# Measurement Of Thermophysical Properties by Laminar Flow Methods

## Descrição

In technical processes involving liquids, there is a need to be able to measure their thermophysical properties (thermal conductivity, thermal diffusivity, and specific heat) efficiently and effectively. The authors believe that conventional methods and devices for measuring thermophysical properties are not adequate for measuring liquid in flow conditions. They assert that laminar flow methods and devices provide advantages over conventional TPP measurement methods and devices for assessing liquid flow. Following a review of traditional practices, they present information about, and examples of laminar flow methods and measuring devices. Most of the references cited are from Russian research.

277 pages,
© 2001

## Table of contents:

CHAPTER ONE REVIEW OF METHODS FOR THE MEASUREMENT OF THERMOPHYSICAL PROPERTIES OF LIQUIDS

1.1 Basic Information About the Traditional Methods of Thermophysical Measurements

1.2 Methods of Thermophysical Property Measurement with Liquid Laminar Flow in a Tube

1.3 Methods of Laminar Flow, Based on the Laws of Heat Transfer in Liquid Shear Flows in the Clearance Between Moving Surfaces

1.4 Methods of Laminar Flow, Based on the Laws of Heat Transfer in Laminar Flow of a Liquid (Gas) Across a Wire

1.5 Advantages and Drawbacks of Laminar Flow Methods

CHAPTER TWO METHODS OF LAMINAR FLOW IN A MEASURING TUBE, WITH THE WALLS OF THE TEST SECTION AT CONSTANT TEMPERATURE

2.1 The Main Measuring Technique for the Determination of the Thermal Diffusivity of Liquids

2.2 Mathematical Models of Methods for the Determination of Thermal Diffusivity

i.2.2.1 The Main Calculation Euations

i.2.2.2 Simplified Relations for Liquid Thermal Diffusivity Calculations

i.2.2.3 Differentiation Method for Liquid Thermal Diffusivity Calculations

i.2.2.4 Thermal Diffusivity Measurements with Two Measuring Tubes

2.3 Thermal Diffusivity Measurement Methods Using Devices with Negative Feedback

i.2.3.1 Optimal Experimental Conditions During Thermal Diffusivity Measurements

i.2.3.2 Liquid Thermal Diffusivity Measurement Method, Providing a Given Value of the Dimensionless Temperature at the Outlet of the Mesuring Tube Test Section by Means of Liquid Volumetric Flow Rate Change

i.2.3.3 Liquid Thermal Diffusivity Measurement Method, Providing a Given Dimensionless Bulk Temperature at the Outlet of the Test Section by Means of a Test Section Length Change

2.4 Measurement Methods of Thermophysical Parameter of the Product of Dynamic Viscosity and Thermal Diffusivity

i.2.4.1 Basic Operations and Design of a Tube for Measurement of the Thermophysical Parameter μ·α

i.2.4.2 Mathematucal Model and Basic Calculating Relations to Measure the Thermophysical Parameter μ·α

2.5 Measurements Methods of Thermal Diffusivity of Liquids with Internal Heat Sources

i.2.5.1 Mathematucal Model of Measurement Method of Thermal Diffusivity of Liquids with Internal Heat Sourses

i.2.5.2 Use of Method of Differentiation for the Calculation of Liquid Thermal Diffusivities

2.6 Methods of Non-Newtonian Liquids Thermal Diffusivity Measurements

i.2.6.1 Spesial Features of the Mathematical Modeling of non-Newtonian Liquids Laminar Flows Temperature Patterns

i.2.6.2 Derivation of Calculated Formula for Determination of non-Newtonian Liquids Thermophysical Properties

i.2.6.3 Simplified Equations for the Calculation of Liquid Thermal Diffusivity

CHAPTER THREE LAMINAR FLOW METHODS BASED ON LIQUID LAMINAR FLOW IN WHICH THE WALLS OF THE TEST SECTION ARE HEATED BY AN ELECTRIC HEATER

3.1 Measuring Operations of Liquid Thermophysical Properties Determination

3.2 Methods of Thermal Conductivity and Thermal Diffusivity Determination

i.3.2.1 Calculating Equations for Thermophysical Properties of Liquids with Internal Heat Sources

i.3.2.2 Equations for Thermophysical Properties when Using Short Measuring Tubes

i.3.2.3 Optimal Conditions of Experiments for Thermal Diffusivity and Thermal Conductivity Measurements

i.3.2.4 Liquid Thermal Diffusivity and Thermal Conductivity Measurement Method, Providing a Given Value of Themperature Difference Relationship by Volumetric Flow Rate Change

3.3 Measurement Method of Thermal Conductivity and Thermophysical Parameter μ·α

i.3.3.1 Mathematical Model and Main Calculation Equations jf Measurement Method of Thermal Conductivity λ and Complex Thermophysical Parameter μ·α

i.3.3.2 Optimum Cnditions of Experiment for Thermal Conductivity λ and Complex Parameter μα Measurements

3.4 Method and Device for the Determination of Thermal Conductivity and Thermal Diffusivity, Using a Measuring Tube, on the Wall of Which Both an Electric Heater and Resistance Thermometers are Placed

i.3.4.1 The Construction of the Tube and the Main Measuring Operations for the Experimental Determination of Liquid Thermopysical Properties

i.3.4.2 Derivation of Equations for the Calculation of Thermal Diffusivity and Thermal Conductivity from Experimental Data

i.3.4.3 Choice of Optimal Mode and Parameters for Measuring Liquid Thermal Diffusivity and Thermal Conductivity

i.3.4.4 Equations for Calculating Thermal Conductivity λ and Property μ·α

i.3.4.5 Device for Measuring Thermal Diffusivity α, Thermal Conductivity λ and Thermophysical Parameter μ·α of Liquid Under Study

3.5 Method and Devices for Determining Heat Capacity, Complex Thermophysical Parameter с·ρ/μ and Internal Heat Sources W

i.3.5.1 Apparatus and Method for Determining Additional Thermophysical Properties

i.3.5.2 Equations for Calculating Heat Capacity, Complex Thermophysical Parameter с·ρ/μ and Internal Heat Source W

CHAPTER FOUR MATHEMATICAL MODEL OF METHOD AND DEVICE FOR THE INVESTIGATION OF LIQUID’S THERMOPHYSICAL PROPERTIES DEPENDENCE ON SHEAR RATE

4.1 Scheme of Measurement Device and the Main Measuring Operations for Investigation of Liquid’s Thermophysical Properties Dependence on Shear Rate

4.2 Mathematical Model Describing the Temperature Field of the Investigated Liquid Layer in the Measurement Device

i.4.2.1 Problem of Calculating the Liquid Laminar Flow Temperature Field in a Shear Flow

i.4.2.2 Basic Assumptions for Shear Flow in Clearance Between Cylinders

i.4.2.3 Calculation of the Steady State Velocity Profile in the Shear Flow of the Liquid in the Clearance between the Stationary Internal Cylinder and the Roating External Cylinder

i.4.2.4 Mathematical Model of the Liquid Temperature Field in the Clearance between Internal Cylinder and External Cylinders

4.3 Measurement Method and Device Mathematical Model Algorithms of the Desired Thermophysical Properties Calculations According to Experimental Information

i.4.3.1 Dynamic Viscosity Calculating Algorithm

i.4.3.2 Thermal Conductivity and Thermal Diffusivity Calculating Algorithms

i.4.3.3 Additional Auxiliary Calculating Formulae

4.4 Composition and Function Algorithm of the Automated System for the Investigation of the Thermophysical Properties of Liquids in Shear Flow

CHAPTER FIVE ANALYSIS OF ERROR SOURCES IN THE DETERMINATION OF THERMOPHYSICAL PROPERTIES BY LAMINAR FLOW METHODS

5.1 Analysis and Discussion of Error Sources in the Determination of Thermophysical Properties of Liquids by Laminar Flow Methods with the Use of Measuring Tubes

i.5.1.1 Error Sources, Induced by Incomplete Correspondence of Mathematical Model to Real Physical Prcesses

i.5.1.2 The Problem of Influence of the Temperature Dependence of Viscosity and Density in the Results of Liquid TPP Measurements by Laminar Flow Methods

5.2 Analysis and Discussion of Error Sources in the Investigation of the Second Diagonal Components of Liquid Thermal Conductivity and Thermal Diffusivity Tensors Dependence on Shear Rate

i.5.2.1 Sourses of Errors, Caused by Incomplete Correlation of Mathematical Model to Actual Physical in the Measuring Device

i.5.2.2 Error Sourses Which Wer Not Taken Into Consideration by the Mathematical Model of the Veasuring Device

CHAPTER SIX MEASURING DEVICES AND EXPERIMENTAL APPARATUS FOR LIQUIDS TPP INVESTIGATIONS

6.1 Experimental Apparatus for Liquid TPP Measurements with the Use of Tube Devices

i.6.1.1 Block-diagram of the Experimental Apparatus

i.6.1.2 Measuring Tubes Designs

i.6.1.3 Designs of the Bulk Temperature Meters

i.6.1.4 Hydraulic Block Design

i.6.1.5 Design and Operation of Flowmeters

6.2 Automated System for Scientific Research of the Measurement of Liquid’s TPP Dependence on Shear Rate

i.6.2.1 Structure of the Automated System for Scientific Research of Liquid's TPP

i.6.2.2 Measuring Device Design

i.6.2.3 Mating Block of the Measuring Device with the Personal Computer

i.6.2.4 System of the Outher Cylinder Rotation of the Measuring Device

CHAPTER SEVEN ESTIMATION OF ERRORS IN LIQUIDS THERMOPHYSICAL PROPERTIES MEASUREMENTS

7.1 Results of Preliminary Estimation of Measurement Errors of Liquids TPP

i.7.1.1 Results of Preliminary Estimation of Liquids' TPP Measurement Errors with Tube Measuring Device

i.7.1.2 Results of Preliminary Estimation of Errors of Liquids TPP with Shear Rate in the Clearance Between Co-axially Mounted Cylinders with Outher Cylinder Rotating

7.2 Experimental Estimations of TPP Measurements Errors in the Case of Laminar Flow Methods

i.7.2.1 Results of the Experimental Estimation Liquids TPP Measurement Errors with the Use of Tube Measuring Devices of the First, Second, Third and Fourth Types

i.7.2.2 Results of Experimental Estimation of Measurements Errors of TPP with the Use of the Measuring Devices of the Fifth Type

CHAPTER EIGHT EXAMPLES OF APPLICATION OF LAMINAR FLOW METHODS

8.1 Application of the Developed Methods and Apparatus for Experimental TPP Determination

i.8.1.1 The TPP Measurement of Acetyl Propyl Alcohol Aqueous Solutions

i.8.1.2 TPP Measurement of Tambov Agrarian Industrial Complex Sewage

i.8.1.3 Investigation of the Second Diagonal Components of Thermal Diffusivity and Thermal Conductivity Tensors Dependence on Shear Rate

8.2 Application of Developed Methods and Measuring Devices for the Control of Technological Processes and for Liquids TPP Measurement During an Experiment

i.8.2.1 Control of Sugar Solutions Concentration by the Laminar Mode Method

i.8.2.2 Molasses Solution Fermentation Technological Process Control with the Use of a Laminar Flow Method

i.8.2.3 Control of the TPP of Solutions of Polymethyl Methacrylate Prepolymer in Methylmethacrylate During a Scientific Experiment

8.3 Methods and Devices for Liquids Viscosity Experimental Determination and for Control Over the Moment of the Diazotization Reaction Termination

i.8.3.1 Method of the Liquids Viscosity Determination Based on the Transition of Laminar to Turbulent Flow

i.8.3.2 Diazotization Reaction Termination Time Control Method

Ap.l.l Application of the Green Function Method to Determine the Temperature Fields in Laminar Flows in Tubes

i.Ap.1.1.1 Temperature Fields in Liquid Laminar Flows

i.Ap.1.1.2 Heat Transfer in Laminar Flow in a Flat Tube

i.Ap.1.1.3 Heat Transfer in Laminar Flow in a Cylindrical Tube

Ap.l.2 Calculation of Temperature Pattern in Multilayer System in Form of Two Coaxially Mounted Cylinders with Liquid in Clearance between them

i.Ap.1.2.1 Use of Green Function Method for Multilayer System Temperature Pattern Calculation

i.Ap.1.2.2 Algorithm of Numerical Problem Solution of Calculation of Temperature Pattern in Multilayer System in Form of Two Coaxially Mounted Cylinders with Liquid in Clearance between them