Optimisation of plateplatefin heat exchanger design. In this case fins will greatly aid in the transfer of heat to or from the object. Pdf analytical solution for different profiles of fin with. Twodimensional modeling of steady state heat transfer. In the special case of constant cross section and constant thermal conductivity. Thus, adding a fin to an object, increases the surface area and can sometimes be an economical solution to heat transfer problems. The forming section of a plastics plant puts out a continuous sheet of plastic that is 1. Freestudy heat transfer tutorial 3 advanced studies this is the third tutorial in the series on heat transfer and covers some of the advanced theory of convection.
Mech302heat transfer homework10 solutions problem 10. Finned surfaces are commonly used in practice to enhance heat transfer in the analysis of fins, we consider steady operation with no heat generation. The product of bi and fo numbers yields the parameter bf hxpdf. There is also heat transfer around the perimeter on the top, bottom, and sides of the fin. Heat transfer problems using finite element methods. If the heat transfer coefficient is 70 wm2k, with a surface temperature of 50oc and an air temperature of 20oc, what is the heat transfer with and without the fin. The temperature distribution, fin efficiency, and fin heat transfer rate are presented for three fin profiles and a range of values of heat transfer parameters. It will provide several examples demonstrating the use of solver and goal seek tools of excel in solving problems requiring iterative processes. Optimisation of plateplatefin heat exchanger design kunpeng guo the university of manchester 2015 abstractphd thesis with increasing global energy consumption, stringent environmental protection legislation and safety regulations in industrialised nations, energy saving has been put under high priority.
Fins can be of a variety of geometryplain, wavy or interruptedand can be attached to the inside, outside or to both sides of. Solve conductiondominant heat transfer problems with convection and radiation occurring at boundaries address challenges with thermal management by analyzing the temperature distributions of components based on material properties, external heat sources, and internal heat generation for steadystate and transient problems. Problem 1,2 based on heat transfer from rectangular fin. The walls are constructed from an inner fire brick wall 25 cm. The outer surface of the insulation is exposed to cooler air at 30oc with h 60 wm2oc. Chapter 5 numerical methods in heat conduction heat transfer universitry of technology materials engineering department mae216. The tutorials are designed to bring the student to a level where he or she can solve problems involving practical heat exchangers. This book aims to give students of engineering a thorough grounding in the subject of heat transfer. Use of spreadsheets in solving heat conduction problems in fins. Fins efficiency and effectiveness the fin efficiency is defined as the ratio of the heat transfer to the fin to the heat transfer to an ideal. Heat transfer through fins introduction convection heat transfer between a hot solid surface and the surrounding colder fluid is governed by the newtons cooling law which states that the rate of convection heat transfer is directly proportional to the temperature difference between the hot surface. Heat transfer gate questions conduction, critical radius of insulation, unsteady heat transfer duration. Analytical solution for different profiles of fin with. Freestudy heat transfer tutorial 2 convection and radiation this is the second tutorial in the series on basic heat transfer theory plus some elements of advanced theory.
In the study of heat transfer, fins are surfaces that extend from an object to increase the rate. A compilation of examples for using excell in solving heat. Gradeup gate, ese, psus exam preparation,120 views 21. This study can lead to determining the parameters of a heat sink for a specific application, mainly for electronics industry. Finned surfaces are commonly used in practice to enhance heat transfer, and they often increase the rate of heat transfer from a surface severalfold. We now consider one particular example in heat transfer that involves the analysis of circular fins that are commonly used to. An excel spreadsheet can be employed to solve this problem. Forced convection heat transfer convection is the mechanism of heat transfer through a fluid in the presence of bulk fluid motion. Fins are especially important for situations where the convecting medium is air or some gas with lower h and the surface area of the object that needs to lose or gain heat is relatively small. For validation of the dtm, the heat equation is solved numerically by the. As you recall from undergraduate heat transfer, there are three basic modes of transferring heat. At this stage the student can begin to apply knowledge of mathematics and computational methods to the problems of heat transfer. A numerical model is developed by taking an enclosure, which is formed by two adjacent vertical fins and horizontal base. Finned surfaces are commonly used in practice to enhance heat transfer.
Professor emeritus of mechanical and aerospace engineering and engineering science the university of tennesse knoxville leighton e, sissom, ph. If the convecting medium is a fluid, such as water, then h will. Extended surfaces have fins attached to the primary surface on one side of a twofluid or a multifluid heat exchanger. Application of bessel equation heat transfer in a circular fin bessel type differential equations come up in many engineering applications such as heat transfer, vibrations, stress analysis and fluid mechanics. Adding a fin to an object increases the surface area and can sometimes be an economical solution to heat transfer problems. The thermal conductivity of p 2 times the thermal conductivity of q. Once the theory has been understood, well chosen examples can be used, with modification, as a template to solve more complex, or similar problems. This text is a collection of solutions to a variety of heat conduction. The solutions below will also help you solve some of the problems in bsl an abbreviation often used for this classic textbook based on the initials of its authors. Application of bessel equation heat transfer in a circular fin.
This paper focuses on the application of microsoft excel in solving heat transfer problems. Fins are the extended surface protruding from a surface or body and they are meant for increasing the heat transfer rate between the surface and the surrounding fluid by increasing heat transfer area. Convection is classified as natural or free and forced convection depending on how the fluid motion is initiated. Schaums outline of theory and problems of heat transfer second edition donald r. There is heat flow of magnitude at the lefthand side and heat flow out of magnitude at the right hand side. Fins enhance heat transfer from a surface by exposing a larger surface area to. We assume using the reynolds analogy or other approach that the heat transfer coefficient for the fin is known and has the value. For example, the consideration of the variation of thermal conductivity with temperature, the variation of the heat transfer coefficient over the. The book is comprehensive in its coverage without sacrificing the necessary theoretical details.
From a quasionedimensional point of view, this is a situation similar to that with internal heat sources, but here. To better illustrate the different methods of solving heat conduction problems, we are considering the two. Twodimensional modeling of steady state heat transfer in. A fin is a surface that extends from an object to increase the rate of heat transfer to or from the environment by increase convection. The chip is mounted in a substrate such that its side and back surfaces are insulated, while the front surface is exposed to a coolant. Ht1 introduction to engineering heat transfer these notes provide an introduction to engineering heat transfer. Fins are used in a large number of applications to increase the heat transfer from surfaces. If the convection heat transfer coefficient is 250 wm2k, determine the heat transfer rate from the air to one side of the plate when the plate is maintained at 40c.
The problems on heat transfer particularly in fins continue to be of scientific interest. For validation of the dtm, the heat equation is solved numerically by the fourthorder rungekutta method. Calculate the heat loss from the tube to the air for 10 m of the tube and the temperature drops resulting from the thermal resistances of the hot gas. Calculate the rate of heat loss through the vertical walls of a boiler furnace of size 4 m by 3 m by 3 m high. Me 375 heat transfer 4 19 problem a pin cylindrical fin has a diameter of 4 mm, a length of 5 cm, and a thermal conductivity of 200 wmk. Investigation of nonlinear problems of heat conduction in. We dont need to make this assumption, and if we were looking at the problem in detail we would solve it. Even in simple geometries, heat transfer problems cannot be solved analytically if the thermal conditionsare not sufficiently simple. Heat transfer coefficient at innear side, hhf 400 wm2oc. The heat transfer processes that occur in a heat sink are studied in this work. Forced convection heat transfer for plug flow in circular tube.
The problem of natural convection heat transfer from fin arrays with inclination is studied experimentally and theoretically to find the effect of inclination of the base of the fin array on heat transfer rate. Also, heat transfer problems can not be solved analytically if the thermal conditions are not sufficiently simple. Q chapter 10 429 and therefore r total r plastic r conv 0. Heat transfer conduction problems and solutions solved. Heat transfer exercises 5 preface preface worked examples are a necessary element to any textbook in the sciences, because they reinforce the theory i. Forced convection heat transfer for plug flow in plane slit. Analysis the problem is solved using ees, and the solution is given below. Intermediate heat transfer, a second course on heat transfer for undergraduate seniors and beginning graduate students. Please note that the origin of coordinates is placed at the tapered end of the fin for this formulation.
Our aim is to learn the principles of heat transfer so we can solve. K is of width w 5 mm on a side and of thickness t 1 mm. We also assume the convection heat transfer coefficient h to be constant. Alternatively, the rate of heat transfer from the fin could also be determined by considering heat transfer from a differential. The modeling of rectangular parallel fin heat sinks allows an analytical study. These problems are modeled by highly nonlinear differential equations which are difficult to solve exactly. Assumptions 1 heat transfer along the fin is given to. Classical heat transfer problems and problem solutions in transport phenomena. Heat transfer problems and solutions learning by solving. The temperature distribution, fin efficiency, and fin heat transfer rate are. Fins enhance heat transfer from a surface by exposing a larger surface area to convection and radiation. Conduction is the transfer of heat through a medium by virtue of a temperature gradient in the medium. Common assumptions for fins finned surfaces are commonly used in practice to enhance heat transfer in the analysis of fins, we consider steady operation with no heat generation in the fin, and we assume the thermal conductivity k of the material to remain constant. The tutorials are designed to bring the student to a level where he or she can solve problems ranging from basic level to dealing with practical heat exchangers.
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