Jordanian-German Winter Academy 2006 Jordanian-German Winter Academy 2006

NATURAL CONVECTIONNATURAL CONVECTION

Prepared byPrepared by: : FAHED ABU-DHAIMFAHED ABU-DHAIM

Ph.D studentPh.D student

UNIVERSITY OF JORDANUNIVERSITY OF JORDANMECHANICAL ENGINEERING DEPARTMENTMECHANICAL ENGINEERING DEPARTMENT

HEAT TRANSFER MODES

CONDUCTION CONVECTION RADIATION

CONVECTION HEAT TRANSFER

FORCED FREE

LAMINAR TURBULENTLAMINAR TURBULENT

INTERNAL

EXTERNAL

INTERNAL

EXTERNAL

INTERNAL

EXTERNAL

INTERNAL

EXTERNAL

Natural Convection Heat TransferNatural Convection Heat Transfer

ExamplesExamples::

Electronic devices Electronic devices ((computer boards, T.V, etc).computer boards, T.V, etc).

Baseboard heaters.Baseboard heaters.

Heat transfer from pipes and transmission linesHeat transfer from pipes and transmission lines

Steam radiators-central heating systems to heat a Steam radiators-central heating systems to heat a room, heating elements. room, heating elements.

Refrigeration coils (condenser and evaporator).Refrigeration coils (condenser and evaporator).

Heat transfer from bodies of human or animals.Heat transfer from bodies of human or animals.

Natural Convection Heat TransferNatural Convection Heat TransferWHAT DRIVES THE NATURAL CONVECTION FLOWWHAT DRIVES THE NATURAL CONVECTION FLOW??

In natural convection , or free convection , the fluid In natural convection , or free convection , the fluid flows “naturally” (by it self) , not forced motion. flows “naturally” (by it self) , not forced motion.

It is driven by the effect of the buoyancy. It is driven by the effect of the buoyancy.

It is observed as a result of the fluid motion due to It is observed as a result of the fluid motion due to density change arising from the heating density change arising from the heating processesprocesses..

The motion of the fluid results from the buoyancy The motion of the fluid results from the buoyancy forces imposed on the fluid when its density is forces imposed on the fluid when its density is changed.changed.

The buoyancy forces are present because The buoyancy forces are present because

the fluid is acted upon by gravity, which is an the fluid is acted upon by gravity, which is an

external force field.external force field.

As a conclusionAs a conclusion :: whenever a fluid is heated or whenever a fluid is heated or

cooled in a gravitatational field, there is a cooled in a gravitatational field, there is a

possibility of natural convection. possibility of natural convection.

Natural Convection Heat TransferNatural Convection Heat Transfer

ExampleExample

IMPORTANCE OF NATURAL CONVECTIONIMPORTANCE OF NATURAL CONVECTION: :

Convective heat transfer coefficient h is very Convective heat transfer coefficient h is very small small in multimode heat transfer systems. in multimode heat transfer systems.

Natural convection resistance is large and thus Natural convection resistance is large and thus natural convection affects system design.natural convection affects system design.

Natural convection is Natural convection is preferredpreferred when large heat when large heat rates to be avoided.rates to be avoided.

Natural convection mode is economically Natural convection mode is economically attractive (no need for a pump or blower).attractive (no need for a pump or blower).

Natural Convection Heat TransferNatural Convection Heat Transfer

Natural convection boundary layersNatural convection boundary layers

NaturalNatural Convection Heat Transfer Convection Heat Transfer

The Governing EquationsThe Governing Equations

Similarity SolutionSimilarity Solution

14

Similarity Parameters4

xGry

x

……Continued, SimilarityContinued, Similarity SolutionSolution

s

T-TT* Dimensionless temperature

T -T

1

4

, 4 4

V in terms of stream fn.

xGrx y f

Laminar, free convection boundary layer Laminar, free convection boundary layer conditions on an isothermal, vertical conditions on an isothermal, vertical

surfacesurface a) Velocity profile b) Temperature profilea) Velocity profile b) Temperature profile

Effect of turbulence on Natural Effect of turbulence on Natural Convection Heat TransferConvection Heat Transfer

Empirical CorrelationsEmpirical Correlations

Vertical PlatesVertical Plates laminar flowlaminar flow

Turbulent flowTurbulent flow

Horizontal PlatesHorizontal Plates

Upper Surface of Heated Plate or Lower Surface of Cooled Plate:

Lower Surface of Heated Plate or Upper Surface of Cooled Plate:

Heated Horizontal CylinderHeated Horizontal Cylinder

SpheresSpheres

INTRODUCTIONINTRODUCTION

Natural convection in confined rectangular cavities has Natural convection in confined rectangular cavities has received much attention in recent years. received much attention in recent years.

Such type of flow has a wide range of applications, for Such type of flow has a wide range of applications, for example, multi-pane windows, solar collectors. example, multi-pane windows, solar collectors.

Especially recently, sloped windows and skylights have Especially recently, sloped windows and skylights have been more and more frequently applied in buildings. been more and more frequently applied in buildings.

This study is useful for air conditioning design loads (in This study is useful for air conditioning design loads (in summer or winter) .summer or winter) .

Numerical Study of Natural Convection in Numerical Study of Natural Convection in inclined Rectangular Glazing Cavitiesinclined Rectangular Glazing Cavities

ABSTRACTABSTRACT::

In this study, numerical method is applied to In this study, numerical method is applied to predict the heat transfer in natural convective flow predict the heat transfer in natural convective flow in inclined rectangular glazing cavities. in inclined rectangular glazing cavities.

The inclination orientation changes from vertical The inclination orientation changes from vertical to horizontal position.to horizontal position.

Then 3-D modeling is applied and found to predict Then 3-D modeling is applied and found to predict well the average heat transfer quantities. well the average heat transfer quantities.

A lot of experimental work has been performed A lot of experimental work has been performed and it is found that heat transfer in the inclined and it is found that heat transfer in the inclined cavities is directly related to the flow mode cavities is directly related to the flow mode transition. transition.

Most of these experimental researches only Most of these experimental researches only studied cavities with small to medium aspect studied cavities with small to medium aspect ratios, with the maximum aspect ratio 15.5ratios, with the maximum aspect ratio 15.5

MATHEMATICAL FORMULATIONMATHEMATICAL FORMULATION

The Boussinesq approximation is applied with The Boussinesq approximation is applied with constant fluid properties, and negligible viscous constant fluid properties, and negligible viscous dissipation and internal heat sources. dissipation and internal heat sources.

The derived incompressible three-dimensional The derived incompressible three-dimensional Navier-Stokes equations for a cavity with the Navier-Stokes equations for a cavity with the gravity force pointing in any direction in the x-y gravity force pointing in any direction in the x-y plane are given below:plane are given below:

ResultsResults Two-Dimensional Model with Ideal Boundary Two-Dimensional Model with Ideal Boundary

ConditionsConditions

The average Nusselt number results are plotted The average Nusselt number results are plotted

versus tilt angle, and compared with the versus tilt angle, and compared with the numerical results.numerical results.

Very good agreement is shown, which can be a Very good agreement is shown, which can be a proof that the current 2-D numerical method is proof that the current 2-D numerical method is correct in the aspects of mathematical model correct in the aspects of mathematical model and the numerical manipulation. and the numerical manipulation.

The average Nusselt number results are plotted versus tilt angle

THREE-DIMENSIONAL NUMERICAL METHODTHREE-DIMENSIONAL NUMERICAL METHOD

The finite volume is used for 3-D The finite volume is used for 3-D

numerical simulation .numerical simulation .

All the three-dimensional calculations are All the three-dimensional calculations are initialized with a random velocity field and initialized with a random velocity field and a uniform mean-temperature field. a uniform mean-temperature field.

Then the steady state governing Then the steady state governing equations are solved. equations are solved.

The heat transfer results are shown belowThe heat transfer results are shown below

ResultsResults

The average Nusselt no versus tilt angle for a 3-D The average Nusselt no versus tilt angle for a 3-D cavity with aspect ratio 20 and Rayleigh no 9320. cavity with aspect ratio 20 and Rayleigh no 9320.

CONCLUSIONSCONCLUSIONS

A two-dimensional finite element model A two-dimensional finite element model is used firstly and found not able to is used firstly and found not able to predict correct heat transfer results. predict correct heat transfer results.

Only three-dimensional modeling is an Only three-dimensional modeling is an effective way to predict heat transfer effective way to predict heat transfer results. results.

ThanksThanks