Conduction heat transfer Hardcover – January 1, 1974 by Paul J. Schneider (Author) 5.0 out of 5 stars 1 rating. See all formats and editions Hide other formats. Karel et.Schneider, P. Conduction Heat Transfer, Addison-Wesley Pub. Conduction involves the transfer of heat by the interactions of atoms or molecules of a.Unsteady one and multi-dimensional heat conduction. Conduction heat transfer schneider ebook Schneider, P.I, Conduction Heat Transfer, Addison-Wesley, Reading, MA, 1955.
Heat transfer coefficient is a quantitative characteristic of convective heat transfer between a fluid medium (a fluid) and the surface (wall) flowed over by the fluid. This characteristic appears as a proportionality factor a in the Newton-Richmann relation
Conduction Heat Transfer Schneider Pdf
where is the heat flux density on the wall, Tw the wall temperature, Tt the characteristic fluid temperature, e.g., the temperature Te far from the wall in an external flow, the bulk flow temperature Tb in tubes, etc. The unit of measurement in the international system of units (SI) (see International system of units) is W/(m2K), 1 W/(m2K) = 0.86 kcal/(m2h°C) = 0.1761 Btu/(hft2°F) or 1 kcal/(m2h°C) = 1.1630 W/(m2K), 1 Btu/(hft2°F) = 5.6785 W/(m2K). The heat transfer coefficient has gained currency in calculations of convective heat transfer and in solving problems of external heat exchange between a heat conducting solid medium and its surroundings. Heat transfer coefficient depends on both the thermal properties of a medium, the hydrodynamic characteristics of its flow, and the hydrodynamic and thermal boundary conditions. Using the methods of similarity theory, the dependence of heat transfer coefficient on many factors can be represented in many cases of practical importance as compact relations between dimensionless parameters, known as similarity criteria. These relations are said to be generalized or similarity equations (formulas). The Nusselt number Nu = αl/λf or the Stanton number St = is used as a dimensionless number for heat transfer in these equations, where 1 is the characteristic dimension of the surface in the flow, the mass velocity of the fluid flow, λf and Cpf the fluid thermal conductivity and heat capacity. When solving the problems of heat conduction in a solid, the distribution of heat transfer coefficient α between the body and its surroundings is often given as a boundary condition. Here, it is useful to use a dimensionless independent parameter, the Biot number Bi = αl/λs , where λs is the thermal conductivity of a solid and 1 its characteristic dimension. The dependence of the Nu and St numbers on the Re and Pr numbers plays an essential role in heat transfer by forced convection. In the case of fully developed heat transfer in a circular tube with laminar fluid flow the Nusselt number is a constant, namely Nu = 3.66 at a constant wall temperature and 4.36 at a constant heat flux (see Tubes (single-phase heat transfer in)). In the case of free convection, the Nu number depends on the Gr and Pr numbers. When the heat capacity of the fluid varies substantially, the heat transfer coefficient is frequently determined in terms of enthalpy difference (hw – hf). The concept of heat transfer coefficient is also used in heat transfer with phase transformations in liquid (boiling, condensation). In this case the liquid temperature is characterized by the saturation temperature Ts. The order of magnitude of heat transfer coefficient for different cases of heat transfer is presented in Table 1.
Conduction Heat Transfer by Schneider, Paul J. At AbeBooks.co.uk - ISBN 10: - ISBN 13: 507 - Addison-Wesley Educational Publishers Inc - 1955 - Hardcover.
When analyzing internal heat transfer in porous bodies, i.e., convective heat transfer between a rigid matrix and a fluid permeating through it, use is often made of the volumetric heat transfer coefficient
where qv is the heat flux passing from the rigid matrix to the fluid in a unit volume of a porous body, Tw the local temperature of the matrix, and Tf the local bulk temperature of the fluid.
It should be emphasized that the constancy of α over a wide range of and ΔT (other conditions being equal) is encountered only in the case of convective heat transfer when the physical properties of fluid change only slightly during heat transfer. Under convective heat transfer in a fluid with varying properties and in boiling, heat transfer coefficient may substantially depend on and ΔT . In these cases an increase of heat flux may give rise to hazardous phenomena such as burnout (transition heat flux) and deterioration of turbulent heat transfer in tubes. If the (ΔT ) is nonlinear, it appears inappropriate to represent it in terms of the coefficient α when analyzing, for example, boiling stability.
An overall heat transfer coefficient
where Tf1 and Tf2 are the temperatures of the heating and heated liquids, is used in calculations of heat transfer between two fluids through the separating wall. The U values for the most commonly used wall configurations are determined by the formulas
for a plane multilayer wall,
for a cylindrical multilayer wall, and
for a spherical multilayer wall.
Here D1 and D2 are the internal and external diameters of the wall, D the reference diameter by which a reference heat transfer surface is determined, Si, Di, Di+1 and λi are the thickness, internal and external diameters, and the thermal conductivity of the ith layer. The first and the third terms in brackets are said to be thermal resistances of heat transfer. In order to lower them the walls are finned and various methods of heat transfer augmentation are used. The second term in brackets is said to be the thermal resistance of the wall, which may greatly increase as a result of wall contamination, such as scale and ash build-up, or poor heat transfer between the wall layers. The values of α and U for a small element of heat transfer surface are called local ones. If they do not vary greatly then, in practical calculations of heat transfer on finite-size surfaces, we use the mean values of the coefficients and the heat transfer equation
where A is the reference heat transfer surface, and (ofen mean logarithmic ) temperature drop (see Mean Temperature Difference).
Table 1. Approximate values of heat transfer coefficient
REFERENCES
Jakob, M. (1958) Heat Transfer, Wiley, New York, Chapman and Hall, London.
Schneider, P. J. (1955) Conduction Heat Transfer, Addison-Wesley Publ. Co., Cambridge.
Adiutory, E. F. (1974) The New Heat Transfer, vols. 1,2, Ventuno Press, Cincinnati.
References
- Jakob, M. (1958) Heat Transfer, Wiley, New York, Chapman and Hall, London.
- Schneider, P. J. (1955) Conduction Heat Transfer, Addison-Wesley Publ. Co., Cambridge.
- Adiutory, E. F. (1974) The New Heat Transfer, vols. 1,2, Ventuno Press, Cincinnati.
Conduction Heat Transfer Model
Conduction Heat Transfer Schneider Motor
It was an engineering laboratory report on heat conduction in metals and non-metals
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Executive Summary
Thermal conducting or heat conduction is an important subject under the broad topic of heat transfer, and it mainly coves all phases of materials, that is, gases, liquids and solids. In more specific terms, thermal conductivity refers to the process through which collision and diffusion of microscopic particles or quasi-particles occur within a material, resulting in the transfer of internal energy due to thermal gradient. According to the P607 Climate and Energy Lecture 4(n.d) and the Physics classroom (2014), the internal energy is a combination of the microscopic potential and kinetic energy, which gets disorganized during the conduction process. Thermal conduction is also defined by parameters referred to as thermal coefficients, and these are usually determined experimentally through diverse laboratory tests. This report covers an investigation of three techniques of experimentally finding thermal coefficients of materials and summarize. The procedures followed in performing the experiment are highlighted, and the tests’ advantages and disadvantages given. A case study of a poor heat-conducting material that has been tested for its thermal conductivity values is also examined and the case study findings reviewed. The experimental computations or calculations are also presented in this report.
Introduction
Heat conduction is one of the heat transfer mechanisms which smooth temperature or thermal gradient (QPedia, n.d, Spring, 2008). The material heat transfer coefficients are vital parameters as far as heat transfer through conduction is concerned, since the characteristically define the conduction properties of a given material. Kurganov (2011) and Jakob (1958) say that the heat transfer coefficient has is a significant factor in addressing calculations and problems related to the external heat exchange between solid medium that conducts heat and its surroundings. It is a material characteristic that distinguishes between good heat conductors and poor heat conductors as well as determining different the different conductivities of conductive materials (Schneider, 1955). It is worth noting that there exist numerous means of determining the conduction coefficients, and this is the main concern of this experiment.
Theory for Experiment 1
The value of the thermal conductivity coefficient can also be obtained from the expression;
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where Q is the power, Ri is the inner radius l temperature, Ro is the outer radius, L is the length and Ti is the preceding temperature while To is the succeeding temperature recorded.
Theory for Experiment 2
The following are the parameters used in computing the heat transfer coefficient, each denoted by its respective letter: H is the total heat emitted, TA is the steady state temperature at disc A, TB is the steady state temperature at disc B, TC is the steady state temperature at disc C, V=potential difference across the element, I=the amperage of current, hs is the heat energy flowing through the specimen K is the thermal conductivity coefficient, t is the thickness, r is the radius of the disc, while aA, aB, aC, aS, are the exposed surface areas of discs A, B , C, and S. The energy e, emitted from each exposed unit area in Joules, is related to the total heat emitted H as shown in the following relation:
0001
This equation is derived from the mathematical integration of the energy equation as shown by Knudsen, Hottel, Sarofim, Wankat and Knaebel (1997) and Venkanna (2010), who also show mathematically that the heat-transfer coefficient is a function of temperature gradients.
The heat supplied to the heating element is the given by 0013 QUOTE 0001 001400010015 , the product of the potential difference and the amperage is equivalent to the power supplied to the heater (Adiutory, 1974 and Alifanov, Artioukhine and Rumyantsev, 1995). Therefore, it is seen that from the two expressions, the following equation of energy is obtained:
0001
Rearranging this equation to make K the subject of the expression yields the following equation:
0001
Assumptions
The heat transfer between an object and its surroundings depends on the exposed area of the object and the temperature difference between the two for all the specimen discs.
The conditions of equilibrium are met and the temperature of the specimen S is the mean temperature of the discs A and B.
Procedure for Experiment 1
The spacing between the output probes, the disc and the thickness was measured and recorded. The output probes leads were then attached to the numbered probes, and it was ensured that the water was flowing on the heater to a low power of about 5 watts. All the temperatures were recorded once T1 was fairly stable. The power was increased to 15 watts, and the recordings repeated, and this was done for 20 watts too, after giving time for stabilization. The power was then turned off, and water allowed to flow for 5 minutes before being turned off.
Procedure for Experiment 1
The sample material to be tested was prepared in the form of a thin disc of the same diameter as the copper discs that constituted the apparatus. It was ensured that the disc was flat and smooth for good thermal contact to be achieved before the thicknesses and the diameters of the discs labeled A, B, C and the specimen S were measured. The discs and the heater were wiped clean of dust, and placed in the frame in the following order: disc A, specimen S, disc B, heater disc C. Before the clamp screw was tightened to firmly hold the discs, it was certified that all the thermometer holes were pointing in the upward direction, and then, a small quantity of glycerin was placed in each thermometer hole, followed by the thermometer. The heater terminals were then connected to a 6V power supply via a rheostat and an ampere, while a voltmeter was connected across the heater terminals. For the purposes of measuring the ambient temperature, a fourth thermometer was placed fairly close to the apparatus, followed by the connection of the electrical circuit, where the current was allowed to flow through the heater, and the apparatus left to achieve equilibrium: all the readings were then taken and recorded.
Other Methods of Experimentally Finding Thermal Coefficients
The Two-Phase Thermosyphons Method
This is one of the methods used in obtaining heat conduction coefficients, and it entails measuring the temperature variation for small material blocks with time. According to Milanez and Mantelli (2004), aluminum blocks are polished, painted black and then tested for temperature and heat transfer coefficients in an enclosure system. The temperature distribution test entails obtaining the temperature of different points of the enclosure control volume dimensionally designed in parallelepiped form using thermocouples. On the other hand, the measurement of the heat transfer coefficients entails measuring the heat flux distribution inside the cavity of the enclosure using the metallic blocks. Mathematical expressions that relate the mass of the blocks and their specific heat capacities are then applied to compute the coefficients of heat transfer.
Procedure for the Two-Phase Thermosyphons Method
Some sheets of mild steel with the desired experimental dimensions, preferably 0.38m x 0.48m x 0.61m, are arranged into a rectangular enclosure. This is followed by attaching four pairs of thermosyphons to the inner side of the enclosure side walls so that these side walls serve as fins that assist in dissipating the heat from the thermosyphon condensers. The evaporators of the thermosyphon are situated inside a combustion chamber and tilted at 45° below the enclosure. At the back and the front of the enclosure, two metal sheets are riveted, and the enclosure walls and thermosyphons are wrapped with an insulating blanket of glass wool, with some mild steel sheets that are placed on the external side being used for the purpose of protecting this blanket. The enclosure is completed by a front door that comprises of metal sheets which sandwiches glass wool, with an inspection glass window being located at the center of the front door. With this setup, the transient and steady state temperatures are measured by the thermocouples and then applied to compute the heat conduction coefficients.
Advantages and Disadvantages
The advantages of this method include low thermal resistance and uniformity in temperature distribution. The disadvantages constitute concentrating more on the radiation and convective coefficients than on conductivity coefficients.
Inverse Heat Conduction Iterative Technique
The other method is the inverse heat conduction iterative technique commonly used in quenching process, where an iterative regularization algorithm is used to solve the problem (Felde, Réti, Sarmiento, Smoljan and Deus, n.d). This method relies on the parameters that govern temperature distribution patterns with regard to a homogeneous isotropic domain that constitutes constant material characteristics. The heat transfer coefficient is then predicted iteratively as a function of surface temperature using software called SQintegra. The data needed for this method include temperature-time>