Group Description

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 , thermal diffusivity and thermal expansion coefficient , for fluids at various temperatures: [url]http://www.mhtl.uwaterloo.ca/old/onlinetools/airprop/airprop.html[/url]

Authors:

Grigore Bentea, Lucian Bentea (November 2006)

Interface

#include <codecogs/engineering/heat_transfer/convection/parameters.h>

using namespace Engineering::Heat_Transfer::Convection;

	double	Prandtl (double mu, double a)[inline] Module containing parameters used in some of the heat transfer modules.
	Real	cc_Prandtl (Real mu, Real a) This function is available as a Microsoft Excel add-in.
	double	Grashof (double mu, double beta, double dT, double L)[inline] Returns the Grashof number for a fluid with given parameters.
	Real	cc_Grashof (Real mu, Real beta, Real dT, Real L) This function is available as a Microsoft Excel add-in.
	double	Reynolds (double mu, double w, double L)[inline] Evaluates the Reynolds number of given parameters.
	Real	cc_convectionReynolds (Real mu, Real w, Real L) This function is available as a Microsoft Excel add-in.

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Function Documentation

The Prandtl number is a dimensionless parameter of a convecting system that gives the regime of convection. It has the formula

where is the kinematic viscosity and is the thermal diffusivity of the fluid.

Example:

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:

mu	the kinematic viscosity (sq. meters per second)
a	the thermal diffusivity (sq. meters per second)

Returns:

the Prandtl number for the fluid with given parameters

Source Code:

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The Grashof number approximates the ratio of the buoyancy forces to the viscous forces in a fluid. It is given by the formula

where is the gravitational acceleration constant, is the thermal expansion coefficient of the fluid, is the temperature difference between the fluid and the wall, is the characteristic length and is the kinematic viscosity of the fluid.

Example:

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

Parameters:

mu	the kinematic viscosity (sq. meters per second)
beta	the thermal expansion coefficient (1 / Kelvin)
dT	the temperature difference (Kelvin)
L	the characteristic length (meters)

Returns:

the Grashof number for the fluid with given parameters

References:

Dan Stefanescu, Mircea Marinescu - "Termotehnica"

Source Code:

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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 is the characteristic length, is the average velocity of the flow and 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:

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.

Parameters:

mu	kinematic viscosity of fluid (sq. meters per second)
w	mean velocity of flow (meters per second)
L	characteristic length (meters)

Returns:

the Reynolds number corresponding to the given parameters

References:

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

Source Code:

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