Birla Vishvakarma Mahavidyalaya

Production engineering department

140080125009 Harsh Parekh140080125010 Viraj Javia140080125011 Chintan Joshi140080125012 Meet Kansara Guided by: Dr. Manish Mehta

Topics

Basic concept Types of convection Boundary layer Turbulent flow Laminar flow Reynolds number Nusselt number Prandl number

What is Convection?

Convection is a mode of heat transfer between a solid (or liquid) surface and its adjacent liquid or gas that is in bulk motion. It involves combined effect of conduction and fluid motion.

Newton’s Law of Cooling

Types of Convection

1. Forced Convection:- when the fluid is forced to flow over the surface by external means such as a fan, pump or wind.

1. Natural (or Free) Convection:- when fluid flow is caused by buoyancy forces that are induced by density differences due to variation of temperature of the fluid.

Boundary Layer

Dimensional analysis

Dimension analysis can be used to: Derive an equation . Check whether an equation is dimensionally correct.

However, dimensionally correct doesn’t necessarily mean the equation is correct

Find out dimension or units of derived quantities.

There are physical quantities which are dimensionless:

Numerical value Ratio between the same

quantity angle Some of the known constants

like ln , log etc.

Turbulent And laminar flow Laminar flow:

Where the fluid moves slowly in layers in a pipe, without much

mixing among the layers. Turbulent flow Opposite of laminar, where considerable

mixing occurs, velocities are high.

Reynolds Number: The Reynolds number is defined as the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions . They are also used to characterize different flow regimes within a

similar fluid, such as laminar or turbulent flow: laminar flow occurs at low Reynolds numbers, where viscous forces are

dominant, and is characterized by smooth, constant fluid motion; turbulent flow occurs at high Reynolds numbers and is dominated by

inertial forces, which tend to produce eddies, vortices and other flow instabilities.

where:  is the mean velocity of the object relative to the fluid (SI units: m/s)  is a characteristic linear dimension, (travelled length of the

fluid; hydraulic diameter when dealing with river systems) (m)  is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))  is the kinematics viscosity ( ) (m²/s)  is the density of the fluid (kg/m³).

Nusselt Number:

In heat transfer at a boundary (surface) within a fluid, the Nusselt number (Nu) is the ratio of convective to conductive heat transfer across (normal to) the boundary.

A Nusselt number close to one, namely convection and conduction of similar magnitude, is characteristic of "slug flow" or laminar flow. A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range.

Prandtl Number

The Prandtl number   is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity (kinematics viscosity) to thermal diffusivity. That is, the Prandtl number is given as:

 : kinematics viscosity,  , (SI units : m2/s)  : thermal diffusivity,  , (SI units : m2/s)  : dynamic viscosity, (SI units : Pa s = N s/m2) :  thermal conductivity, (SI units : W/(m K) )  : specific heat, (SI units : J/(kg K) )  : density, (SI units : kg/m3 )

 Pr<1 means thermal diffusivity dominates., Pr>1momentum diffusivity dominates

Dependence Of transition and laminar flow The transition from laminar to

turbulent flow depends on the surface geometry, surface roughness, upstream velocity, surface temperature, and the type of fluid, among other things, and is best characterized by the Reynolds number

Laminar and Turbulent Flow In Tubes Flow in a tube can be laminar or turbulent,

depending on the flow conditions. Fluid flow is streamlined and thus laminar at low

velocities, but turns turbulent as the velocity is increased beyond a critical value.

Transition from laminar to turbulent flow does not occur suddenly; rather, it occurs over some range of velocity where the flow fluctuates between laminar and turbulent flows before it becomes fully turbulent.

Most pipe flows encountered in practice are turbulent.

Laminar flow is encountered when highly viscous fluids such as oils flow in small diameter tubes or narrow passages.

Temperature profile in forced convection

Now consider a fluid at a uniform temperature entering a circular tubewhose surface is maintained at a different temperature. This time, the fluidparticles in the layer in contact with the surface of the tube will assume thesurface temperature. This will initiate convection heat transfer in the tube andthe development of a thermal boundary layer along the tube. The thickness ofthis boundary layer also increases in the flow direction until the boundarylayer reaches the tube center and thus fills the entire tube, as shown inFigure

Laminar And Turbulent Flow over Flat plates

PARALLEL FLOW OVER FLAT PLATESConsider the parallel flow of a fluid over a flat plate of length L in theflow direction, as shown in Fig. 7–6. The x-coordinate is measured alongthe plate surface from the leading edge in the direction of the flow. The

fluidapproaches the plate in the x-direction with a uniform velocity V and

temperature T`. The flow in the velocity boundary layers starts out as laminar,but if the plate is sufficiently long, the flow becomes turbulent at a

distancexcr from the leading edge where the Reynolds number reaches its criticalvalue for transition.The transition from laminar to turbulent flow depends on the surface

geometry,surface roughness, upstream velocity, surface temperature, and the type

offluid, among other things, and is best characterized by the Reynolds

number.

Forced Convection In Laminar And Turbulent Flow In Pipes

Turbulent flow over cylinders

Characteristic length Lc=diameter of the cylinder DThe co-relation used is: Nu=hD/k=C(Re)^n (Pr)^0.33The constants C and n depends upon flow Reynolds number.Further,all properties are evaluated at mean film temperature.

Turbulent flow over spheres

Characteristic length Lc=diameter D of sphereFor flow of gases over sphere Nu=0.37(Re)^0.6For 25<Re<10^5For flow of liquids over sphereNu=[0.97+0.68(Re)^0.5](Pr)^0.33 for 1<Re<2000Generalized equation for flow over sphere can also be given asNu=2+[0.4(Re)^0.5+0.06(Re)^0.67] (Pr)^0.4(µ/µs)^0.25Where µs=dynamic viscosity

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