How to reduce the space from top of page to chapter heading and from under chapter heading to top of text?

Question

The height from the top of the page is currently 3.5cm to top of chapter. I want to reduce to 1.5cm. Height from bottom of chapter is currently 1.5cm and I want to reduce to 0.5cm if possible. I have tried to resolve Questions 407843 and 28195992 and 148747 without success. I've put the code in the preamble and I'm not sure if that was correct?

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I have an example but etoolbox example is not correct and I do not know why. My book has 14 chapters and I have used in this example some of the info in the preamble of it. Btw, the bibliography that was an issue was solved, thanks to those who worked on it.

\documentclass[pdftex,11pt,a4paper]{book} % report maybe book??
\usepackage{titlesec}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{amsthm}
\usepackage{afterpage}
\usepackage{color}
\usepackage{fancyhdr}
\usepackage{float}
\usepackage{typearea}
\usepackage{titlesec}
\usepackage{graphicx}
\usepackage[all]{xy}
\usepackage{pdfpages}
\usepackage{multicol}
\usepackage{url}
\usepackage{textcomp}
\usepackage{lmodern}% http://ctan.org/pkg/lm
\usepackage{hyperref} % Needs to be last package included

\usepackage[alphabetic,initials,nobysame]{amsrefs} %must be loaded after hyperref to work properly
%\texorpdfstring{tex}{string}
\hypersetup{
    unicode=false,          % non-Latin characters in Acrobat’s bookmarks
    pdftoolbar=true,        % show Acrobat’s toolbar?
    pdfmenubar=true,        % show Acrobat’s menu?
    pdffitwindow=false,     % window fit to page when opened
    pdfstartview={FitH},    % fits the width of the page to the window
    pdftitle={Thermal Fluid Heating, A Practical Guide for the Thermal Fluid Practitioner},    % title
    pdfauthor={Geoff Senior},     % author
    pdfsubject={Thermal Fluid Heating},   % subject of the document
    pdfcreator={Geoff Senior},   % creator of the document
    pdfproducer={Geoff Senior}, % producer of the document
    pdfkeywords={Thermal Fluid Heating, Hot Oil Heating, High Temperature Oil Heating}, % list of keywords
    pdfnewwindow=true,      % links in new window
    colorlinks=true,        % false: boxed links; true: colored links
    linkcolor=black, %red,          % color of internal links      % black for print, red for electronic
    citecolor=black, %green,        % color of links to bibliography      % black for print, green for electronic
    filecolor=black, %magenta,      % color of file links      % black for print, magenta for electronic
    urlcolor=black %cyan           % color of external links      % black for print, cyan for electronic
}
% Set margins
\usepackage[inner=20mm, outer=10mm, textwidth=150mm, paperwidth=210mm, paperheight=297mm]{geometry}
\setlength{\voffset}{-1.45in}
\setlength{\textwidth}{18cm}
\setlength{\textheight}{27cm}
\setlength{\topmargin}{1.5cm}
\setlength{\headsep}{15pt} % Optional - separation between header and top of text - default is 25pt
\setlength{\footskip}{-0.25in} % Optional - separation between footer and bottom of text - default is 30pt
% Fancyhdr commands
\setlength{\headheight}{15pt}
\pagestyle{fancy}
\fancyhf{}
\makeatletter
\renewcommand{\chaptermark}[1]{\markboth{@chapapp\ \thechapter:\ #1}{}}
\makeatother
\renewcommand{\sectionmark}[1]{\markright{\thesection:\ #1}{}}
\fancyhead[LE]{\slshape \leftmark}
\fancyhead[RO]{\slshape \rightmark}
\fancyfoot[C]{\thepage}
\setlength{\parindent}{0pt}
% setting level of subsections
\setcounter{secnumdepth}{4}
\pdfminorversion=7
\usepackage{etoolbox}
%etoolbox
\makeatletter
\patchcmd{@makeschapterhead}{50\p@}{\chapheadtopskip}{}{}
\patchcmd{@makeschapterhead}{40\p@}{\chapheadbelowskip}{}{}
\makeatother
% Set new lengths
\newlength{\chapheadtopskip}\setlength{\chapheadtopskip}{20pt}
\newlength{\chapheadsep}\setlength{\chapheadsep}{40pt}
\newlength{\chapheadbelowskip}\setlength{\chapheadbelowskip}{15pt}
\newcommand{\blanknonumber}{\newpage \thispagestyle{empty}}
\makeatletter
\renewcommand{\chaptermark}[1]{\markboth{@chapapp\ \thechapter:\ #1}{}}
\makeatother
\renewcommand{\sectionmark}[1]{\markright{\thesection:\ #1}{}}
\titleformat{\chapter}[display]
{\bfseries\Huge}
{\LARGE\filright\MakeUppercase{\chaptertitlename} \Huge\thechapter}
{2ex}
{\titlerule
\vspace{1ex}%
\filright}
[\vspace{1ex}%
\titlerule]
%\frontmatter            %Set pages to roman (i, ii, ...)
\makeatletter
@openrighttrue
\makeatother
\begin{document}
\texorpdfstring{tex}{string}
\addcontentsline{toc}{chapter}{Table of Contents}
\tableofcontents
\addcontentsline{toc}{chapter}{List of Figures}
\listoffigures
\newgeometry{textwidth=150mm}
\restoregeometry
\chapter{Introduction}
\label{chapter_introduction}
\fancyhead[LE]{\slshape \leftmark}
\fancyhead[RO]{\slshape \rightmark}
\fancyfoot[C]{\thepage}
\flushbottom
The motive behind writing this book is to provide, as a guide, some practical information about thermal fluid heating systems as used in industrial heating applications. \
\chapter{Thermal Fluid Systems}
\label{chapter_Thermal Fluid Systems}
\noindent
\section{Historical}
\label{history}
There is not much that can be found regarding the history of hot oil heating, however it is  believed that its inception was as a result of Oil Companies or Road Paving Organisations (circa 1940's) wanting to heat bitumen without the use of steam, particularly so in a road making environment, away from the refinery locations where high pressure equipment was paramount.
\end{document}

Answer 1

To long for a comment …

Your mistake here is, to try to use both: Patching \@makeschapterhead and the titlesec interface to change the chapter headings. Using titlesec result in a changed definition of \@makeschapterhead, so the patch is no longer successful. You can test this, by adding an patch failure handling to your \patchcmd commands, e.g.

\makeatletter
\patchcmd{\@makeschapterhead}{50\p@}{\chapheadtopskip}{}{\errmessage{Cannot
    patch \string\@makeschapterhead\space above skip value}}
\patchcmd{\@makeschapterhead}{40\p@}{\chapheadbelowskip}{}{\errmessage{Cannot
    patch \string\@makeschapterhead\space below skip value}}
\makeatother

would result in

Cannot patch \@makeschapterhead above skip value.
<argument> ...chapterhead \space above skip value}
l.83 ...@makeschapterhead\space above skip value}}
Cannot patch @makeschapterhead below skip value.
<argument> ...chapterhead \space below skip value}
l.85 ...@makeschapterhead\space below skip value}}

So have to either remove the titlesec package and the titlesec code and use the patch from Mico's answer to the already linked question. In this case please also note, that \@makeschapterhead is the command used by \chapter* (with star) only. For \chapter (without star) you also need to patch \@makechapterhead as shown in the already linked answer. Alternatively you can remove the patch and use the titlesec interface as shown in chadoulis' answer to the already linked question.

Note that there are several other things about your code that I consider questionable. I have written some comments about this. For this reason I will not post the complete code again. A minimized complete example using titlesec would be:

\documentclass[12pt,a4paper]{book}
\usepackage{titlesec}
\titleformat{\chapter}[display]{\normalfont\Huge\bfseries}{\chaptertitlename

  \thechapter}{0.25cm}{\Huge}% see titlesec manual
\titlespacing{\chapter}{0pt}{1.5cm}{0.5cm}% see titlesec manual
\usepackage{lipsum}% for demonstration only.
\begin{document}
\chapter{Title of Chapter}
\lipsum
\end{document}

You can reduce the 1.5cm even to a negative value, if your 1.5cm are from the top of the page instead of from the start of the text area.

A minimized complete example not using titlesec but patching the class would be:

\documentclass[12pt,a4paper]{book}
\usepackage{etoolbox} % for "\patchcmd" macro
\makeatletter
% Reduce extra space between start of text area and and chapter header lines:
\patchcmd{@makechapterhead} {50\p@}{1.5cm }{}{\errmessage{Cannot patch \string@makechapterhead\space above skip value}}% for \chapter
\patchcmd{@makeschapterhead}{50\p@}{1.5cm }{}{\errmessage{Cannot patch \string@makeschapterhead\space above skip value}} % for \chapter*
% Reduce extra space between chapter header and section header lines by 50%:
\patchcmd{@makechapterhead} {40\p@}{0.5cm }{}{\errmessage{Cannot patch \string@makechapterhead\space below skip value}}% for \chapter
\patchcmd{@makeschapterhead}{40\p@}{0.5cm }{}{\errmessage{Cannot patch \string@makeschapterhead\space below skip value}} % for \chapter*
% Optionally reduce the extra space between number line and title text
\patchcmd{@makechapterhead} {20\p@}{0.25cm }{}{\errmessage{Cannot patch \string@makechapterhead\space number title skip value}}% for \chapter only
\makeatother
\usepackage{lipsum}% for demonstration only.
\begin{document} 
\chapter{Background}
\lipsum
\end{document}

Once again, the cm values could even be negative, if you would like.