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parameters

Module containing parameters used in the convective heat transfer modules.
Controller: CodeCogs

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Interface

C++
Excel

Overview

This module contains parameters which are used in studying various convective heat transfer phenomena.

References:

Fluid Properties Calculator giving the values of the kinematic viscosity \mu, thermal diffusivity a and thermal expansion coefficient \beta, for fluids at various temperatures: [url]http://www.mhtl.uwaterloo.ca/old/onlinetools/airprop/airprop.html[/url]

Authors

Grigore Bentea, Lucian Bentea (November 2006)

Prandtl

 
doublePrandtldoublemu
doublea )[inline]
The Prandtl number is a dimensionless parameter of a convecting system that gives the regime of convection. It has the formula

where \mu is the kinematic viscosity and a is the thermal diffusivity of the fluid.

Example 1

The code below computes the Prandtl number in the case of Ethylene Glycol at 17 degrees Celsius.
#include <codecogs/engineering/heat_transfer/convection/parameters.h>
#include <stdio.h>
 
int main()
{
  double mu = 2.1936E-5, a = 9.3834E-8;
 
  printf("\nEthylene Glycol at 17 deg. Celsius\n\n");
  printf("Pr = %.4lf\n\n", 
  Engineering::Heat_Transfer::Convection::Prandtl(mu, a));
 
  return 0;
}

Output

Ethylene Glycol at 17 deg. Celsius
 
Pr = 233.7745

Parameters

muthe kinematic viscosity (sq. meters per second)
athe thermal diffusivity (sq. meters per second)

Returns

the Prandtl number for the fluid with given parameters
Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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Grashof

 
doubleGrashofdoublemu
doublebeta
doubledT
doubleL )[inline]
The Grashof number approximates the ratio of the buoyancy forces to the viscous forces in a fluid. It is given by the formula

where g is the gravitational acceleration constant, \beta is the thermal expansion coefficient of the fluid, \Delta T is the temperature difference between the fluid and the wall, L is the characteristic length and \mu is the kinematic viscosity of the fluid.

Example 2

In the following example the Grashof number is calculated for air at 25 degrees Celsius going through a pipe at 15 degrees Celsius with internal diameter of 0.1 meters.
#include <codecogs/engineering/heat_transfer/convection/parameters.h>
#include <stdio.h>
 
int main()
{
  double mu = 1.5571E-5, beta = 3.3540E-3, dT = 10, L = 0.1;
 
  printf("\nAir at 25 deg. Celsius\n\n");
  printf("Gr = %.4lf\n\n", 
  Engineering::Heat_Transfer::Convection::Grashof(mu, beta, dT, L));
 
  return 0;
}

Output

Air at 25 deg. Celsius
 
Gr = 1356596.6005

References

Dan Stefanescu, Mircea Marinescu - "Termotehnica"

Parameters

muthe kinematic viscosity (sq. meters per second)
betathe thermal expansion coefficient (1 / Kelvin)
dTthe temperature difference (Kelvin)
Lthe characteristic length (meters)

Returns

the Grashof number for the fluid with given parameters
Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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Reynolds

 
doubleReynoldsdoublemu
doublew
doubleL )[inline]
Reynolds number, named after Osborne Reynolds who proposed it in 1883, is the ratio of inertial forces to viscous forces in a fluid. Besides other applications, it can be used to determine whether a flow inside a pipe is laminar, turbulent or in the so-called critical zone. The formula for this dimensionless measure is: where L is the characteristic length, w is the average velocity of the flow and \mu is the kinematic viscosity of the fluid.

It has been established that in the case of a fluid going through pipes, for Reynolds values less than 2000 the flow is laminar, for values greater than 4000 the flow is turbulent, while for numbers between 2000 and 4000 the flow becomes unpredictable. For this reason the domain from 2000 to 4000 is also called the "critical zone".

Example 3

In the following example the Reynolds number is computed for carbon dioxide at 75 degrees Celsius going through a pipe with internal diameter of 1.5 meters, having a velocity of 5 meters per second.
#include <codecogs/engineering/heat_transfer/convection/parameters.h>
#include <stdio.h>
 
int main()
{
  double mu = 1.1203E-5, velocity = 5, length = 1.5,
  Re = Engineering::Heat_Transfer::Convection::Reynolds(mu, velocity, length);
 
  printf("Carbon Dioxide at 75 deg. Celsius\n\n");
  printf("Re = %.4lf\n", Re);
 
  if (Re < 2000) printf("Laminar flow.\n");
  else if (Re > 4000) printf("Turbulent flow.\n");
  else printf("Unpredictable flow (critical zone).\n");
 
  printf("\n");
  return 0;
}

Output

Carbon Dioxide at 75 deg. Celsius
 
Re = 669463.5366
Turbulent flow.

References

The Engineering Division, Crane Co., "Flow of fluids through valves, fittings, and pipe", Chicago, 1957

Parameters

mukinematic viscosity of fluid (sq. meters per second)
wmean velocity of flow (meters per second)
Lcharacteristic length (meters)

Returns

the Reynolds number corresponding to the given parameters
Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

Not a member, then Register with CodeCogs. Already a Member, then Login.