Convection Prepared by: Nimesh Gajjar

CONVECTIVE HEAT TRANSFER Convection heat transfer involves fluid motion heat conduction The fluid motion enhances the heat transfer, since it brings hotter and cooler chunks of fluid into contact, initiating higher rates of conduction at a greater number of sites in fluid. Therefore, the rate of heat transfer through a fluid is much higher by convection than it is by conduction. In fact, the higher the fluid velocity, the higher the rate of heat transfer. AIR 20°C 5 m/s 20°C Warmer air rising AIR No convection current AIR a) Forced Convection b) Free Convection c) Conduction

Convection heat transfer strongly depends on fluid properties dynamic viscosity, thermal conductivity k, density and specific heat fluid velocity V Geometry and the roughness of the solid surface Type of fluid flow (such as being laminar or turbulent). NEWTON’S LAW OF COOLING h = Convection heat transfer coefficient A s = Heat transfer surface area T s = Temperature of the surface T  = Temperature of the fluid sufficiently far from the surface LOCAL HEAT FLUX h l is the local convection coefficient

TOTAL HEAT TRANSFER RATE Local and total convection transfer (a) Surface of arbitrary shape. (b) Flat plate. q” x dx L A s, T s dA s q” A s, T s

A fluid flowing over a stationary surface comes to a complete stop at the surface because of the no-slip condition. A similar phenomenon occurs for the temperature. When two bodies at different temperatures are brought into contact, heat transfer occurs until both bodies assume the same temperature at the point of contact. Therefore, a fluid and a solid surface will have the same temperature at the point of contact. This is known as NO-TEMPERATURE-JUMP CONDITION. Zero velocity at the surface Relative velocity of fluid layers Uniform approach velocity, V Solid Block

An implication of the no-slip and the no-temperature jump conditions is that heat transfer from the solid surface to the fluid layer adjacent to the surface is by pure conduction, since the fluid layer is motionless, T represents the temperature distribution in the fluid is the temperature gradient at the surface.

NUSSELT NUMBER k is the thermal conductivity of the fluid L c is the characteristic length Heat transfer through a fluid layer of thickness L and temperature difference Heat transfer through the fluid layer will be by convection when the fluid involves some motion and by conduction when the fluid layer is motionless. Nusselt number - enhancement of heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid layer. Larger the Nusselt number, the more effective the convection. Nu = 1 for a fluid layer - heat transfer across the layer by pure conduction Fluid layer T2T2 T1T1 ΔT = T 2 – T 1

Internal and external flows EXTERNAL FLOW - The flow of an unbounded fluid over a surface such as a plate, a wire, or a pipe INTERNAL FLOW - flow in a pipe or duct, if the fluid is completely bounded by solid surfaces External flow Air Internal flow Water

Laminar versus Turbulent Flow Some flows are smooth and orderly while others are rather chaotic. The highly ordered fluid motion characterized by smooth streamlines is called laminar. The flow of high-viscosity fluids such as oils at low velocities is typically laminar. The highly disordered fluid motion that typically occurs at high velocities characterized by velocities fluctuations is called turbulent. The flow of low-viscosity fluids such as air at high velocities is typically turbulent. The flow regime greatly influences the heat transfer rates and the required power for pumping Dye Streak Smooth well rounded Entrance Q = VA Pipe Dye Laminar Transitional Turbulent

Osborne Reynolds in 1880’s, discovered that the flow regime depends mainly on the ratio of the inertia forces to viscous forces in the fluid. The Reynolds number can be viewed as the ratio of the inertia forces to viscous forces acting on a fluid volume element.

One, Two and Three Dimensional Flows V(x, y, z) in cartesian or V(r, , z) in cylindrical coordinates One-dimensional flow in a circular pipe

VELOCITY BOUNDARY LAYER Development of a boundary layer on a surface is due to the no-slip condition BOUNDARY LAYER REGION INVISCID FLOW REGION Boundary-layer thickness, δ x cr Laminar boundary-layer Turbulent boundary-layer Transition region Turbulent layer Laminar layer Buffer layer V y x δ 0.99V Zero velocity at the surface (No slip condition ) V Relative velocity of fluid layers

Surface Shear Stress Skin friction coefficient Friction force over the entire surface

THERMAL BOUNDARY LAYER Thermal boundary layer on a flat plate (the fluid is hotter than the plate surface) The thickness of the thermal boundary layer, at any location along the surface is define as the distance from the surface at which the temperature difference T – T s equals 0.99(T  – T s ). For the special case of T s = 0, we have T = 0.99 at the outer edge of the thermal boundary layer, which is analogous to u = 0.99 for the velocity boundary layer. Thermal boundary layer Uniform Temperature Free Stream

 Shape of the temperature profile in the thermal boundary layer dictates the convection heat transfer between a solid surface and the fluid flowing over it.  In flow over a heated (or cooled) surface, both velocity and thermal boundary layers will develop simultaneously.  Noting that the fluid velocity will have a strong influence on the temperature profile, the development of the velocity boundary layer relative to the thermal boundary layer will have a strong effect on the convection heat transfer. PRANDTL NUMBER The relative thickness of the velocity and the thermal boundary layers is described by the dimensionless parameter Prandtl number, defined as

FluidPr Liquid metals Gases Water Light organic fluids5-50 Oils50-100,000 Glycerin ,000 TYPICAL RANGES OF PRANDTL NUMBERS FOR COMMON FLUIDS

AVERAGE SKIN FRICTION COEFFICIENT

Problem: Engine oil at 60° C flows over the upper surface of a 5-m long flat plate whose temperature is 20° C with a velocity of 2 m/s (Fig 2.12). Determine the total drag force and the rate of heat transfer per unit width of the entire plate. Known: Engine oil flows over a flat plate. Find: The total drag force and the rate of heat transfer per unit width of the plate are to be determined. Assumptions: The flow is steady and incompressible. The critical Reynolds number is. L= 5 m A

= N which is less than the critical Reynolds number Note that, heat transfer is always from the higher-temperature medium to the lower- temperature one. In this case, it is from the oil to the plate. The heat transfer rate is per m width of the plate. The heat transfer for the entire plate can be obtained by multiplying the value obtained by the actual width of the plate.

Problem: A long 10-cm diameter steam pipe whose external surface temperature is 110 o C passes through some open area that is not protected against the winds (Fig. 2.23). Determine the rate of heat loss from the pipe per unit length of its length when the air is at 1 atm pressure and 10 o C and the wind is blowing across the pipe at a velocity of 8 m/s. Schematic: Known: A steam pipe is exposed to windy air. Find: The rate of heat loss from the steam is to be determined.

Assumptions: Steady operating conditions exist. Radiation effects are negligible. Air is an ideal gas. The properties of air at the average film temperature of = ( )/2 =60 =

Important numbers Inertial force Viscous force Reynolds number Momentum diffusivity Thermal diffusivity Prandtl number Buoyancy forces Viscous forces Conduction Convection Nusselt number thermal internal resistance surface film resistance Grashof number Biot number Reference book: Fundamentals of Heat and Mass Transfer, Incropera & DeWitt