Natural Convection of a Vertical Surface | Online Calculator

Natural Convection Calculators







Natural Convection for Vertical Surface

In this calculation, the process of natural convection for a vertical flat surface sized A × B and surface temperature Ts is considered. The surface is in contact with a liquid or gaseous medium having an average temperature Tf, dynamic viscosity μ, density ρ, volumetric expansion β, fluid thermal conductivity λ, and fluid specific heat Cp.

Following the calculations, the convective film coefficient α, heat flow Q and power P, transmitted from surface to the fluid are determined. In addition, similarity criteria for free convection are determined, including Grashof number Gr, Prandtl number Pr, Rayleigh number Ra and Nusselt number Nu.

Calculation of natural convection for vertical surface
Natural convection calculation

INITIAL DATA

A - Surface height;


B - Surface width;


Ts - Surface temperature;


Tf - Enviromental temperature (temperature of the fluid);


μ - Fluid dynamic viscosity;


ρ - Fluid density;


β - Volumetric expansion coefficient of a fluid;


λ - Thermal conductivity coefficient of a fluid;


Cp - Specific heat of a fluid;


Characteristics of fluid are taken according to average temperature of the boundary layer, equal to:
( Ts + Tf ) / 2.

RESULTS DATA

α - Convective film coefficient;


Q - Heat flow;


P - Power, transmitted from surface to fluid.


Gr - Grashof number.


Pr - Prandtl number.


Ra - Rayleigh number.


Nu - Nusselt number.

Height (A)

Width (B)

Temperature of surface (Тs)

Temperature of fluid (Тf)

Dynamic viscosity (μ)

Density (ρ)

Volumetric expansion( β)

Fluid thermal conductivity (λ)

Fluid specific heat (Сp)

Film coefficient (α)

Heat flow (Q)

Transmitted power (Р)

Grashof number (Gr)

Prandtl number (Рr)

Rayleigh number (Ra)

Nusselt number (Nu)

BASIC FORMULAS

Grashof number:

Gr = g*B3*β*[(Тf - Тs) / 2] / (μ / ρ)2;

Prandtl number:

Pr = μ*Cp / λ;

Rayleigh number:

Ra = Gr*Pr;

Nusselt number:

Nu = c*Ran ;

Film coefficient:

α = Nu*λ / B

Heat flow:

Q = α*(Ts - Tf);

Transmitted power:

P = α*A*B*(Ts - Tf).

INITIAL DATA

A - Surface height;


B - Surface width;


Ts - Surface temperature;


Tf - Enviromental temperature (temperature of the fluid);


μ - Fluid dynamic viscosity;


ρ - Fluid density;


β - Volumetric expansion coefficient of a fluid;


λ - Thermal conductivity coefficient of a fluid;


Cp - Specific heat of a fluid;


Characteristics of fluid are taken according to average temperature of the boundary layer, equal to:
( Ts + Tf ) / 2.

RESULTS DATA

α - Convective film coefficient;


Q - Heat flow;


P - Power, transmitted from surface to fluid.


Gr - Grashof number.


Pr - Prandtl number.


Ra - Rayleigh number.


Nu - Nusselt number.

FLUID PROPERTIES

Fluid properties at 20ºC (68 ºF)

Fluid

Density

Kg/m³

(lb/ft³)

Dynamic viscosity

Pa*s

(lb*s/ft²)

Volumetric

expansion

1/ºC

(1/ºF)

Thermal

conductivity

W/m*ºC

(W/in*ºF)

Specific heat

J/kg*ºC

(J/lb*ºF)

Water

998

(62.3)

0.001

(0.0000209)

0.00021

(0.00016)

0.599

(0.084)

4182

(1053)

Air

1.205

(0.075)

0.000018

(0.000000377)

0.00365

(0.00202)

0.0259

(0.00036)

1005

(253)

Water vapor

0.01

(0.00063)

0.0000096

(0.0000002)

0.00365

(0.00202)

0.0178

(0.00025)

1859

(468)

Engine Oil SAE

15W-40

879

(54.9)

0.287

(0.006)

0.00655

(0.0036)

0.134

(0.00190)

2039

(513)

Fluid properties at 40ºC (104 ºF)

Fluid

Density

Kg/m³

(lb/ft³)

Dynamic viscosity

Pa*s

(lb*s/ft²)

Volumetric

expansion

1/ºC

(1/ºF)

Thermal

conductivity

W/m*ºC

(W/in*ºF)

Specific heat

J/kg*ºC

(J/lb*ºF)

Water

992

(62)

0.00065

(0.0000135)

0.00021

(0.00016)

0.635

(0.0090)

4170

(1050)

Air

1.128

(0.07)

0.000019

(0.000000397)

0.00365

(0.00202)

0.0276

(0.00039)

1005

(253)

Water vapor

0.05

(0.0031)

0.0000104

(0.000000217)

0.00365

(0.00202)

0.0195

(0.000275)

1860

(468)

Engine Oil SAE

15W-40

866

(54.1)

0.091

(0.0019)

0.00655

(0.0036)

0.131

(0.00184)

2106

(530)

Fluid properties at 60ºC (140 ºF)

Fluid

Density

Kg/m³

(lb/ft³)

Dynamic viscosity

Pa*s

(lb*s/ft²)

Volumetric

expansion

1/ºC

(1/ºF)

Thermal

conductivity

W/m*ºC

(W/in*ºF)

Specific heat

J/kg*ºC

(J/lb*ºF)

Water

963

(60.2)

0.00046

(0.0000096)

0.00021

(0.00016)

0.659

(0.0093)

4184

(1054)

Air

1.060

(0.066)

0.000020

(0.00000042)

0.00365

(0.00202)

0.0290

(0.00041)

1005

(253)

Water vapor

0.14

(0.0088)

0.0000112

(0.00000023)

0.00365

(0.00202)

0.0212

(0.00029)

1870

(471)

Engine Oil SAE

15W-40

853

(53.3)

0.038

(0.00079)

0.00655

(0.0036)

0.129

(0.00180)

2165

(545)

Fluid properties at 80ºC (176 ºF)

Fluid

Density

Kg/m³

(lb/ft³)

Dynamic viscosity

Pa*s

(lb*s/ft²)

Volumetric

expansion

1/ºC

(1/ºF)

Thermal

conductivity

W/m*ºC

(W/in*ºF)

Specific heat

J/kg*ºC

(J/lb*ºF)

Water

972

(60.7)

0.00035

(0.0000073)

0.00021

(0.00016)

0.675

(0.0095)

4196

(1057)

Air

1.00

(0.063)

0.000021

(0.00000044)

0.00365

(0.00202)

0.0305

(0.00043)

1009

(254)

Water vapor

0.29

(0.018)

0.0000119

(0.00000025)

0.00365

(0.00202)

0.0229

(0.00032)

1880

(474)

Engine Oil SAE

15W-40

841

(52.6)

0.019

(0.00039)

0.00655

(0.0036)

0.127

(0.00178)

2227

(561)

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