CodeCogs

Module containing parameters used in the convective heat transfer modules.

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Interface

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

using namespace Engineering::Thermodynamics::Convection;

inline double Prandtl(double mu, double a)
inline double Grashof(double mu, double beta, double dT, double L)
inline double Reynolds(double mu, double w, double L)

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]

FUNCTION

Prandtl

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

${\rm Pr} = \frac{\mu}{a} = \frac{\mbox{viscous diffusion rate}}{\mbox{thermal diffusion rate}}$

(1)

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

the kinematic viscosity (sq. meters per second)

the thermal diffusivity (sq. meters per second)

Returns

the Prandtl number for the fluid with given parameters

Interactive Calculator

Result –

FUNCTION

Grashof

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

${\rm Gr} = \frac{g\beta \Delta T L^3}{\mu^2} = \frac{\mbox{buoyancy forces}}{\mbox{viscous forces}}$

(2)

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 1

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

the kinematic viscosity (sq. meters per second)

beta

the thermal expansion coefficient (1 / Kelvin)

the temperature difference (Kelvin)

the characteristic length (meters)

Returns

the Grashof number for the fluid with given parameters

References

Dan Stefanescu, Mircea Marinescu - "Termotehnica"

Interactive Calculator

beta

Result –

FUNCTION

Reynolds

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:

${\rm Re} = \frac{wL}{\mu} = \frac{\mbox{inertial forces}}{\mbox{viscous forces}}$

(3)

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 1

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

kinematic viscosity of fluid (sq. meters per second)

mean velocity of flow (meters per second)

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

Interactive Calculator

Result –