MECHANISM BEHIND FREE /NATURAL CONVECTION

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1 CONVECTIVE HEAT TRANSFER By: Prof K. M. Joshi, Assi. Professor, MED, SSAS Institute of Technology, Surat.

2 MECHANISM BEHIND FREE /NATURAL CONVECTION The stagnate layer of fluid in immediate vicinity of hot body receives heat energy by conduction. The energy transfer by this, increases temperature and internal energy of fluid particles. AIR. Q Warmer air rising Because of temperature rise particles become less dance and hence lighter. The lighter particles move upward in low temperature region. These particles mix with the cool particles and transfer a part of energy. Simultaneously cool heavier particles moves downward to fill the space vacated by warm particles The circulation pattern, upward movement of hot particles and downward movement of cool particles causes convective currents. The se currents are set up naturally due to gravitational force only.

3 MECHANISM BEHIND FORCED CONVECTION 20 C 5 m/s AIR. Q 20 C Fluid flow causing by the pump, fan or atmospheric wind Therefore the rate of heat transfer is much higher by forced convection thanitisbythenaturalconvectionorbyconduction. Infact,thehigherthefluidvelocity,thehighertherateofheattransfer.

4 EXAMPLES OF NATURAL AND FORCED CONVECTION Design of house heating, furnace, architectural projects, roads and concrete structures concerns with the free convection. Cooling in IC engines, air condition installations, temperature control in nuclear plant, condenser tubes or other heat exchangers are example of forced convection.

5 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 & ( ) Q conv = ha s T s T 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 Heat flux, q conv =

6 The value of convective heat transfer coefficient (as well as temp difference may also) is not constant for entire surface it depends on location there for we can define LOCAL HEAT FLUX q conv ( ) = qconv = hl Ts T h l is the local convection coefficient Local and total convection transfer (a) Surface of arbitrary shape. (b) Flat plate. V,T A s, T s q da s U,T x q dx A s, T s L

7 TOTAL HEAT TRANSFER RATE Q & conv Q& = q da conv conv s A s Q& T T h da = ( ) conv s l s A s ( ) = qconv = hl Ts T putting value of Q & conv h 1 = A Q & & ( ) Q& ( Q ) = T T conv = has Ts T h da s A s conv s l s h da l s A s

8 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, q& = q& = k conv cond fluid T dy y = 0 Trepresents the temperature distribution in the fluid is the temperature gradient at the surface. ( T y ) y = 0 ( ) = qconv hl Ts T h = fluid ( ) k T y T s T y= 0

9 A fluid flowing over a stationary surface comes to a complete stop at the surface because of the no-slip condition. Uniform approach velocity, V Relative velocity of fluid layers Zero velocity at the surface Solid Block 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.

10 A steam pipe is passed through a room in which air and wall temperature are al 30 o C while surface temperature of the pipe is 400 o C If the diameter of the pipe is 40 mm and average heat transfer coefficient is 20 W/m 2 o C, what is the rate of heat loss from the pipe for one meter length of pipe. Schematic: Known: surface temperature and air temp Find: The rate of heat loss Assumptions: Steady operating conditions exist. Radiation effects are negligible. Constant properties.

11 Analysis: Q = h X A X (T s - T α ) = 20 X (πdl) X (400-30) = (20 W/m 2 o C ) X ( π X 40 X 10 3 X 1 m 2 ) X ( 370 o C ) = 0.93 kw

15 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 lowviscosity fluids such as air at high velocities is typically turbulent. This flow greatly influences the heat transfer rates and the required power for pumping Pipe Dye Q = VA Dye Streak Smooth well rounded Entrance Laminar Turbulent Transitional

16 Osborne Reynolds The Reynolds number can be viewed as the ratio of the inertia forces to viscous forces acting on a fluid volume element.

17 Dimensionless numbers and their Physical significance. Reynolds Number Leads to turbulent flow

WILHEM NUSSELT (1882-1957) was a German engineer. Nusselt studied mechanical engineering at the Munich Technical University where he got his doctorate in 1907.

19 WILHEM NUSSELT ( ) was a German engineer. Nusselt studied mechanical engineering at the Munich Technical University where he got his doctorate in Doctoral thesis CONDUCTIVITY OF INSULATING MATERIALS Professor at Technical university of Karlsruhe Professor at Technical university of Munchen Worked till the age of 70 years. Lived for 75 years and died in Munchen on September 1, 1957.

22 CHARACTERISTIC LENGTH OR EQUIVALENT DIAMETER In the non-dimensional number expressions there has appeared a characteristic length L or diameter D e. The equivalent diameter is usually defined as: For simple tube having internal diameter D,

25 Ludwig Prandtl Professor of Applied Mechanics at Gottingen for forty-nine years (from 1904 until his death there on August 15, 1953)

29 Grashof Number The Grashof number represents the product of bouyant force and inertia force to the square of viscous force. Gr 2 3 ( ρ l βg T ) = 2 µ ( ρ l βg T ) ( ρv l ) ( µ Vl) ( inertia ( viscous force) force) = = ( buoyant force) The natrual convection start with very small value of Gr and increase with significant increses in Gr. The role of Grashof number in natural convection is similar to the Reynold number in forced convection. Gr provides criteria whether the flow is laminar or turbulent. The critical Gr is 109 for a flow over a vertical plate for change over from laminar to turbulent.

30 Stanton Number Kg 3 m m s KJ Kg K KJ K

31 Peclet Number

32 Graetz Number Heat capacity of Fluid (in pipe) Per unit Length Thermal conductivity of pipe

PHYSICAL MECHANISM OF CONVECTION

Tue 8:54:24 AM Slide Nr. 0 of 33 Slides PHYSICAL MECHANISM OF CONVECTION Heat transfer through a fluid is by convection in the presence of bulk fluid motion and by conduction in the absence of it. Chapter