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Free Convection: External Surface

  • Patrick H. Oosthuizen
Reference work entry

Abstract

Some representative recent basic studies involving external free convective heat transfer in situations that are of practical interest are discussed in this chapter. Most of the results considered have been obtained numerically, and a very brief discussion of the methodology used to generate these results is presented. Attention has here first been given to the heat transfer rate from narrow vertical plane surfaces with the effect of the width-to-height ratio of the surface on the heat transfer rate in particular being discussed. Heat transfer from horizontally and vertically spaced pairs of narrow plates has also been considered. Consideration has then been given to the heat transfer rate from horizontal heated surfaces of complex shape, to adjacent pairs of horizontal heated surfaces, and to heat transfer from two-sided circular horizontal surfaces. The effect of a covering surface on the heat transfer from a horizontal heated surface has also been considered. The heat transfer rate from bodies with wavy surfaces has been considered next with attention being given to situations involving two-dimensional flow over vertical and horizontal surfaces and to the effect of surface waviness on the heat transfer rate from cylindrical bodies. The heat transfer from relatively short vertical circular and square cylinders with exposed top surfaces is also considered. Lastly, brief attention is given to external free convective heat transfer to nanofluids.

Nomenclature

A

Total surface area

Abottom

Area of bottom surface

Ac

Area of cylindrical outer surface of cylinder

Atop

Area of top surface

At

Area of top surface of cylinder

Atotal

Total surface area

AR

Aspect ratio

a

Mean side length

cpf

Specific heat of fluid in which nanoparticles are placed

cpnf

Specific heat of nanofluid

cps

Specific heat of nanoparticles

Di

Dimensionless diameter of inner adiabatic section of surface

D

Diameter of circular surface

d

Heated surface diameter

di

Diameter of inner adiabatic section of surface

G

Gap between heated surfaces

Gap

Gap between vertically spaced heated surfaces

g

Gravitational acceleration

HGap

Dimensionless size of gap between surfaces

H

Height of surface and dimensionless recess depth, h/d

h

Recess depth

k

Thermal conductivity

h

Recess depth

L

l/d

Lout

Dimensionless side length of rectangular adiabatic covering surface, Lout = lout/w

l

Reference length and cylinder height

lout

Side lengths of rectangular adiabatic covering surface

m

Characteristic length scale of surface

Nu

Nusselt number

Nu0

Reference Nusselt number

Nua

Mean Nusselt number based on the mean side length, a, of rectangular heated surface

Nubottom

Mean Nusselt number averaged over bottom surface

Nuc

Mean Nusselt number averaged over vertical side surface of cylinder

Num

Mean Nusselt number based on m

Nur

Mean Nusselt number based on r

Nurbottom

Mean Nusselt number based on r averaged over bottom surface

Nurtop

Mean Nusselt number based on r averaged over top surface

Nut

Mean Nusselt number averaged over horizontal top surface of cylinder

Nutop

Mean Nusselt number averaged over top surface

Nutotal

Mean Nusselt number averaged over entire surface

n

Coordinate normal to surface or number of surface waves

P

Total perimeter of heated surface

Pr

Prandtl number

\( {\overline{Q}}^{\prime } \)

Total mean heat transfer rate

\( {{\overline{Q}}^{\prime}}_{\mathrm{bottom}} \)

Total mean heat transfer rate from bottom surface

\( {{\overline{Q}}^{\prime}}_{\mathrm{top}} \)

Total mean heat transfer rate from top surface

q

Local heat transfer rate per unit area

\( {\overline{q}}^{\prime } \)

Mean heat transfer rate per unit area from entire cylinder

\( \overline{q_c^{\prime }} \)

Mean heat transfer rate per unit area from cylindrical outer surface of cylinder

\( \overline{q_s^{\prime }} \)

Mean heat transfer rate per unit area from vertical side surface of square cylinder

\( \overline{q_t^{\prime }} \)

Mean heat transfer rate per unit area from top surface of cylinder

\( \overline{q_w^{\prime }} \)

Mean heat transfer rate per unit area

R

Dimensionless cylinder radius, r/l

Ra

Rayleigh number

Raa

Rayleigh number based on the mean side length, a, of rectangular heated surface

Ram

Rayleigh number based on m

Rar

Rayleigh number based on r

Ra*

Heat Flux Rayleigh number

r

Characteristic length scale of surface and the radius of cylinder

rbottom

Characteristic length scale of bottom surface

rtop

Characteristic length scale of top surface

s

Arm size of +- shaped and I-shaped heated surfaces

S

Dimensionless distance between sides of square heated surfaces

T

Temperature

Tf

Fluid temperature far from surface

Tw

Wall temperature

T0

Reference fluid temperature

VGap

Dimensionless size of gap between surfaces, Gap/h

W

Dimensionless surface width, w/h

Wout

The dimensionless side lengths of the rectangular surrounding adiabatic surface Wout = wout/w

w

Surface width

wout

Side lengths of the rectangular surrounding adiabatic surface

Greek Symbols

α

Thermal diffusivity

β

Bulk coefficient of thermal expansion

δ

Measure of the boundary layer thickness

ϕ

Nanoparticle volumetric fraction

ν

Kinematic viscosity

ξ

1/(R Ra0.25) or 1/(W Ra0.25)

φ

Angle of inclination

μ

Viscosity

ρ

Density

ρ0

Reference density value

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Materials Engineering, Faculty of Engineering and Applied ScienceQueen’s UniversityKingstonCanada

Section editors and affiliations

  • Sumanta Acharya
    • 1
  1. 1.Herff College of Engineering,Department of Mechanical EngineeringThe University of MemphisMemphisUSA

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