Natural Convection of a Horizontal Surface | Online Calculator

Natural Convection Calculators

Natural Convection for Horizontal Surface

The process of heat transfer during natural convection is widespread. As a physical phenomenon, convection occurs due to the variable density in different layers of a liquid or gas, when the temperature changes. For heat transfer calculation, a similarity equation of the following form is used:

Num = c×Ramn ;

Where Ram - Rayleigh number, with the average temperature of the boundary layer taken as the determining temperature for its calculation:

Tm = (Tf + Ts) / 2;

The defining dimension in this calculation is the width or height of the free convection surface, depending on its location.

In this calculation, the process of natural convection for a horizontal 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.

Natural convection for horizontal surface
Natural convection calculation

INITIAL DATA

A - Surface length;

B - Surface width;

Ts - Surface temperature;

Tf - Enviromental temperature (temperature of the fluid);

μ - Dynamic fluid 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.

Length (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)

Surface facing up

Surface facing down

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] / (μ / ρ)2;

Prandtl number:

Pr = μ*Cp / λ;

Rayleigh number:

Ra = Gr*Pr;

Nusselt number:

Nu = c*Ran ;

Film coefficient:

α = 1.3*Nu*λ / B - for surface facing up;
α = 0.7*Nu*λ / B - for surface facing down.

Heat flow:

Q = α*(Ts - Tf);

Transmitted power:

P = α*A*B*(Ts - Tf).

INITIAL DATA

A - Surface length;

B - Surface width;

Ts - Surface temperature;

Tf - Enviromental temperature (temperature of the fluid);

μ - Dynamic fluid 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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