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Pavel Danilochkin COMSOL module developer and technical writer. At City College, we would like to offer our modest attempts to introduce mechanical engineering students taking undergraduate level heat transfer course to have a first glimpse of how the finite element method may be useful. Most of the institutions are doing so on the graduate level only. In recent times, many universities, technical institutes, and colleges have adopted programs that introduce students to this relatively new and powerful tool. Universities around the world have much advanced the development of different finite element techniques to attack a wide variety of technical issues. Today, an undergraduate student with enough ingenuity can accurately simulate the complex vortices produced by the fluid flow on his or her notebook computer. That is what was meant by the qualitative content of the equations.
A theoretician of those days had to have boundless imagination in order to extract information such as vortex shedding in a fluid flow past an object from the well known Navier Stokes equations. Some fifty years ago, an undertaking of the above examples was simply not possible. With the ever increasing number crunching power of modern computing machines, it is possible today to solve and visualize complicated physical phenomena, such as wet water flow and temperature field in steam turbines, body fluid redistribution in human organs subject to unfamiliar gravitational environments, or investigate aerodynamic performance of an entire aircraft without having to setup up an overly expensive experimental lab.
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Todays expanding research and developing industry, scientists and engineers, experimentalists and theoreticians, and many other professional analysts who deal with complex mathematical analysis rely more and more on finite element method as a tool to solve insuperably difficult problems. Today, we are privileged to live in time to see this prediction begin to come true. RADI ATION MODELING Radiation in a triangular cavity 275 - i - INTRODUCTION TO COMSOL MULTIPHYSICS A MESSAGE TO THE STUDENT Dear student, Half a century ago, a great American scientist said: The next great era of awakening of human intellect may well produce a method of understanding the qualitative content of equations.
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CONDUCTI ON AND CONVECTI ON MODELI NG Laminar forced convection over an isothermal flat plate 101 Laminar forced convection over a heated flat plate 127 Laminar flow in a tube 155 Temperature development in tubes (Uniform Surface Temperature) 169 Temperature development in tubes (Uniform Surface Heat Flux) 185 Free convection of air over a vertical plate (Isothermal) 201 Free convection of air over a vertical plate (Heated) 225 Free convection of air over a horizontal cylinder (Isothermal) 249 Cross flow heat exchanger - I V. CONDUCTI ON MODELI NG WI TH CONSTANT HEAT TRANSFER COEFFI CI ENT Fin tip insulation: effect on Qf 1 Heat loss from a rod 19 Limits of the fin approximation 35 Test chamber insulation (rectangular) 55 Test chamber insulation (circular) 69 Transient cooling of a rod 85 I I I. I NTRODUCTI ON Table of Contents i A Message to the Student ii Introduction to COMSOL Multiphysics iii File Naming and Saving Conventions vii I I.
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COMSOL Multiphysics Instruction Manual COMSOL Multiphysics Instruction Manual THE CITY COLLEGE OF NEW YORK THE CITY COLLEGE OF NEW YORK MECHANICAL ENGINEERING DEPARTMENT MECHANICAL ENGINEERING DEPARTMENT ME 433: HEAT TRANSFER ME 433: HEAT TRANSFER PROFESSOR LATIF M.
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