68.3 \\
\bottomrule
\end{tabular}
}
\end{table}

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

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

% note column set as a 3 cm wide paragraph with 1 em hanging indentation. See array package documentation.
% note numbers centered on "." (with d{3.3}) and on "," (with ,{3.3}).  See dcolumn package documentation.
\begin{table}[t]
\caption{Table with more complicated columns}\label{tab:2}%
\centering{%
\tagpdfsetup{table/header-rows={1}}%
\begin{tabular}{!{\hspace*{0.5cm}} >{\raggedright\hangindent=1em} p{3cm} d{3.3} @{\hspace*{1cm}} ,{3.3} !{\hspace*{0.5cm}}}
\toprule
Experiment & \multicolumn{1}{c@{\hspace*{1cm}}}{$u$ [m/s]} & \multicolumn{1}{c!{\hspace*{0.5cm}}}{$T$ [\textdegree C]} \\
\midrule
The first test we ran this morning   & 124.3     &   68,3   \\
The second test we ran this morning  &  82.50    &  103,46  \\
Our competitor's test                &  72.321   &  141,384 \\
\bottomrule
\end{tabular}
}
\end{table}

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

%%%%%%%%%%%%%%% begin two column table %%%%%%%%%%%%%%%%%% 
\begin{table*}
\caption{A table spanning two columns}\label{tab:3}%
\centering{%
\tagpdfsetup{table/header-rows={1}}%
\begin{tabular*}{0.8\textwidth}{@{\hspace*{1.5em}}@{\extracolsep{\fill}}ccc!{\hspace*{3.em}}ccc@{\hspace*{1.5em}}}
\toprule
\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}}}{$\textrm{erfc}(x)$} \\ \midrule
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]
\bottomrule\end{tabular*}
}
\end{table*}

%%%%%%%%%%%%%%%%% end two column table  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Tables and Figures}

Table \ref{tab:1} is an example of a simple table. Table captions should be placed above tables.
The class loads the \texttt{booktabs} package (used for horizontal rules in Tables \ref{tab:1} and \ref{tab:2}), and the \texttt{array} and \texttt{dcolumn} packages which provide extended capabilities for columns in the \texttt{tabular} environment (see Table \ref{tab:2}).  Table \ref{tab:3} is an example of a table that spans two columns. Two column tables (and figures) will always float to the top of a later page.

Figure captions go below figures. Figure~\ref{fig:2} is an example of a figure that spans two columns and includes subfigures. The text in figures (and tables) should be no smaller than 6~point type. Images in figures are handled by the standard \texttt{graphicx} package.

Landscape figures and tables may be produced at full-page size by putting \verb|\usepackage[figuresright]{rotating}| in your \texttt{.tex} file's preamble and using the \texttt{sidewaystable*} and \texttt{sidewaysfigure*} environments~\cite{fairbairns}.


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

\section{Reference Formatting with \NoCaseChange{\texttt{asmeconf.bst}}\footnote{To prevent capitalization of text in a section heading or caption, such as an SI unit, enclose it in a \texttt{\textbackslash NoCaseChange} command. As of the July 2022 release of \LaTeX, commands used in a heading or caption may be protected globally by putting this in the preamble: \texttt{\textbackslash AddToNoCaseChangeList\{\textbackslash MyCommand\}}}}\label{sec:references}

The {\upshape\texttt{asmeconf.bst}} \BibTeX\   style follows the reference styles shown on ASME's conference web site in  2025.\footnote{\texttt{asmeconf.bst} is intended as a replacement for the old \texttt{asmems4.bst}, which does not follow ASME's current reference formats or support DOI and URL.}
Examples for these and many other cases are given in the \texttt{asmeconf-sample.bib} file, which is part of this distribution. Citations and references are managed by the standard \texttt{natbib} package.  Nevertheless, a few comments are necessary. 

%% sub-subsections should *not* be numbered according to ASME's style

\subsubsection*{DOI, URL, and eprint} Include DOI numbers when they are available.  URL's may alternatively be given. ASME requests that URLs point to a document's abstract.

Basic 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, google\-books, hdl, jstore, oclc}, or \texttt{pubmed} (e.g., \texttt{archive=hdl},  \emph{without} braces). Both \texttt{eprint} and \texttt{archive} fields \emph{must} be given. Other root urls may be invoked using \verb|archive = {https://another.url.org/}|.

\subsubsection*{Online Sources} A bibliography entry \verb|@online{..| is included for citation of online sources, such as web pages. A \texttt{url} or \texttt{eprint} with \texttt{archive} must be included. See the examples of use in the \texttt{asmeconf-sample.bib} file. 

\subsubsection*{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.

\subsubsection*{Conference Location and Date} To specify the city and date of a conference, you can use \verb|venue={..}| and \verb|eventdate={..}| with the entries \verb|@inproceeedings{..| and \verb|@proceeedings{..|

\subsubsection*{Capitalization of Titles} ASME's bibliography style requires that document titles be in title case. The first letters of principal words are capitalized. Do this in the \texttt{.bib} file.



%%%%%%%%%%%%%%%%%  begin two column figure  %%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure*}
\begin{subfigure}[b]{\columnwidth}% subfigure is basically the same as minipage
\centering{
  \includegraphics[width=0.9\linewidth, alt={Nusselt number data for isothermal wall}]{sample-figure-2a.pdf}%
}
\subcaption{Uniform temperature wall\label{fig:isothermal}}
\end{subfigure}%
\hspace*{\columnsep}% with this space added, puts each figure at column center
%%%%%%%%%%%%% no line break between these two subfigures
\begin{subfigure}[b]{\columnwidth}
\centering{%
\includegraphics[width=0.927\linewidth, alt={Nusselt number data for uniform heat flux wall}]{sample-figure-2b.pdf}%
}%
\subcaption{Uniform heat flux wall with unheated starting length\label{fig:uniform-flux}}
\end{subfigure}
\caption{A figure with two subfigures~\cite{lienhard2020}\label{fig:2}}
\end{figure*}

%%%%%%%%%%%%%%%%%%%  end two column figure  %%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%  MORE ON MATH   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Here is an example of managing complicated math in a section or subsection heading: 
%%    the optional argument to \section will provide the pdf bookmark
%%    without losing most characters or producing warnings/errors.
%%
%% In this heading, letter u is forced to be upright with \mathrm{u}
%%
\section[More on math: u\cdot\omega=0]{More on math: $\vec{\mathrm{u}}\cdot\vec{\omega}=0$}\label{sec:moremath}

In most cases, the need for a wide equation can be eliminated by using one of the multiline equation environments defined by 
\texttt{amsmath}, such as \texttt{align}, \texttt{split}, or \texttt{multline}~\cite{amsmath}. The following equation is set with the 
\texttt{multline} environment:
\begin{multline}\label{eqn:energy}
\frac{\partial}{\partial t}\left[\rho\bigl(e + \lvert\vec{u}\rvert^2\big/2\bigr)\right]  + \nabla\cdot\left[\rho\bigl(h + \lvert\vec{u}\rvert^2\big/2 \bigr)\vec{u}\right] \\
 ={}-\nabla \cdot \vec{q} +  \rho \vec{u}\cdot\vec{g}+ \frac{\partial}{\partial x_j}\bigl(d_{ji}u_i\bigr) + \dot{Q}_v
\end{multline}
An example using \texttt{align} appears in Appendix~\ref{appendix:a}.

An experimental package for setting equations that span two columns, \texttt{asmewide.sty}, can be loaded as well, but that code may require hand-fitting around figures, tables, and page breaks. See the examples in~\cite{lienhard2022}. An alternative solution may be to set large equations into two-column-wide tables or figures. 

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:dw}
\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}

\subsection{The \texttt{newtxmath} and \texttt{unicode-math} Packages~\cite{sharpe1,robertson2023}} The \texttt{newtxmath} package, loaded by default with \pdfTeX, includes many options for mathematics, most of which can be called as options to \verb|\documentclass|. For example, the \texttt{upint} option selects upright integral signs (rather than slanted integral signs):
\begin{quote}
\verb|\documentclass[upint]{asmeconf}|. 
\end{quote}  
The option \verb|subscriptcorrection| improves the spacing of math subscripts. Math options are discussed further in the \texttt{asmeconf-template.tex} file.  The \texttt{newtxmath} package is also loaded with the \texttt{[nofontspec]} option.

To get additional symbols in bold math with \pdfTeX, use \verb|\bm{..}| from the \texttt{bm} package, which is loaded by the class. 

If using \LuaLaTeX, the math features of \texttt{unicode-math} are available.  These include commands to select a boldface, upright symbol, \verb|\symbfup{..}| or \verb|\mathbfup{..}|, to select boldface fraktur 
symbol, \verb|\symbffrak{..}| or \verb|\mathbffrak{..}|, and so on.  See the documentation of \texttt{unicode-math} for details~\cite{robertson2023}.

The \texttt{[upint]} option also works under \LuaLaTeX.

For longer passages of bold math, you can use \verb|{\mathversion{bold}..}| with either \pdfTeX\  or \LuaLaTeX: 
\verb|{\mathversion{bold} $A\otimes\mathfrak{F}$ }| gives {\mathversion{bold} $A\otimes\mathfrak{F}$}. Note that the math version must be changed \emph{before} starting math mode.


\subsection{Sans-Serif Greek Letters}
The class file also provides upright sans-serif Greek letters with \verb|\sfalpha| and similar expressions (e.g., $\sfalpha, \sfbeta, \sfgamma, \sfdelta$ \ldots ), in case they are needed. 

Under \pdfTeX\  boldface, upright, sans-serif Greek letters can be obtained with \verb|\bm{\sfalpha}|, etc.  The \texttt{newtx} package also includes options that affect whether Greek letters are upright or slanted (see that package's documentation for details).

Under \LuaLaTeX, boldface, sans-serif, upright Greek can be obtained with \verb|\sfbfalpha|, etc., or by using \verb|\symbfsfup{\alpha}|.  In the first case, the glyphs are drawn from the Lete Sans Math font, while in the second case, the glyphs are from the TeX Gyre Termes Math font.   Why are two different fonts being used? Unicode does not include medium-weight, upright, sans-serif Greek as a component of a serif font (like Termes), although it does include both upright and italic boldface Greek. However, in a sans-serif font (like Lete), Greek letters are sans-serif by default, including medium weight. (You can also invoke \verb|\symbfsfit{\alpha}| for  boldface, sans-serif, slanted type.) 

\subsubsection*{Sans-serif Math Versions} Two additional math versions, \texttt{sansbold} and \texttt{sans} are available in \texttt{asmeconf}.  The former is used by default in captions and section headings.  The latter is available in case you find a use for it. In \LuaLaTeX, both versions use the Lete Sans Math fonts. In \pdfTeX, the glyphs are from the \texttt{newtxsf} package.
  
  
\subsection{Controlling Calligraphic, Script, Fraktur, or BB Fonts}
With \pdfTeX, the \texttt{[mathalpha]} package may be loaded in the preamble~\cite{sharpe2}.\footnote{As of v1.41, the \texttt{[mathalfa]} class option has been dropped.} This package supports variety of font for calligraphic, fraktur, script, and blackboard bold fonts. For example,
\begin{center}
\verb|\usepackage[cal=euler,frak=boondox]{mathalpha}| 
\end{center}
selects the Euler font for \verb|\mathcal| and the Boondox font for \verb|\mathfrak|. Refer to the \texttt{mathalpha} documentation for details~\cite{sharpe2}.  The \texttt{[nofontspec]} option also supports \texttt{mathalpha}.

Under \LuaLaTeX, the \texttt{unicode-math} \texttt{range} function can be used to select such fonts~\cite{robertson2023}. For example, the following code in the preamble would select the Euler Math font for calligraphic, script, fraktur, and blackboard bold fonts:
\begin{quote}\raggedright
\verb|\setmathfont{Euler-Math}[|
\verb| range={cal,scr,frak,bb},|
\verb| Extension=.otf,Scale=MatchUppercase]|
\end{quote}


%%%%%%%%%%%%%%%  ADDITIONAL PACKAGE OPTIONS  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Additional Options for \NoCaseChange{\texttt{asmeconf.cls}}}
The class accepts a number of options in addition to those already described. These options are discussed next.

\subsection{Colored Hyperlinks}
ASME requires that all text be \textbf{in black} when the paper is submitted for publication.  For other uses, authors may
obtain colored hyperlinks with the [\texttt{colorlinks}] option.

\subsection{Final Column Balancing} The option \texttt{[balance]} invokes the the \texttt{flushend} package~\cite{tolusis}.
This package will attempt to give equal height to the two columns on the last page. The performance of this package is sometimes inconsistent (with odd page layout or, very rarely, errors), so use this option with caution.

\subsection{Grid-Style Author Block} The option \texttt{[grid]} invokes ASME's grid-style arrangement of author names. In the \verb|\SetAuthors{..}| command, individual author's names are recognized by the commas that separate them. (To include a comma \emph{in} a name, enclose the name in braces.) Line breaks (\verb|\\|) may be inserted into the address of \verb|\SetAffiliation{n}{address}| as needed. 

Note that ASME interprets the author order in the grid style by reading names from left-to-right in the top row, then left-to-right in each subsequent row.

\subsection{Line Numbers} The option \texttt{[lineno]} invokes the the \texttt{lineno} package~\cite{bottcher}. This option will produce line numbers in the margins. You must run \LaTeX\ \emph{twice} for proper placement of the numbers. Tables, captions, and footnotes will not be numbered.  Line numbers can be helpful for review and editing, but should not be used in your final manuscript. See the documentation of the \texttt{lineno} package for further commands to control line numbering. 

The \texttt{lineno} package is not compatible with the \texttt{flushend} package that makes final short columns the same height. Balancing is automatically disabled when this option is called. 

\subsection{Changing the Copyright Footer} The option \texttt{[nofoot]} will omit the ASME copyright from the page footer. The option \texttt{[govt]} will produce a copyright notice for authors who are employees of the U.\ S.\ Government.  
The option \texttt{[contractor]} will produce a copyright
notice for authors who are employed by a U.\ S.\ Government contractor.
The option \texttt{[somegovt]} gives a copyright notice for the case when only some authors are employees of the U.\ S.\ Government.

The footers are generated with the \texttt{fancyhdr} package~\cite{oostrum} and can be changed using the commands of that package. Only the default arrangement matches ASME's style, however.

In addition, the conference header on the title page can be omitted using the option \texttt{[nohead]}.

\subsection{Archivability:~PDF/A} In June 2022, the \LaTeX{}3 team added support for PDF/A to the \LaTeX\ kernel through the command \verb|\DocumentMetadata{..}|. This approach works with \emph{both} \pdfTeX\  and \LuaLaTeX. Note that accessible  conformance~(\texttt{a} or \texttt{UA-2} level, a.k.a.\ ``well-tagged PDF'') is still under development by the  \LaTeX3 team.

As of \texttt{asmeconf} v1.41, the legacy options \texttt{[pdf-a]}, \texttt{[pdfapart=]}, and \texttt{[pdfaconformance=]} have been dropped.

\subsection{Typewriter Font Options} This font is the sans-serif \texttt{inconsolata}. By default, the word spacing is variable, but option \texttt{[mono]} switches to monospacing. A slashed zero is the default; option \texttt{[var0]} removes the slash. Option \texttt{[hyphenate]} enables hyphenation. (The hyphenation option is not available under \LuaLaTeX\  with \texttt{fontspec}.)

\subsection{Support for Other Languages}  This package can be adapted to incorporate (or entirely use) languages other than English. See Appendix \ref{appendix:c} for details.


%%%%%%%%%%%%%%%  Nomenclature Environment  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Nomenclature Environment}
A nomenclature environment is included, as illustrated just after the abstract.  Each item in the nomenclature list is entered as \verb|\entry{symbol}{meaning}|.  Optional subheadings can be included as well: \verb|\EntryHeading{Roman letters}|.  The environment includes an optional argument for changing the space between symbols and definitions, 
\verb|\begin{nomenclature}[Xcm]|, where X is a number and cm can be replaced by any LaTeX dimensional unit: pt, in, ex, em, pc, etc. The default value is~2~em.

The title of the nomenclature can be also changed, e.g.\ \verb|\renewcommand*{\nomname}{List of Symbols}|



%%%%% Conclusions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Conclusion}
Provide a brief conclusion (3 to 4 lines).


%%%%% Acknowledgments %%%%%%%%%%%%%%%%%%%%%%%%%%%

\section*{Acknowledgments}
Place any acknowledgments here.


%%%  REFERENCES  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% Put your references into your .bib file in the usual way. Run latex once, bibtex once, then latex twice.
%% The asmeconf.bst style allows @inproceedings and @proceedings to include: 
%%		venue = {Location of Conference}, 
%%		eventdate = {Month, days},

\nocite{*}%% <=== Delete this line unless you want to typeset the entire contents of your .bib file !!

\bibliographystyle{asmeconf}  %% .bst file following ASME conference format. Do not change.
\bibliography{asmeconf-sample}%% <=== change this to the name of your bib file


%%%  APPENDICES  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\appendix

%% Note that appendices will be "numbered" A, B, C, ... etc. Use \section, not \section*
%% Equations will be numbered sequentially following those in the paper. Do not reset the equation counter.

%% Here we use the optional argument of section to control the pdf bookmark and prevent errors.
\section[The Vector Product A\times B]{The vector product $\vec{A}\times\vec{B}$}\label{appendix:a}

This brief illustration of an appendix shows the numbering of the appendix and equations. Equations are numbered
consecutively, following those in the paper. Consider $\rho \neq \textrm{fn}(p)$:
\begin{align}
\frac{d\Gamma}{dt} &{}= \frac{d}{dt} \int_{\mathcal{C}} \mathbf{u} \cdot d\mathbf{r}\\
				   &{}= \int_{\mathcal{C}} \frac{D\mathbf{u}}{Dt} \cdot d\mathbf{r} + \underbrace{\int_{\mathcal{C}} \mathbf{u}\cdot d\biggl( \frac{d\mathbf{r}}{dt}\biggr)}_{=\, 0} \\[-2pt]
                   &{}= \iint_{\mathcal{S}} \nabla \times \frac{D\mathbf{u}}{Dt}  \cdot d\mathbf{A}\\
                   &{}= \iint_{\mathcal{S}}  \nabla p \times \nabla \left( \frac{1}{\rho}\right) \cdot d\mathbf{A}
\end{align}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section[Use with LuaLaTeX]{Use with \NoCaseChange{LuaLaTeX} }\label{appendix:b}

The \LuaLaTeX\  engine is useful with \texttt{asmeconf} in at least three situations:

\begin{description}

\item[Executing lua code directly in your \LaTeX\ file.] With lua code, complicated functions can be plotted or numerical integration can be executed. An example file in the distribution demonstrates this capability~\cite{lienhard2025}. In this situation, you can use the class option \texttt{[nofontspec]} to stay with the \texttt{newtx} fonts. (This setting does not support for non-Latin alphabets.)

\item[Using complex alphabets.] With \pdfTeX, \texttt{asmeconf} supports Latin alphabets, as well as Cyrillic, Greek, and Vietnamese. With \LuaLaTeX\  with the \texttt{fontspec} package you can use non-Latin fonts available on your computer if you call the \texttt{[loadscripts]} option.\footnote{For Latin scripts (including English) under \LuaLaTeX, you \emph{must} have these OpenType fonts (\texttt{.otf}) installed (all are in TeX Live and will be present if your installation is complete and up-to-date): TeX Gyre Termes X, TeX Gyre Termes Math, TeX Gyre Heros, Inconsolatazi4, LeteSansMath, STIX Two Math. For Greek and Russian, the Noto Serif, Sans, and Mono TrueType fonts (\texttt{.ttf}) are used, and other Noto fonts are used for south and east Asian scripts. The Noto fonts are \textbf{not} currently in TeX Live (go here: \hrefurl{https://github.com/googlefonts/noto-fonts}{github.com/googlefonts/noto-fonts}).}\footnote{The \texttt{[loadscripts]} option was added in v1.42 of \texttt{asmeconf}, in order to reduce compilation time when non-Latin scripts are not needed.}   For Japanese in particular, use the class option \texttt{[japanese]}. See the example file in this distribution for more details~\cite{lienhard2021}.

\item[Producing tagged PDF.] Under \LuaLaTeX{}  with \texttt{unicode-math} (which loads by default), \texttt{asmeconf} PDF files can meet the PDF 2.0/UA-2 accessibility standard using appropriate arguments to \verb|\DocumentMetadata{..}| provided that: a) subcaptions are not used; b) any figure files meet the standard; and c) language options are used cautiously (some languages are compatible with tagging, but others currently are not). As of the Nov.~2025 released of \LaTeX{}, accessible PDF can be produced with the following settings:
\begin{quote}
	\verb|\DocumentMetadata{ | \newline
	\verb| pdfstandard = { ua-2 , a-4f },| \newline
	\verb| tagging = on }|
\end{quote}
Tagged PDF files can render accurately as HTML files (see \hrefurl{https://ngpdf.com}{ngpdf.com}). Version 1.44 of \texttt{asmeconf} includes a CSS style sheet control web appearance, \texttt{asmeconf-style.css}. 

\end{description}

For clarity, \texttt{fontspec} and \texttt{unicode-math} are automatically loaded when \texttt{asmeconf} is run under \LuaLaTeX. Those packages require that the necessary fonts are available on your computer.  If you wish to use \LuaLaTeX\  without the features of \texttt{unicode-math} and \texttt{fontspec}, use the class option \texttt{[nofontspec]}. 

Over the long-term, \LuaLaTeX\  will become the preferred engine for using \LaTeX\ (see \href{https://www.latex-project.org/news/latex2e-news/ltnews40.pdf}{\emph{LaTeX\ News}, Issue~40}). Access to \LuaLaTeX\  is different in each \LaTeX\ platform. Check the documentation for your platform to load \LuaLaTeX.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Multilingual Support}\label{appendix:c}

ASME publishes in English, but the \texttt{babel} package is loaded for 
users who may wish to include other languages. For example, an author might wish to include an appendix that provides the 
abstract in another language.

When more than one language option is included in \verb|\documentclass[..]{asmeconf}|, English will be 
set as the document's main language. (To choose a different main language, set \texttt{[main=..]}).
If no language options are given, the package defaults to English.  As examples, a passage in German is 
shown in  \selectlanguage{german}\appendixname~\ref{app:pohlhausen}\selectlanguage{english},
%\selectlanguage{french}\appendixname~\ref{app:fourier}\selectlanguage{english}, 
followed by abstracts in other languages.

The input encoding can be utf-8, as for these glyphs:
%% If you have trouble with the next line, your file may not be saved in utf-8 format. You can delete that line to resolve the issue.
\typeout{If you have trouble with the next line, your file may not be saved in utf-8 format. You can delete that line to resolve the issue. Under LuaLaTeX, you can load the fontspec will support these characters if you have the relevant systems fonts installed}%
àáâäæãåā  èéęëêēė  îïíīįì ôöòóœøōõ ûüùúū çćč ł ñń ßśš ÿ žźż.

Fonts similar to Times/Helvetica are used when Greek, Vietnamese, or selected cyrillic-alphabet languages are called as options under {\upshape\pdfTeX}. Using {\upshape\LuaLaTeX}, which loads the fontspec package, many additional scripts are available; see the supplemental notes for such usage~\cite{lienhard2021}. Possibilities include Arabic, Bengali, Chinese, Devanagari (e.g., for Hindi), Hangul (for Korean), Kana (for Japanese), and Tamil. \emph{These options require an up-to-date \LaTeX\ installation.}

The \texttt{asmeconf} class defines several switches that can be used to call languages only when certain class options have been called, as \verb|\if...\fi|: \verb|\ifScriptsLoaded|, \verb|\ifFontspecLoaded|, \verb|\ifpdftex|, and \verb|\ifJapaneseLoaded|.

The bibliography style, \texttt{asmeconf.bst}, is designed in English and aimed at \BibTeX.  

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

\begin{selectlanguage}{german}%
\section{Wärmeaustausch und Reibungswiderstand (\NoCaseChange{von} E. Pohlhausen)}\label{app:pohlhausen}
In einer strömenden Flussigkeit sind Wärmeleitung und Wärmekonvektion Vorgänge, die mit der inneren Reibung (oder Impulsleitung) und mit der Impulskonvektion große Aehnlichkeit besitzen. Mathematisch findet dies seinen Ausdruck in dem gleichartigen Bau der Differentialgleichungen, die einerseits für die Temperatur und anderseits für den Geschwindigkeitsvektor in der Flüssigkeit bestehen. Man kann daraus auf eine Beziehung
zwischen dem Wärmeaustanch und dem Reibungswiderstand schließen, die eine strömende Flüssigkeit an einem festen Körper hervorrufen. Dies ist zuerst von Prandtl ausgesprochen und durchgeführt worden, und zwar für turbulente Vorgänge, unter der vereinfachenden Annahme von Wärmequellen und -senken im Innern der Flüssigkeit~\cite{pohlhausen1921}. 
\end{selectlanguage}%



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

\end{document}

