Jordanian-German Winter Academy 2006 NATURAL CONVECTION Prepared by : FAHED ABU-DHAIM Ph.D student UNIVERSITY OF JORDAN MECHANICAL ENGINEERING DEPARTMENT

HEAT TRANSFER MODES CONDUCTIONCONVECTIONRADIATION

CONVECTION HEAT TRANSFER FORCED LAMINAR INTERNAL EXTERNAL TURBULENT INTERNAL EXTERNAL FREE LAMINAR INTERNAL EXTERNAL TURBULENT INTERNAL EXTERNAL

Natural Convection Heat Transfer Examples:  Electronic devices (computer boards, T.V, etc).  Baseboard heaters.  Heat transfer from pipes and transmission lines  Steam radiators-central heating systems to heat a room, heating elements.  Refrigeration coils (condenser and evaporator).  Heat transfer from bodies of human or animals.

Natural Convection Heat Transfer WHAT DRIVES THE NATURAL CONVECTION FLOW?  In natural convection, or free convection, the fluid flows “naturally” (by it self), not forced motion.  It is driven by the effect of the buoyancy.  It is observed as a result of the fluid motion due to density change arising from the heating processes.  The motion of the fluid results from the buoyancy forces imposed on the fluid when its density is changed.

 The buoyancy forces are present because the fluid is acted upon by gravity, which is an external force field. As a conclusion : whenever a fluid is heated or cooled in a gravitatational field, there is a possibility of natural convection. Natural Convection Heat Transfer

Example

IMPORTANCE OF NATURAL CONVECTION :  Convective heat transfer coefficient h is very small in multimode heat transfer systems.  Natural convection resistance is large and thus natural convection affects system design.  Natural convection is preferred when large heat rates to be avoided.  Natural convection mode is economically attractive (no need for a pump or blower). Natural Convection Heat Transfer

Natural convection boundary layers Natural Convection Heat Transfer

The Governing Equations

Similarity Solution

…Continued, Similarity Solution

Laminar, free convection boundary layer conditions on an isothermal, vertical surface a) Velocity profile b) Temperature profile a) Velocity profile b) Temperature profile

Effect of turbulence on Natural Convection Heat Transfer

Empirical Correlations Vertical Plates laminar flow laminar flow Turbulent flow Turbulent flow

Horizontal 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 Cylinder

Spheres

INTRODUCTION Natural convection in confined rectangular cavities has received much attention in recent years. Natural convection in confined rectangular cavities has received much attention in recent years. Such type of flow has a wide range of applications, for example, multi-pane windows, solar collectors. Such type of flow has a wide range of applications, for example, multi-pane windows, solar collectors. Especially recently, sloped windows and skylights have been more and more frequently applied in buildings. Especially recently, sloped windows and skylights have been more and more frequently applied in buildings. This study is useful for air conditioning design loads (in summer or winter). This study is useful for air conditioning design loads (in summer or winter). Numerical Study of Natural Convection in inclined Rectangular Glazing Cavities

ABSTRACT:  In this study, numerical method is applied to predict the heat transfer in natural convective flow in inclined rectangular glazing cavities.  The inclination orientation changes from vertical to horizontal position.  Then 3-D modeling is applied and found to predict well the average heat transfer quantities.

 A lot of experimental work has been performed and it is found that heat transfer in the inclined cavities is directly related to the flow mode transition.  Most of these experimental researches only studied cavities with small to medium aspect ratios, with the maximum aspect ratio 15.5

MATHEMATICAL FORMULATION  The Boussinesq approximation is applied with constant fluid properties, and negligible viscous dissipation and internal heat sources.  The derived incompressible three-dimensional Navier-Stokes equations for a cavity with the gravity force pointing in any direction in the x-y plane are given below:

Results Two-Dimensional Model with Ideal Boundary Conditions Two-Dimensional Model with Ideal Boundary Conditions The average Nusselt number results are plotted versus tilt angle, and compared with the numerical results. The average Nusselt number results are plotted versus tilt angle, and compared with the numerical results. Very good agreement is shown, which can be a proof that the current 2-D numerical method is correct in the aspects of mathematical model and the numerical manipulation. Very good agreement is shown, which can be a proof that the current 2-D numerical method is correct in the aspects of mathematical model and the numerical manipulation.

The average Nusselt number results are plotted versus tilt angle

THREE-DIMENSIONAL NUMERICAL METHOD  The finite volume is used for 3-D numerical simulation.  All the three-dimensional calculations are initialized with a random velocity field and a uniform mean-temperature field.  Then the steady state governing equations are solved.

The heat transfer results are shown below Results

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

CONCLUSIONS A two-dimensional finite element model is used firstly and found not able to predict correct heat transfer results. A two-dimensional finite element model is used firstly and found not able to predict correct heat transfer results. Only three-dimensional modeling is an effective way to predict heat transfer results. Only three-dimensional modeling is an effective way to predict heat transfer results.

Thanks