View Factor Orientation (or View factor or shape factor) plays an important role in radiation heat transfer. View factor is defined as, "fraction of radiation leaving surface 'i' and strike 'j' ". Summation Rule (View Factor) If there is are similar surfaces 'i' and 'j' , then: Blackbody Radiation Exchange Radiation Exchange between Opaque, Diffuse, Gray surfaces in an Enclosure 1. Opaque 2. Surfaces 3. Two surface enclosure Radiation Shield It is used to protect surfaces from radiation act like a reflective surface. References: Material from Class Lectures + Book named Fundamentals of Heat and Mass Transfer by Theodore L. Bergman + My knowledge. Photoshoped pics are developed. Some pics and GIF from Google. Videos from YouTube ( Engineering Sights ).
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Differential Analysis of Fluid Flow_A
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Fluid Element Kinematics
We need to know inlet and outlet conditions ⇋ Integral or CV Analysis or No flow properties.
We need to follow fluid particles ⇋ Flow domain or Differential analysis.
Ques: How fluid flows (i.e. all four types of motion)?
All these motion take place all at a time because of difference in velocities (evidence: velocity profile in a pipe is look like parabolic i.e. velocity change).
OR
Pressure due to the fluid or wall friction changes.
Linear Motion & Deformation
Angular Motion & Deformation
For Pure rotation ⇋ Ý = 0 & Pure angular deformation ⇋ ω = 0.
The continuity equation reflects the fact that mass is conserved in any non-nuclear continuum mechanics analysis.
The equation is developed by adding up the rate at which mass is flowing in and out of a control volume, and setting the net in-flow equal to the rate of change of mass within it.
Change in the stream function is related to volume flowrate.
If lines of constant stream function plotted with provided the family of streamlines ⇋ help in visualization of flow pattern.
Velocity Potential Function
Velocity Potential Function⇋ consequence of irrotationality of flow field, 3D flow.
Stream Function⇋ consequence of mass conservation, 2D flow.
Basic or Elementary or Plane Potential Flows
Plane potential flows is defined as, "the inviscid, incompressible, irrotational, 2D flows".
For simplicity → only 2D plane flows will be considered.
A. Uniform Flow
It is defined as, "Flow in which streamlines are all straight and parallel, the magnitude of the velocity is constant".
B. Source Flow
It is defined as, "Fluid flows radially outward from a line (point) through origin perpendicular to x-y plane".
Streamlines are straight lines directed radially outward from a point.
Strength of source: m = 2πrVr.
C. Sink Flow
It is defined as, "Fluid flows radially inward from a point towards the origin (i.e. opposite to source flow".
Same as Source flow but opposite sign.
D. Free Vortex Flow
It is defined as, "streamlines are in the form of concentric circles".
Fluid particles do not rotate while revolving around the vortex center.
Strength of Vortex: K' = 2πrVӨ.
Tangential velocity varies inversely with the distance from the origin.
Method of Superposition
It is defined as, "the combination of basic velocity potential and stream functions to yield a streamline that corresponds to a particular body shape of interest which describe flow around the body".
Potential flows are governed by Laplace's equation, which is a linear partial differential equation.
1. Source & Sink Pair
2. Doublet
It is formed by combining a source and sink in a special way infinitely close to each other.
Uniform flow and source → flow past a half body.
Uniform flow and a Source and Sink pair → flow past a Rankine Oval.
3. Uniform Flow and Doublet
A doublet combine with a uniform flow in positive X-direction can be used to represent a flow around a stationary circular cylinder.
Pressure Distribution & Resultant Force on the Cylinder Surface
Pressure distribution on the cylinder surface is obtained from the Bernoulli equation by neglecting elevation differences.
These results indicate that both drag and lift are predicted by Potential Theory.
For a fixed cylinder in a uniform flow → Fx and Fy = 0.
From experience, there is a significant drag developed on a cylinder when it is placed in a moving fluid.
This discrepancy is known as D' Almbert's Paradox.
4. Uniform Flow, Doublet and Free Vortex
An additional potential flow can be developed by adding free vortex to the flow around a cylinder → Flow past a rotating cylinder.
This flow field type can be approximately created by placing a rotating cylinder in a uniform stream.
Because of viscosity, the fluid in contact with the rotating cylinder would rotate with the same velocity as the cylinder.
Pressure Distribution & Resultant Force on the Cylinder Surface
Pressure distribution on the cylinder surface is obtained from the Bernoulli equation by neglecting elevation differences.
For the rotating cylinder, no force in the direction of the uniform flow is developed → FX = 0.
Lift is developed equal to the product of fluid density, upstream velocity and circulation → Lift Force.
References:
Material from Class Lectures + Book named Fundamentals of Fluid Mechanics by Munson, Young & Okiishi's (8th Edition) + my knowledge.
TAPING CORRECTIONS There are two types of corrections depending upon the type of errors in tape due to the different conditions. 1. Systematic Errors : Slope Erroneous tape length Temperature Tension Sag 2. Random Errors : Slope Alignment Marking & Plumbing Temperature Tension & Sag 1. Temperature Correction It is necessary to apply this correction, since the length of a tape is increased as its temperature is raised, and consequently, the measured distance is too small. It is given by the formula, C t = 𝛼 (T m – T o )L Where, C t = the correction for temperature, in m. 𝛼 = the coefficient of thermal expansion. T m = the mean temperature during measurement. T o = the tempe...
Diffusion It is defined as, " The transportation of one atom from one state into other state " . Used for hardening of surfaces like die parts, gear, bolt, machine element. Hardening can be done using Temperature-Heat treatment ( diffusion couple ). There are two types of diffusion: Inter-diffusion ↔ in which atoms tend to migrate from region of high concentration to low concentration . Self-diffusion ↔ in which atoms migrate within a solid. Diffusion Mechanism There can be two conditions of moving atoms Empty spaces between adjacent sites. Atoms have sufficient energy to break bond with neighbors atoms which cause lattice distortion during displacement. If we rise temperature, small fractions of atoms is capable of diffusive motion (which cause lattice distortion). Types of Diffusion 1. Vacancy Diffusion It is defined as, " interchange of an atom from a normal lattice position to the adjacent vacant lattice site " . Extent of vacancy diffusion is a function...
Projection: The term Projection is defined as: Presentation of an image or an object on a surface. The principles used to graphically represent 3-D objects and structures on 2-D media and it based on two variables: Line of Sight. Plane of Projection. Line of Sight & Plane of Projection: Line of sight is divided into 2 types: Parallel Projection Converging Projection & A plane of projection is an imaginary flat plane upon which the image created by the lines of sight is projected. Orthographic Projection: When the projectors are parallel to each other and perpendicular to the plane of projection. The lines pf sight of the observer create a view on the screen. The screen is referred to as the Plane of Projection (POP). The lines of sight are called Projection lines or projectors. Rules of Orthographic Projection: Edges that are parallel to a plane of projection appear as lines. Edges that are incl...
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