This document discusses natural convection, including:
- The physical mechanism of natural convection involving buoyancy forces and density differences.
- Deriving the governing equations and introducing the dimensionless Grashof number.
- Evaluating the Nusselt number for natural convection over vertical, horizontal, and inclined plates as well as cylinders and spheres.
- Examining natural convection from finned surfaces and determining the optimum fin spacing.
- Analyzing natural convection inside enclosures such as double-pane windows.
- Considering combined natural and forced convection, and assessing the relative importance of each mode.
The document discusses internal forced convection in circular pipes. It covers topics like laminar and turbulent flow, hydrodynamic and thermal entry lengths, constant surface temperature and constant surface heat flux conditions, and the fully developed region. It provides equations for average velocity, Reynolds number, Nusselt number, and logarithmic mean temperature difference. Analytic relations are given for velocity profile, pressure drop, and heat transfer coefficients in fully developed laminar flow.
External forced convection involves fluid flow over solid surfaces. Key topics covered include drag and heat transfer mechanisms of friction and pressure drag, flow over flat plates where correlations are developed for friction coefficient and heat transfer coefficient as a function of Reynolds number, and flow over cylinders, spheres, and tube banks where empirical correlations describe the variations in drag and heat transfer with Reynolds number and surface characteristics.
This document discusses natural convection, beginning with defining natural convection and examining the physical mechanisms that drive it. It then derives the governing equations for natural convection by considering forces, introduces the dimensionless Grashof and Rayleigh numbers, and evaluates the Nusselt number for different surface geometries. It also examines natural convection in enclosures and combined natural and forced convection. The objectives are to understand natural convection fundamentals and derive correlations to evaluate heat transfer.
The document discusses heat exchangers, including:
- Different types of heat exchangers are described such as compact, cross-flow, shell-and-tube, plate-and-frame, and regenerative.
- Methods for analyzing heat exchangers are presented, including calculating the overall heat transfer coefficient, log mean temperature difference (LMTD) method, and effectiveness-NTU method.
- The LMTD method allows determining the required heat exchanger size given inlet/outlet temperatures and flow rates, while the effectiveness-NTU method allows determining outlet temperatures for a given heat exchanger.
This chapter discusses heat conduction through plane walls, cylinders, spheres, and multilayer geometries under steady conditions. It introduces the concept of thermal resistance networks to model conduction and convection resistances. Contact resistance is analyzed, and applications like insulation and fins are discussed. Fins enhance heat transfer by increasing surface area, and the fin equation models temperature variation along a fin.
This document discusses cryocoolers, including what they are, their classification, and an overview of Joule-Thomson cryocoolers. Cryocoolers are mechanical devices that generate low temperatures through gas compression and expansion in a closed cycle. They consist of a compressor, heat exchanger, and expander. Joule-Thomson cryocoolers use compression, expansion through a valve, and counterflow heat exchange to produce temperatures as low as 77K or 4.2K for applications such as cooling sensors, electronics, and liquefying natural gas.
The document discusses internal forced convection in circular pipes. It covers topics like laminar and turbulent flow, hydrodynamic and thermal entry lengths, constant surface temperature and constant surface heat flux conditions, and the fully developed region. It provides equations for average velocity, Reynolds number, Nusselt number, and logarithmic mean temperature difference. Analytic relations are given for velocity profile, pressure drop, and heat transfer coefficients in fully developed laminar flow.
External forced convection involves fluid flow over solid surfaces. Key topics covered include drag and heat transfer mechanisms of friction and pressure drag, flow over flat plates where correlations are developed for friction coefficient and heat transfer coefficient as a function of Reynolds number, and flow over cylinders, spheres, and tube banks where empirical correlations describe the variations in drag and heat transfer with Reynolds number and surface characteristics.
This document discusses natural convection, beginning with defining natural convection and examining the physical mechanisms that drive it. It then derives the governing equations for natural convection by considering forces, introduces the dimensionless Grashof and Rayleigh numbers, and evaluates the Nusselt number for different surface geometries. It also examines natural convection in enclosures and combined natural and forced convection. The objectives are to understand natural convection fundamentals and derive correlations to evaluate heat transfer.
The document discusses heat exchangers, including:
- Different types of heat exchangers are described such as compact, cross-flow, shell-and-tube, plate-and-frame, and regenerative.
- Methods for analyzing heat exchangers are presented, including calculating the overall heat transfer coefficient, log mean temperature difference (LMTD) method, and effectiveness-NTU method.
- The LMTD method allows determining the required heat exchanger size given inlet/outlet temperatures and flow rates, while the effectiveness-NTU method allows determining outlet temperatures for a given heat exchanger.
This chapter discusses heat conduction through plane walls, cylinders, spheres, and multilayer geometries under steady conditions. It introduces the concept of thermal resistance networks to model conduction and convection resistances. Contact resistance is analyzed, and applications like insulation and fins are discussed. Fins enhance heat transfer by increasing surface area, and the fin equation models temperature variation along a fin.
This document discusses cryocoolers, including what they are, their classification, and an overview of Joule-Thomson cryocoolers. Cryocoolers are mechanical devices that generate low temperatures through gas compression and expansion in a closed cycle. They consist of a compressor, heat exchanger, and expander. Joule-Thomson cryocoolers use compression, expansion through a valve, and counterflow heat exchange to produce temperatures as low as 77K or 4.2K for applications such as cooling sensors, electronics, and liquefying natural gas.
1) The chapter discusses heat conduction and the governing equation for one-dimensional, steady-state heat conduction through a plane wall.
2) It derives the transient, one-dimensional heat conduction equations for plane walls, long cylinders, and spheres. These equations can be simplified for steady-state and cases without heat generation.
3) The chapter also covers boundary and initial conditions like specified temperature, heat flux, convection, radiation, and interfaces. Governing equations are developed for multidimensional and transient heat conduction problems.
The document discusses heat exchangers, including:
- Different types of heat exchangers are described such as compact, cross-flow, shell-and-tube, plate and frame, and regenerative.
- Methods for analyzing heat exchangers are presented, including calculating the overall heat transfer coefficient, log mean temperature difference (LMTD) method, and effectiveness-NTU method.
- The LMTD method is used to determine the required heat exchanger size given inlet/outlet temperatures and flow rates, while the effectiveness-NTU method determines outlet temperatures for a given heat exchanger.
This document discusses internal forced convection in pipes and tubes. It covers topics such as:
1) Defining average velocity and temperature for internal flows and how they differ from external flows.
2) Analyzing fully developed laminar and turbulent flow regimes using empirical relations for friction factor and Nusselt number.
3) Discussing developing flow and entrance regions and providing correlations for estimating hydrodynamic and thermal entry lengths.
4) Thermal analysis methods including constant surface temperature and constant heat flux conditions, and using the logarithmic mean temperature difference approach.
This document provides an introduction to heat transfer and thermodynamics concepts. It discusses how heat transfer is related to thermodynamics and distinguishes between different forms of energy. The three main modes of heat transfer are conduction, convection and radiation. Heat is defined as the transfer of energy between two systems due to a temperature difference, and will flow from the higher temperature object to the lower temperature one. The document provides objectives and outlines concepts like thermal energy, mechanisms of heat transfer, Fourier's law of conduction and applications of heat transfer.
This document discusses two-phase flow boiling in small channels. It begins with an introduction and classification of boiling as pool or flow boiling. Pool boiling is described along with the boiling curve and common correlations. Flow boiling is then discussed, noting it can be external or internal. Internal flow boiling, or two-phase flow, is the focus. Common flow boiling regimes and the challenges modeling microchannels are outlined. The document then presents the annular flow model for microchannels, including assumptions, parameters, equations, and results showing improved accuracy over empirical correlations. In conclusion, the annular flow model is shown to better capture heat transfer trends in microchannels with low error compared to other correlations.
Here are the key steps to solve this problem:
1. Draw a schematic of the system and define the parameters. You have a pipe with water flowing through it at a rate of 0.15 kg/s. The inlet temperature is 20°C and desired outlet temperature is 50°C.
2. Write the energy balance equation:
Rate of heat transfer into the water = Rate of increase of thermal energy of water
Q = mCpΔT
Where:
Q = Rate of heat transfer (W)
m = Mass flow rate (0.15 kg/s)
Cp = Specific heat of water (4.18 kJ/kg-K)
ΔT = Increase in
This document discusses natural convection, including definitions, examples, theory, and an experimental setup. Natural convection is the transfer of heat by the movement of a fluid due to density differences from temperature gradients, without any external forcing. Examples given include boiling water and radiators. The document outlines the theory of natural convection over a vertical hot plate, defining terms like the Grashof number and buoyancy force. It then describes an experimental apparatus used to study heat transfer over different surfaces like flat, finned, and pinned plates.
This document discusses boiling and condensation processes. It defines boiling as a liquid to vapor phase change and condensation as a vapor to liquid phase change. The document describes different types of boiling including nucleate, critical heat flux, transition, and film boiling. It also discusses pool boiling and flow boiling. For condensation, it covers film condensation and dropwise condensation. The key applications of boiling and condensation are in heat exchangers and refrigeration systems.
Introduction to convection
The dimensionless number and its physical significance
Similarity parameters from the differential equation
Dimensional analysis approach and its application
Numerical on Dimensional analysis approach
Review of Navier-Stokes equation
This document discusses the overall heat transfer coefficient (U-value), which measures the ability of multiple conductive and convective barriers to transfer heat. It is influenced by the thickness and conductivity of materials transferring heat. The document provides an equation relating heat transfer rate, surface area, and U-value. It lists common convective heat transfer coefficients for fluids like water and steam. Finally, it calculates the U-value for a single plate heat exchanger using different wall materials like polypropylene, steel, and aluminum.
Understand the physical mechanism of convection and its classification.
Visualize the development of velocity and thermal boundary layers during flow over surfaces.
Gain a working knowledge of the dimensionless Reynolds, Prandtl, and Nusselt numbers.
Distinguish between laminar and turbulent flows, and gain an understanding of the mechanisms of momentum and heat transfer in turbulent flow.
Derive the differential equations that govern convection on the basis of mass, momentum, and energy balances, and solve these equations for some simple cases such as laminar flow over a flat plate.
Non dimensionalize the convection equations and obtain the functional forms of friction and heat transfer coefficients.
Use analogies between momentum and heat transfer, and determine heat transfer coefficient from knowledge of friction coefficient.
HEAT EXCHANGERS. Heat exchangers are devices that facilitate the exchange of heat between two fluids that are at different temperature while keeping them from mixing with each other.
2. Double Pipe Heat Exchangers
3. A typical double pipe heat exchanger basically consists of a tube or pipe fixed concentrically inside a larger pipe or tube They are used when flow rates of the fluids and the heat duty are small (less than 5 kW) These are simple to construct, but may require a lot of physical space to achieve the desired heat transfer area.
4. Double-pipe exchangers is the generic term covering a range of jacketed 'U' tube exchangers normally operating in countercurrent flow of two types which is true double pipes and multitubular hairpins. One fluid flows through the smaller pipe while the other fluid flows through the annular space between the two pipes. Two types of flow arrangement: Parallel flow Counter flow
5. • The fluids may be separated by a plane wall but more commonly by a concentric tube (double pipe) arrangement shown in fig. If both the fluids move in the same direction, the arrangement is called a parallel flow type. In the counter flow arrangement the fluids move in parallel but opposite directions. In a double pipe heat exchanger, either the hot or cold fluid occupies the annular space and the other fluid moves through the inner pipe. The method of solving the problem using logarithmic mean temperature difference is typical and more iteration must be done. So it takes more time for the problem to solve. Therefore another method is practiced for solving this type of problems. This method is known as Effectiveness and Number of Transfer Units or simply ε-NTU method.“Effectiveness of heat exchangers is defined as actual heat transfer rate by maximum possible heat transfer rate”.The LMTD method may be applied to design problems for which the fluid flow rates and inlet temperatures, as well as a desired outlet temperature, are prescribed.
6. Application of Double Pipe Heat Exchanger Pasteurization or sterilization of food and bioproducts Condensers and evaporators of air conditioners Radiators for internal combustion engines Charge air coolers and intercoolers for cooling supercharged engine intake air of diesel engines.
Heat exchangers are devices that transfer heat between two fluids to control the temperature of one fluid. There are various types of heat exchangers that differ based on their flow arrangement, surface compactness, construction technique, and whether they use direct or indirect contact between fluids. Common examples include shell and tube heat exchangers, which contain multiple tubes in a shell, and plate heat exchangers, which use metal plates to transfer heat. Coaxial heat exchangers consist of an inner corrugated tube within an outer tube to efficiently transfer heat between fluids flowing separately within the tubes.
This document discusses the advantages of considering compact heat exchangers like plate-and-frame exchangers early in the process design stage. Plate-and-frame exchangers can be significantly smaller than traditional shell-and-tube exchangers while meeting the same heat transfer needs. Specifying design requirements without considering the characteristics of different exchanger types can lead to oversized and more expensive designs. Charts are provided to help estimate the required area of plate-and-frame exchangers for preliminary sizing.
This document provides an overview of topics related to heat and mass transfer, including:
- Fins and their applications (Unit I)
- Convection boundary layer concepts including velocity and thermal boundary layers (Unit II)
- Heat exchangers including concentric tube, cross flow, and shell and tube designs (Unit III)
- Boiling and condensation processes including boiling curves and regimes (Unit IV)
- Mass transfer concepts and analogies to heat transfer including diffusion, convection, and concentration boundary layers (Unit V)
It defines key terms and concepts for each topic and provides illustrations of processes like boundary layer development, boiling curves, and mass transfer mechanisms like diffusion and convection.
The document discusses heat exchangers, which transfer heat from one medium to another. It classifies heat exchangers based on their processes, fluid motion direction, mechanical design, and physical state of fluids. It then describes several common types of heat exchangers - shell and tube, plate, adiabatic wheel, plate fin, and pillow plate. It notes that shell and tube exchangers use tubes to transfer heat between two fluids, while plate exchangers use thin stacked plates. Heat exchangers have applications in engines, industries like oil/gas and chemicals, power generation, and HVAC systems like air conditioners and furnaces.
Heat can be transferred through three mechanisms: conduction, convection, and radiation. Conduction involves the transfer of heat between objects in direct contact through collisions of molecules. Convection involves the transfer of heat by the movement of fluids like gases and liquids. Radiation involves the emission and absorption of electromagnetic waves and can occur through a vacuum. The rate of heat transfer by conduction follows Fourier's Law and depends on factors like thermal conductivity, area, and temperature difference. Materials with high thermal conductivity like metals are good conductors while materials with low conductivity like wood and air are good insulators. Radiation transfer follows the Stefan-Boltzmann law and depends on emissivity, area, and the temperature difference between objects.
The document summarizes natural convection, including:
1) The physical mechanism of natural convection involves buoyancy forces causing fluid motion and heat transfer when a fluid is heated from a surface.
2) The governing equations for natural convection involve the Grashof number, which represents the relative strength of buoyancy and viscous forces.
3) Heat transfer correlations for natural convection depend on geometry and orientation, and are expressed in terms of the Rayleigh number and Nusselt number.
This document discusses forced convection, including:
1) It introduces key concepts in convection including boundary layers, dimensionless parameters like Reynolds and Nusselt numbers, and classifications of convection.
2) It discusses physical mechanisms of convection like development of velocity and thermal boundary layers for external flows over flat plates and cylinders/spheres.
3) It provides empirical correlations to calculate heat transfer coefficients and Nusselt numbers for different flows.
1) The chapter discusses heat conduction and the governing equation for one-dimensional, steady-state heat conduction through a plane wall.
2) It derives the transient, one-dimensional heat conduction equations for plane walls, long cylinders, and spheres. These equations can be simplified for steady-state and cases without heat generation.
3) The chapter also covers boundary and initial conditions like specified temperature, heat flux, convection, radiation, and interfaces. Governing equations are developed for multidimensional and transient heat conduction problems.
The document discusses heat exchangers, including:
- Different types of heat exchangers are described such as compact, cross-flow, shell-and-tube, plate and frame, and regenerative.
- Methods for analyzing heat exchangers are presented, including calculating the overall heat transfer coefficient, log mean temperature difference (LMTD) method, and effectiveness-NTU method.
- The LMTD method is used to determine the required heat exchanger size given inlet/outlet temperatures and flow rates, while the effectiveness-NTU method determines outlet temperatures for a given heat exchanger.
This document discusses internal forced convection in pipes and tubes. It covers topics such as:
1) Defining average velocity and temperature for internal flows and how they differ from external flows.
2) Analyzing fully developed laminar and turbulent flow regimes using empirical relations for friction factor and Nusselt number.
3) Discussing developing flow and entrance regions and providing correlations for estimating hydrodynamic and thermal entry lengths.
4) Thermal analysis methods including constant surface temperature and constant heat flux conditions, and using the logarithmic mean temperature difference approach.
This document provides an introduction to heat transfer and thermodynamics concepts. It discusses how heat transfer is related to thermodynamics and distinguishes between different forms of energy. The three main modes of heat transfer are conduction, convection and radiation. Heat is defined as the transfer of energy between two systems due to a temperature difference, and will flow from the higher temperature object to the lower temperature one. The document provides objectives and outlines concepts like thermal energy, mechanisms of heat transfer, Fourier's law of conduction and applications of heat transfer.
This document discusses two-phase flow boiling in small channels. It begins with an introduction and classification of boiling as pool or flow boiling. Pool boiling is described along with the boiling curve and common correlations. Flow boiling is then discussed, noting it can be external or internal. Internal flow boiling, or two-phase flow, is the focus. Common flow boiling regimes and the challenges modeling microchannels are outlined. The document then presents the annular flow model for microchannels, including assumptions, parameters, equations, and results showing improved accuracy over empirical correlations. In conclusion, the annular flow model is shown to better capture heat transfer trends in microchannels with low error compared to other correlations.
Here are the key steps to solve this problem:
1. Draw a schematic of the system and define the parameters. You have a pipe with water flowing through it at a rate of 0.15 kg/s. The inlet temperature is 20°C and desired outlet temperature is 50°C.
2. Write the energy balance equation:
Rate of heat transfer into the water = Rate of increase of thermal energy of water
Q = mCpΔT
Where:
Q = Rate of heat transfer (W)
m = Mass flow rate (0.15 kg/s)
Cp = Specific heat of water (4.18 kJ/kg-K)
ΔT = Increase in
This document discusses natural convection, including definitions, examples, theory, and an experimental setup. Natural convection is the transfer of heat by the movement of a fluid due to density differences from temperature gradients, without any external forcing. Examples given include boiling water and radiators. The document outlines the theory of natural convection over a vertical hot plate, defining terms like the Grashof number and buoyancy force. It then describes an experimental apparatus used to study heat transfer over different surfaces like flat, finned, and pinned plates.
This document discusses boiling and condensation processes. It defines boiling as a liquid to vapor phase change and condensation as a vapor to liquid phase change. The document describes different types of boiling including nucleate, critical heat flux, transition, and film boiling. It also discusses pool boiling and flow boiling. For condensation, it covers film condensation and dropwise condensation. The key applications of boiling and condensation are in heat exchangers and refrigeration systems.
Introduction to convection
The dimensionless number and its physical significance
Similarity parameters from the differential equation
Dimensional analysis approach and its application
Numerical on Dimensional analysis approach
Review of Navier-Stokes equation
This document discusses the overall heat transfer coefficient (U-value), which measures the ability of multiple conductive and convective barriers to transfer heat. It is influenced by the thickness and conductivity of materials transferring heat. The document provides an equation relating heat transfer rate, surface area, and U-value. It lists common convective heat transfer coefficients for fluids like water and steam. Finally, it calculates the U-value for a single plate heat exchanger using different wall materials like polypropylene, steel, and aluminum.
Understand the physical mechanism of convection and its classification.
Visualize the development of velocity and thermal boundary layers during flow over surfaces.
Gain a working knowledge of the dimensionless Reynolds, Prandtl, and Nusselt numbers.
Distinguish between laminar and turbulent flows, and gain an understanding of the mechanisms of momentum and heat transfer in turbulent flow.
Derive the differential equations that govern convection on the basis of mass, momentum, and energy balances, and solve these equations for some simple cases such as laminar flow over a flat plate.
Non dimensionalize the convection equations and obtain the functional forms of friction and heat transfer coefficients.
Use analogies between momentum and heat transfer, and determine heat transfer coefficient from knowledge of friction coefficient.
HEAT EXCHANGERS. Heat exchangers are devices that facilitate the exchange of heat between two fluids that are at different temperature while keeping them from mixing with each other.
2. Double Pipe Heat Exchangers
3. A typical double pipe heat exchanger basically consists of a tube or pipe fixed concentrically inside a larger pipe or tube They are used when flow rates of the fluids and the heat duty are small (less than 5 kW) These are simple to construct, but may require a lot of physical space to achieve the desired heat transfer area.
4. Double-pipe exchangers is the generic term covering a range of jacketed 'U' tube exchangers normally operating in countercurrent flow of two types which is true double pipes and multitubular hairpins. One fluid flows through the smaller pipe while the other fluid flows through the annular space between the two pipes. Two types of flow arrangement: Parallel flow Counter flow
5. • The fluids may be separated by a plane wall but more commonly by a concentric tube (double pipe) arrangement shown in fig. If both the fluids move in the same direction, the arrangement is called a parallel flow type. In the counter flow arrangement the fluids move in parallel but opposite directions. In a double pipe heat exchanger, either the hot or cold fluid occupies the annular space and the other fluid moves through the inner pipe. The method of solving the problem using logarithmic mean temperature difference is typical and more iteration must be done. So it takes more time for the problem to solve. Therefore another method is practiced for solving this type of problems. This method is known as Effectiveness and Number of Transfer Units or simply ε-NTU method.“Effectiveness of heat exchangers is defined as actual heat transfer rate by maximum possible heat transfer rate”.The LMTD method may be applied to design problems for which the fluid flow rates and inlet temperatures, as well as a desired outlet temperature, are prescribed.
6. Application of Double Pipe Heat Exchanger Pasteurization or sterilization of food and bioproducts Condensers and evaporators of air conditioners Radiators for internal combustion engines Charge air coolers and intercoolers for cooling supercharged engine intake air of diesel engines.
Heat exchangers are devices that transfer heat between two fluids to control the temperature of one fluid. There are various types of heat exchangers that differ based on their flow arrangement, surface compactness, construction technique, and whether they use direct or indirect contact between fluids. Common examples include shell and tube heat exchangers, which contain multiple tubes in a shell, and plate heat exchangers, which use metal plates to transfer heat. Coaxial heat exchangers consist of an inner corrugated tube within an outer tube to efficiently transfer heat between fluids flowing separately within the tubes.
This document discusses the advantages of considering compact heat exchangers like plate-and-frame exchangers early in the process design stage. Plate-and-frame exchangers can be significantly smaller than traditional shell-and-tube exchangers while meeting the same heat transfer needs. Specifying design requirements without considering the characteristics of different exchanger types can lead to oversized and more expensive designs. Charts are provided to help estimate the required area of plate-and-frame exchangers for preliminary sizing.
This document provides an overview of topics related to heat and mass transfer, including:
- Fins and their applications (Unit I)
- Convection boundary layer concepts including velocity and thermal boundary layers (Unit II)
- Heat exchangers including concentric tube, cross flow, and shell and tube designs (Unit III)
- Boiling and condensation processes including boiling curves and regimes (Unit IV)
- Mass transfer concepts and analogies to heat transfer including diffusion, convection, and concentration boundary layers (Unit V)
It defines key terms and concepts for each topic and provides illustrations of processes like boundary layer development, boiling curves, and mass transfer mechanisms like diffusion and convection.
The document discusses heat exchangers, which transfer heat from one medium to another. It classifies heat exchangers based on their processes, fluid motion direction, mechanical design, and physical state of fluids. It then describes several common types of heat exchangers - shell and tube, plate, adiabatic wheel, plate fin, and pillow plate. It notes that shell and tube exchangers use tubes to transfer heat between two fluids, while plate exchangers use thin stacked plates. Heat exchangers have applications in engines, industries like oil/gas and chemicals, power generation, and HVAC systems like air conditioners and furnaces.
Heat can be transferred through three mechanisms: conduction, convection, and radiation. Conduction involves the transfer of heat between objects in direct contact through collisions of molecules. Convection involves the transfer of heat by the movement of fluids like gases and liquids. Radiation involves the emission and absorption of electromagnetic waves and can occur through a vacuum. The rate of heat transfer by conduction follows Fourier's Law and depends on factors like thermal conductivity, area, and temperature difference. Materials with high thermal conductivity like metals are good conductors while materials with low conductivity like wood and air are good insulators. Radiation transfer follows the Stefan-Boltzmann law and depends on emissivity, area, and the temperature difference between objects.
The document summarizes natural convection, including:
1) The physical mechanism of natural convection involves buoyancy forces causing fluid motion and heat transfer when a fluid is heated from a surface.
2) The governing equations for natural convection involve the Grashof number, which represents the relative strength of buoyancy and viscous forces.
3) Heat transfer correlations for natural convection depend on geometry and orientation, and are expressed in terms of the Rayleigh number and Nusselt number.
This document discusses forced convection, including:
1) It introduces key concepts in convection including boundary layers, dimensionless parameters like Reynolds and Nusselt numbers, and classifications of convection.
2) It discusses physical mechanisms of convection like development of velocity and thermal boundary layers for external flows over flat plates and cylinders/spheres.
3) It provides empirical correlations to calculate heat transfer coefficients and Nusselt numbers for different flows.
This document discusses using computational fluid dynamics (CFD) to model thermal comfort in buildings. It presents a CFD study of transient heat transfer over a mixed radiative/convective system with time- and space-varying boundary conditions. The study analyzes natural convection, forced convection, and heat radiation phenomena. CFD is proposed as a method to model these phenomena and design new conditioning terminal products through simulation-based design. Integrating CFD with design allows simulation of physical fluid dynamics that are difficult to test experimentally.
Convection involves fluid motion and heat conduction. It can be classified as internal, external, compressible, incompressible, laminar, turbulent, natural, or forced flow. Dimensionless numbers like Reynolds, Prandtl, and Nusselt are used to characterize convection problems. Solutions to the convection equations for a flat plate provide important results like boundary layer thicknesses and heat transfer coefficients.
This document provides an overview of fundamentals of convection. It defines convection, discusses the development of boundary layers, and classifies different types of fluid flows such as laminar versus turbulent, internal versus external, and compressible versus incompressible. It also introduces important dimensionless parameters used in convection such as the Reynolds, Prandtl, and Nusselt numbers.
1. The document discusses various modes of heat transfer including conduction, convection, and radiation.
2. Conduction involves the transfer of heat through direct contact of materials. Convection uses fluid motion to transfer heat, and can be natural or forced.
3. Radiation transfers heat via electromagnetic waves and does not require a medium, allowing it to occur even in a vacuum. It occurs as objects emit and absorb thermal radiation.
Heat can be transferred between two systems in three modes: conduction, convection, and radiation. In a heat exchanger, heat is transferred when two fluids at different temperatures flow through the exchanger. The rate of heat transfer depends on the overall heat transfer coefficient, which takes into account the resistances to heat transfer through the solid wall and boundary layers of each fluid. Common types of heat exchangers include shell-and-tube, plate, compact, regenerative, and cross-flow exchangers. The selection of a heat exchanger depends on factors like the fluids used, temperatures, pressures, and space requirements.
This document discusses different modes of heat transfer through convection and boiling. It defines concepts like forced convection, natural convection, nucleate boiling, film boiling, and pool boiling. It also covers condensation and the differences between film condensation and dropwise condensation. Key points covered include boiling curves, critical heat flux, the Leidenfrost point, and heat transfer correlations for film condensation on a vertical surface.
Convection is the transfer of heat by the movement of fluids such as gases and liquids. When a fluid is heated, its particles gain energy and spread out, causing the fluid to become less dense. Cooler, more dense fluids then sink below the warmer, less dense fluids, setting up convection currents that transfer heat through the fluid. Convection occurs through both natural convection, driven by density differences in the fluid, and forced convection, where an external force like a fan drives the fluid flow. The convection heat transfer coefficient depends on factors like the fluid properties, flow characteristics, surface conditions, and geometry.
Convection is the movement of molecules within fluids and is one of the major modes of heat and mass transfer. Forced convection occurs when an external source, like a fan or pump, generates fluid motion. This allows for very efficient heat transport and is commonly used in heating, cooling, and machinery. Extended surfaces like fins and pins can be added normal to a surface to increase the surface area and improve heat transfer between the surface and surrounding fluid according to Newton's Law of Cooling. Comparing finned and unfinned surfaces under the same conditions demonstrates the effect of extended surfaces.
The document outlines an experimental study conducted to evaluate the effect of different heat transfer rates achieved through water-cooled condensers on the production of oil from plastic waste through a pyrolysis process. The experiment involves heating various masses of plastic at different temperatures for varying times and measuring the resulting oil output and temperatures to determine the optimal conditions for maximum oil production. A group of 5 students guided by Dr. M.P. Deosarkar conducted the study using common plastic types and testing equipment like a reactor, condenser, thermocouples and weighing scales.
The document provides an overview of key concepts in heat transfer, including:
1) It defines heat transfer and the three main modes of heat transfer: conduction, convection, and radiation.
2) It explains the relationship between heat transfer and thermodynamics, noting that heat transfer studies the rate and distribution of temperature over time.
3) It provides definitions and examples of key terms used in heat transfer problems, such as steady state, control mass/volume, and uncertainty.
Mass and heat transfer deals with the determination of rates of energy transfer between systems and variations in temperature. There are three main modes of heat transfer: conduction, convection, and radiation. Conduction involves the transfer of energy between adjacent particles through interactions. Convection refers to the combined effects of conduction and bulk fluid motion. Radiation involves the emission and transmission of electromagnetic waves and can occur through a vacuum.
GATE Mechanical Engineering notes on Heat Transfer. Use these notes as a preparation for GATE Mechanical Engineering and other engineering competitive exams. For full course visit https://mindvis.in/courses/gate-2018-mechanical-engineering-online-course or call 9779434433.
This document provides an overview of heat transfer and computational fluid dynamics. It discusses the three main modes of heat transfer: conduction, convection, and radiation. Key concepts covered include the Nusselt number, Grashof number, Prandtl number, Rayleigh number, Reynolds number, and enthalpy equation. Examples are given to illustrate heat transfer through walls, forced convection in pipes, natural convection, and radiation from black bodies. The document also discusses dimensionless numbers, boundary conditions, and modeling techniques such as the Boussinesq approximation used in computational simulations of heat transfer problems.
Convection is the transfer of heat by the motion of liquids and gases. It occurs due to differences in density caused by temperature variations. There are two types of convection: free convection, which occurs due to natural density differences, and forced convection, where an external force circulates the fluid. The rate of convective heat transfer depends on properties of the fluid and surface, and can be calculated using empirical correlations that involve parameters like Reynolds number, Nusselt number, and Prandtl number. Boiling and condensation are specific types of phase-change heat transfer that occur at saturated temperatures. Different regimes like nucleate boiling or film boiling depend on the temperature difference between the surface and fluid.
Visualization of Natural Convection in a Vertical Annular Cylinder with a Par...IJERA Editor
In this work, we visualize the effect of varying wall temperature on the heat transfer by supplying the heat at
three different positions to the vertical annular cylinder embedded with porous medium. Finite element method
has been used to solve the governing equations. Influence of Aspect ratio 𝐴𝑟 , Radius ratio 𝑅𝑟 on Nusselt
number 𝑁 𝑢 is presented. The effect of power law exponent effect for different values of Rayleigh number is
discussed. The fluid flow and heat transfer is presented in terms of streamlines and isotherms.
The three modes of heat transfer are conduction, convection, and radiation. Conduction involves molecular contact and interactions transferring energy between particles through random molecular motion and collisions. Convection occurs when there is bulk fluid motion from density differences, transferring energy between the fluid and a surface. Radiation transfers energy through electromagnetic waves that travel through space like light from the sun.
This document provides information about convection heat transfer, including definitions, concepts, governing parameters, and dimensionless numbers used in convection analysis. It defines convection as the mechanism of heat transfer due to bulk fluid motion. Natural and forced convection are described. Dimensionless parameters that characterize convection include the Nusselt number, Reynolds number, Prandtl number, Grashof number, and thermal expansion coefficient. Reducing the governing equations using dimensional analysis is also discussed.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
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2. 2
Objectives
• Understand the physical mechanism of natural
convection
• Derive the governing equations of natural convection,
and obtain the dimensionless Grashof number by
nondimensionalizing them
• Evaluate the Nusselt number for natural convection
associated with vertical, horizontal, and inclined plates
as well as cylinders and spheres
• Examine natural convection from finned surfaces, and
determine the optimum fin spacing
• Analyze natural convection inside enclosures such as
double-pane windows.
• Consider combined natural and forced convection, and
assess the relative importance of each mode.
3. 3
PHYSICAL MECHANISM OF NATURAL CONVECTION
Many familiar heat transfer applications involve natural convection as the primary
mechanism of heat transfer. Examples?
Natural convection in gases is usually accompanied by radiation of comparable
magnitude except for low-emissivity surfaces.
The motion that results from the continual replacement of the heated air in the
vicinity of the egg by the cooler air nearby is called a natural convection current,
and the heat transfer that is enhanced as a result of this current is called natural
convection heat transfer.
The cooling of a boiled egg in a cooler
environment by natural convection.
The warming
up of a cold
drink in a
warmer
environment
by natural
convection.
4. 4
Buoyancy force: The upward force exerted by a fluid on a body completely or
partially immersed in it in a gravitational field. The magnitude of the buoyancy
force is equal to the weight of the fluid displaced by the body.
The net vertical force acting on a body
Archimedes’ principle: A body
immersed in a fluid will experience
a “weight loss” in an amount equal
to the weight of the fluid it
displaces.
It is the buoyancy force that keeps the
ships afloat in water (W = Fbuoyancy for
floating objects).
The “chimney effect” that induces
the upward flow of hot combustion
gases through a chimney is due
to the buoyancy effect.
5. 5
The coefficient of volume expansion
is a measure of the change in
volume of a substance with
temperature at constant pressure.
Volume expansion coefficient: Variation of
the density of a fluid with temperature at
constant pressure.
ideal gas
The larger the temperature
difference between the fluid adjacent
to a hot (or cold) surface and the
fluid away from it, the larger the
buoyancy force and the stronger the
natural convection currents, and thus
the higher the heat transfer rate.
6. 6
Isotherms in natural convection
over a hot plate in air.
In natural convection, no blowers are used, and
therefore the flow rate cannot be controlled externally.
The flow rate in this case is established by the dynamic
balance of buoyancy and friction.
An interferometer produces a
map of interference fringes,
which can be interpreted as
lines of constant temperature.
The smooth and parallel lines
in (a) indicate that the flow is
laminar, whereas the eddies
and irregularities in (b) indicate
that the flow is turbulent.
The lines are closest near the
surface, indicating a higher
temperature gradient.
7. 7
EQUATION OF MOTION AND THE GRASHOF NUMBER
Typical velocity and temperature
profiles for natural convection
flow over a hot vertical plate at
temperature Ts inserted in a fluid
at temperature T¥.
The thickness of the boundary layer
increases in the flow direction.
Unlike forced convection, the fluid
velocity is zero at the outer edge of the
velocity boundary layer as well as at the
surface of the plate.
At the surface, the fluid temperature is
equal to the plate temperature, and
gradually decreases to the temperature
of the surrounding fluid at a distance
sufficiently far from the surface.
In the case of cold surfaces, the shape
of the velocity and temperature profiles
remains the same but their direction is
reversed.
8. 8
Forces acting on a differential
volume element in the natural
convection boundary layer
over a vertical flat plate.
This is the equation that governs the fluid motion
in the boundary layer due to the effect of
buoyancy. The momentum equation involves the
temperature, and thus the momentum and
energy equations must be solved simultaneously.
Derivation of the
equation of motion
that governs the
natural convection
flow in laminar
boundary layer
9. 9
The Grashof Number
The governing equations of natural convection and the boundary conditions
can be nondimensionalized by dividing all dependent and independent variables
by suitable constant quantities:
Substituting them into the momentum equation and simplifying give
Grashof number: Represents
the natural convection effects in
momentum equation
10. 10
The Grashof number Gr is a
measure of the relative
magnitudes of the buoyancy
force and the opposing viscous
force acting on the fluid.
• The Grashof number provides the main criterion in determining whether the
fluid flow is laminar or turbulent in natural convection.
• For vertical plates, the critical Grashof number is observed to be about 109.
When a surface is subjected to external
flow, the problem involves both natural
and forced convection.
The relative importance of each mode of
heat transfer is determined by the
value of the coefficient Gr/Re2:
• Natural convection effects are
negligible if Gr/Re2 << 1.
• Free convection dominates and the
forced convection effects are negligible
if Gr/Re2 >> 1.
• Both effects are significant and must
be considered if Gr/Re2 » 1.
11. 11
NATURAL CONVECTION OVER SURFACES
Natural convection heat transfer on a surface depends on the geometry of the
surface as well as its orientation. It also depends on the variation of temperature
on the surface and the thermophysical properties of the fluid involved.
With the exception of some simple cases, Heat transfer relations in natural
convection are based on experimental studies.
Natural convection heat
transfer correlations are
usually expressed in terms of
the Rayleigh number raised
to a constant n multiplied by
another constant C, both of
which are determined
experimentally.
Rayleigh
number
The constants C and n depend on the
geometry of the surface and the flow
regime, which is characterized by the
range of the Rayleigh number.
The value of n is1/4 usually for laminar
flow and 1/3 for turbulent flow.
All fluid properties are to be evaluated
at the film temperature Tf = (Ts + T¥)/2.
14. 14
Vertical Plates (qs = constant)
The relations for isothermal plates in the table can also be used for plates
subjected to uniform heat flux, provided that the plate midpoint temperature TL / 2
is used for Ts in the evaluation of the film temperature, Rayleigh number, and the
Nusselt number.
Inclined Plates
Natural convection flows on the
upper and lower surfaces of an
inclined hot plate.
In a hot plate in a cooler environment for
the lower surface of a hot plate, the
convection currents are weaker, and the
rate of heat transfer is lower relative to the
vertical plate case.
On the upper surface of a hot plate, the
thickness of the boundary layer and thus
the resistance to heat transfer decreases,
and the rate of heat transfer increases
relative to the vertical orientation.
In the case of a cold plate in a warmer
environment, the opposite occurs.
15. 15
Horizontal Plates
Natural convection flows on
the upper and lower surfaces
of a horizontal hot plate.
For a hot surface in a cooler
environment, the net force acts
upward, forcing the heated fluid to rise.
If the hot surface is facing upward, the
heated fluid rises freely, inducing
strong natural convection currents and
thus effective heat transfer.
But if the hot surface is facing
downward, the plate blocks the heated
fluid that tends to rise, impeding heat
transfer.
The opposite is true for a cold plate in
a warmer environment since the net
force (weight minus buoyancy force) in
this case acts downward, and the
cooled fluid near the plate tends to
descend.
16. 16
Horizontal Cylinders and Spheres
Natural convection
flow over a
horizontal hot
cylinder.
The boundary layer over a hot horizontal
cylinder starts to develop at the bottom,
increasing in thickness along the
circumference, and forming a rising plume at
the top.
Therefore, the local Nusselt number is
highest at the bottom, and lowest at the top of
the cylinder when the boundary layer flow
remains laminar.
The opposite is true in the case of a cold
horizontal cylinder in a warmer medium, and
the boundary layer in this case starts to
develop at the top of the cylinder and ending
with a descending plume at the bottom.
18. 18
NATURAL CONVECTION FROM FINNED SURFACES AND PCBs
Natural convection flow
through a channel
between two isothermal
vertical plates.
The plates could be the fins of a finned heat
sink, or the PCBs of an electronic device.
The plates can be approximated as being
isothermal (Ts = constant) in the first case, and
isoflux (qs = constant) in the second case.
Boundary layers start to develop at the lower
ends of opposing surfaces, and eventually
merge at the midplane if the plates are vertical
and sufficiently long. In this case, we will have
fully developed channel flow after the merger of
the boundary layers, and the natural convection
flow is analyzed as channel flow.
But when the plates are short or the spacing is
large, the boundary layers of opposing surfaces
never reach each other, and the natural
convection flow on a surface is not affected by
the presence of the opposing surface. In that
case, the problem should be analyzed as natural
convection from two independent plates in a
quiescent medium.
19. 19
Natural Convection Cooling of Finned Surfaces (Ts = constant)
Finned surfaces of various shapes, called heat sinks, are frequently used in the
cooling of electronic devices.
Energy dissipated by these devices is transferred to the heat sinks by conduction
and from the heat sinks to the ambient air by natural or forced convection,
depending on the power dissipation requirements.
Natural convection is the preferred mode of heat transfer since it involves no
moving parts, like the electronic components themselves.
for vertical isothermal
parallel plates
Characteristic lengths
S fin spacing or
L fin height
Heat sinks with (a) widely spaced and
(b) closely packed fins.
Widely spaced: Smaller surface area but
higher heat transfer coefficient
Closely packed: Higher surface area but
smaller heat transfer coefficient
There must be an optimum spacing that
maximizes the natural convection heat
transfer from the heat sink.
20. 20
Various dimensions
of a finned surface
oriented vertically.
All fluid properties are to be
evaluated at the average
temperature Tavg = (Ts + T¥)/2.
When the fins are essentially isothermal and the fin thickness t is small relative
to the fin spacing S, the optimum fin spacing for a vertical heat sink is
21. 21
Natural Convection Cooling of Vertical PCBs (qs = constant)
Arrays of printed circuit boards used in electronic systems can often be modeled as
parallel plates subjected to uniform heat flux. The plate temperature in this case
increases with height, reaching a maximum at the upper edge of the board.
Arrays of vertical printed
circuit boards (PCBs) cooled
by natural convection.
All fluid properties are to be
evaluated at the average
temperature Tavg = (Ts + T¥)/2.
number of plates
The critical surface TL that occurs at the
upper edge of the plates is determined from
22. 22
Mass Flow Rate through the Space between Plates
The magnitude of the natural convection heat transfer is directly related to
the mass flow rate of the fluid, which is established by the dynamic balance
of two opposing effects: buoyancy and friction.
The fins of a heat sink introduce both effects: inducing extra buoyancy as a
result of the elevated temperature of the fin surfaces and slowing down the
fluid by acting as an added obstacle on the flow path. As a result,
increasing the number of fins on a heat sink can either enhance or reduce
natural convection, depending on which effect is dominant.
The buoyancy-driven fluid flow rate is established at the point where these
two effects balance each other.
The friction force increases as more and more solid surfaces are
introduced, seriously disrupting fluid flow and heat transfer. Heat sinks with
closely spaced fins are not suitable for natural convection cooling.
When the heat sink involves widely spaced fins, the shroud does not
introduce a significant increase in resistance to flow, and the buoyancy
effects dominate. As a result, heat transfer by natural convection may
improve, and at a fixed power level the heat sink may run at a lower
temperature.
23. 23
NATURAL CONVECTION INSIDE ENCLOSURES
Enclosures are frequently encountered in practice, and heat transfer through them
is of practical interest. In a vertical enclosure, the fluid adjacent to the hotter
surface rises and the fluid adjacent to the cooler one falls, setting off a rotationary
motion within the enclosure that enhances heat transfer through the enclosure.
Convective currents in a
vertical rectangular
enclosure.
Convective currents
in a horizontal
enclosure with (a)
hot plate at the top
and (b) hot plate at
the bottom.
Ra > 1708, natural
convection currents
Ra > 3´105, turbulent
fluid motion
Nu = 1
Fluid properties at
Lc charecteristic length: the distance between the hot
and cold surfaces,
T1 and T2: the temperatures of the hot and cold surfaces
24. 24
Effective Thermal Conductivity
A Nusselt number of 3 for an enclosure
indicates that heat transfer through the
enclosure by natural convection is three
times that by pure conduction.
effective thermal
conductivity
The fluid in an enclosure behaves like
a fluid whose thermal conductivity is
kNu as a result of convection currents.
Nu = 1, the effective thermal
conductivity of the enclosure is equal
to the conductivity of the fluid. This
case corresponds to pure conduction.
Numerous correlations for the Nusselt
number exist. Simple power-law type
relations in the form of Nu = CRan,
where C and n are constants, are
sufficiently accurate, but they are
usually applicable to a narrow range of
Prandtl and Rayleigh numbers and
aspect ratios.
25. 25
Horizontal Rectangular Enclosures
A horizontal rectangular
enclosure with
isothermal surfaces.
When the hotter plate
is at the top, Nu = 1.
For horizontal enclosures that
contain air, These relations can
also be used for other gases with
0.5 < Pr < 2.
For water, silicone
oil, and mercury
Based on experiments with air. It may be used for liquids with
moderate Prandtl numbers for RaL < 105.
[ ]+ only positive
values to be used
28. 28
Concentric Cylinders
The rate of heat transfer through the
annular space between the cylinders
by natural convection per unit length
Characteristic length
Two concentric horizontal
isothermal cylinders.
For FcylRaL < 100, natural convection
currents are negligible and thus keff = k.
Note that keff cannot be less than k, and
thus we should set keff = k if keff/k = 1.
The fluid properties are evaluated at the
average temperature of (Ti + To)/2.
the geometric factor for
concentric cylinders
30. 30
Combined Natural Convection and Radiation
Gases are nearly transparent to radiation, and thus heat transfer through a
gas layer is by simultaneous convection (or conduction) and radiation.
Radiation is usually disregarded in forced convection problems, but it must be
considered in natural convection problems that involve a gas. This is especially
the case for surfaces with high emissivities.
s = 5.67 ´ 108 W/m2×K4
Stefan–Boltzmann constant
Radiation heat transfer from a surface at temperature Ts surrounded by
surfaces at a temperature Tsurr is
Radiation heat transfer between two large parallel plates is
When T¥ < Ts and Tsurr > Ts, convection and
radiation heat transfers are in opposite
directions and subtracted from each other.
33. 33
COMBINED NATURAL AND FORCED CONVECTION
In assisting flow, natural convection assists forced convection and
enhances heat transfer. Example: upward forced flow over a hot
surface.
In opposing flow, natural convection resists forced convection and
decreases heat transfer. Example: upward forced flow over a cold
surface.
In transverse flow, the buoyant motion is perpendicular to the forced
motion. Transverse flow enhances fluid mixing and thus enhances heat
transfer. Example: horizontal forced flow over a hot or cold cylinder or
sphere.
where Nuforced and Nunatural
are determined from the
correlations for pure forced
and pure natural convection,
respectively.
34. 34
Summary
• Physical Mechanism of Natural Convection
• Equation of Motion and the Grashof Number
• Natural Convection Over Surfaces
ü Vertical Plates (Ts = constant), (qs = constant)
ü Vertical Cylinders
ü Inclined Plates
ü Horizontal Plates
ü Horizontal Cylinders and Spheres
• Natural Convection from Finned Surfaces and PCBs
ü Natural Convection Cooling of Finned Surfaces (Ts = constant)
ü Natural Convection Cooling of Vertical PCBs (qs = constant)
ü Mass Flow Rate through the Space between Plates
• Natural Convection Inside Enclosures
ü Effective Thermal Conductivity
ü Horizontal Rectangular Enclosures
ü Inclined Rectangular Enclosures
ü Vertical Rectangular Enclosures
ü Concentric Cylinders and spheres
ü Combined Natural Convection and Radiation