Heat Transfer : Convection Heat Transfer

1. HeatTransfer: Convection Heat Transfer

2. Objectives Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 2 • Understand the basics of convection heat transfer. • Compare natural convection with forced convection. • Learn how to model density variation. • Identify dimensionless parameters. • Study two examples: • Heat transfer from a heat sink assembly • Flow inside double-paned window cavities

3. Understanding Convection Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 3 • Classified in two main categories: free and forced convection. • Convection can be further classified by the nature of flow, for example: laminar or turbulent. • Heat transfer rates are higher in turbulent compared to laminar flow. • The heat transfer coefficient, denoted by “h”, is the main parameter that needs to be estimated for any kind of convection heat transfer. • Units are Watts per meter squared−Kelvin (W/m2K). The value of “h” is highly dependent on the boundary layer. • “h” is generally found by evaluating the Nusselt number (Nu) using regressions available for common cases of convective flow. Where “x” is the length and “k” is the thermal conductivity of a fluid.

4. Natural / Free Convection Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 4 • Responsible for most natural heat transfer phenomenon and shapes weather systems. • Can be used to advantage for passive cooling or heating. • Should be abated where undesirable by creating flow obstacles. • When modeling natural convection, density variation cannot be ignored. • Rayleigh number provides the strength of natural convection. Where, g = acceleration due to gravity α = thermal expansion coefficient ν= kinematic viscosity d= characteristic length/diameter

5. Natural / Free Convection Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 5 Convection from a horizontal cylinder is one of the most common examples of natural convection. Examples such as heat loss from hot pipes occur frequently. Churchill and Chu, 1975, established the following regression Where, Nu = Nusselt Number Ra = Rayleigh Number Pr = Prandtl Number Hot air plume rising after becoming heated by a hot cylinder. Picture courtesy ofH. Junaidi et al

6. Modeling Density Variation Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 6 • Density variation must be taken into account, as natural convection depends upon the temperature gradient and the variation of density due to that temperature change. • The Boussinesq density approximation model simplifies the estimation of density variation. • Where αis the coefficient of volume expansion. For liquids, α ranges between 10-3 to 10-4 • ρo is the known value of density at temperature To

7. Forced Convection Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 7 • Forced convection can be several times more efficient than natural convection. • Both natural and forced convection can be used in conjunction for efficient designs. • In order to compare the strength of forced and natural convection when both are present, the Peclet number gives us a measure of their relative strengths. Where: U is the velocity L is the characteristic length α is the thermal diffusivity

8. Forced vs. Natural Convection Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 8 Table: Typical ranges of values for the surface convection heat transfer coefficient. (ref: Heat Transfer a problem solving approach; Tariq Muneer, Jorge Kubie and Thomas Grassie)

9. Additional Dimensionless Parameters Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 9 • Dimensionless parameters are frequently used both in fluid mechanics and heat transfer. Their origins lie in prototype testing – in order to simulate similar conditions on a scaled model, dimensionless parameters or ratios of flow / heat transfer entities would be matched. • To study convection in more detail, the following dimensionless numbers should be looked at : • Grashof number • Prandtl number • Archimedes number

10. Example: Heat Sink Assembly Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 10 20° • A heat sink assembly is a common design element in electronics such as desktop computers, laptops and audio systems. • A video presentation for this module is available for setting up and solving a heat sink assembly design that ties with this example. B C Fins (Aluminium) Heat Spreader (Copper) 40 Watts Microprocessor (Silicon)

11. Additional Example: Flow Inside Double-Paned Window Cavities Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 11 • Convective flow inside window cavities has been studied in great detail. • Many studies have looked at convection between two parallel plates even at different angles. • A convective loop forms provided that the distance between the two walls of the cavity is sufficient for the air to move. • MacGregor and Emery [1] proposed the following relationship for cavities with a large aspect ratio (H/L): Where: H = cavity height L = cavity width

12. Summary Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 12 • Heat transfer occurs mainly through convection, particularly in engineering applications. • Natural and forced convection both carry significance as they occur in numerous applications. • Because the presence of buoyancy forces lead to heat transfer in natural convection, modelingthe density variation is required. • The Bousinesq model is most commonly used for modeling density variation because of its simplicity.

13. Summary Section 6 – Thermal Analysis Module3: Convection Heat Transfer Page 13 • Solutions to convection problems are mostly obtained through the use of regressions which involve dimensionless parameters such as Nusselt, Rayleigh and Peclet numbers. • These regressions are available for a large number of generic cases such as convection from a flat plate, sphere, cylinder, series of fins, etc. • Numerical analysis for convection heat transfer is valuable particularly when geometry strays from regular geometry.