# Thermal and Fluids in Architectural Engineering

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1 hermal and Fluids in Architectural Engineering 12. Convection heat transfer Jun-Seo Par, Dr. Eng., Prof. Dept. of Architectural Engineering Hanyang Univ.

2 Where do we learn in this chaper 1. Introduction 2.he first law 3.hermal resistances 4. Fundamentals of fluid mechanics 5. hermodynamics 6. Application 7.Second law 8. Refrigeration, heat pump, and power cycle 15. Ideal Gas Mixtures and Combustion 9. Internal flow 10. External flow 11. Conduction 12. Convection 14. Radiation 13. Heat Exchangers Page 3/17

3 11. Convection Heat ransfer 12.1 Introduction 12.2 Forced Convection in External flows 12.8 Natural Convection over surface

4 12.1 Introduction ΔE Q - W Convection refers an energy transfer between a surface and a fluid moving over the surface - Firstly, Heat from the surface conducts to the fluid - he fluid movement convects the heat away from the surface Fluid movement occurs due to two fundamentally different mechanisms - Force Convection / Natural Convection

5 12.1 Introduction ΔE Q - W Forced convection - the fluid is moved by mechanical means, a fan or pump - the movement of the surface Natural convection (Free convection) - the density of the fluid near by hot surface is decreasing, - the cooler surround fluid displace the hot fluid

6 12.1 Introduction ΔE Q - W In the previous chapter, convection heat transfer coefficient, h, is defined as below h " q s " q f ( s : the solid surface temperature, f :the fluid temperature)

7 11.2 Forced convection in external flows ΔE Q - W Velocity boundary layer - he quantity δ, the velocity boundary layer thicness, is typically defined as the value of y for which u = 0.99u. - With increasing distance from the leading edge, the effects of viscosity grows the boundary layer (δ increases with x) Source: Fundamental of Heat and mass transfer, Wiley, pp331

8 11.2 Forced convection in external flows hermal boundary layer ΔE Q - W - Just as the velocity boundary layer develops when there is fluid flow over a surface, a thermal boundary layer must develop if the fluid free stream and surface temperatures differ. Source: Fundamental of Heat and mass transfer, Wiley, pp332

9 11.2 Forced convection in external flows ΔE Q - W hermal boundary layer - he region of the fluid in which these temperature gradients exist is the thermal boundary layer, and its thicness, δt, is typically defined as the value of y for which the ratio [(s - )/(s - )] = Source: Fundamental of Heat and mass transfer, Wiley, pp332

10 11.2 Forced convection in external flows ΔE Q - W Convection heat transfer coefficient, h, in hermal boundary layer Conduction Heat Flux q " d dx ; at the solid surface In the thermal d dx Δ y boundary layer, f s the temperature gradient approximat ion

11 11.2 Forced convection in external flows Convection heat transfer coefficient, h, in hermal boundary layer - a large boundary decreases the heat transfer coefficient ΔE Q - W f s s f f s s f q q h Δ q " " " h, Convection heat transfer Coefficien t, y ion approximat he heat flux

12 11.2 Forced convection in external flows ΔE Q - W Prandtle number in convection heat transfer - he relative size of the velocity and thermal boundary layer depends on three physical properties;, Cp, μ - hermal conductivity,, > how easily heat is conduct in the fluid. - Specific heat, Cp, > determine the temperature rise - Viscosity, μ, > affects the velocity field and the amounts of heat transfer by convection

13 11.2 Forced convection in external flows ΔE Q - W Prandtle number in convection heat transfer - Prandtle number is dimensionless, and is a thermophysical property - Prandtle number is 1.0, than the velocity and thermal boundary have same thicness - For liquid metal (Prandtle number is low), thermal transport is much more effective than momentum transport. Pr C p C p

14 11.2 Forced convection in external flows ΔE Q - W Nusselt number in convection heat transfer - Nusselt number is the non dimensional heat transfer - Nusselt number is the ratio of thermal boundary layer to the velocity boundary layer Q Q Q Q conv cond conv cond ha A convectionin the thermal boundary layer conductionacrossa stagnant layer of the thermal boundary layer s f h hl Nu s f char

15 11.2 Forced convection in external flows Nusselt number in convection heat transfer - Just as the friction coefficient and Re number, Nusselt number is related to Re number - Nusselt number is also denpends Pr number. ΔE Q - W Nu f (Re, Pr)

16 11.2 Forced convection in external flows An isothermal flat plate ΔE Q - W Laminar flows Nu x h x x Re x Re 1/ 2 5 ; Pr Pr 1/ urbulent flows Nu x h x x Re x Re 5 4/ 5 ; Pr 0.6 1/ 3 Pr 60

17 11.2 Forced convection in external flows Average convection heat transfer coefficient, h - Heat flux at location, x ΔE Q - W he heat flux approximat ion q " ( x) h x ( s f ) he averageheat transfer coefficient is 1 h L 0 L h x dx Source: Fundamental of Heat and mass transfer, Wiley, pp327

18 11.2 Forced convection in external flows Average, h in an isothermal flat plate ΔE Q - W Laminar Nu L flows hx Re x Re 1/ 2 5 ; Pr Pr 1/ urbulent flows Nu L hx Re x (0.037 Re 510 4/ 5 5 ; ) Pr Pr 1/ 3 60

19 11.8 Natural convection over surfaces ΔE Q - W In the forced convection, the heat transfer coefficient depends on flow velocity - the velocity is used to compute Re number >Pr >Nu In a natural convection, the velocity is unnown - the flow is induced by changes in fluid density - here is no single velocity analogous to the free stream - Re number can not be computed

20 11.8 Natural convection over surfaces ΔE Q - W he velocity and thermal boundary layers form along the surface of the solid. - hermal boundary layer is similar to that of forced convection - he velocity boundary layer is different (free stream=0) he boundary layers grow along the surface, the heat transfer coefficient in the natural convection varies with vertical position (density changes) - Natural convection is governed by how the density changes with temperature

21 11.8 Natural convection over surfaces ΔE Q - W Density changes (pressure) density changesat a Pressure P Relative changes in density (volume expansivity ) volume expansivity at a Pressure P

22 11.8 Natural convection over surfaces ΔE Q - W Volume expansivity in an ideal gas PM 1) an ideal gas: R 2) partial derivative of the density with respect totemperature : volume expansivity is P - PM R 2 R R 2 P 1 PM R 2 ( PM ρr )

23 11.8 Natural convection over surfaces ΔE Q - W Grashof number in an natural convection - As lie Re number in the forced convection, Gradhof number is defined as Re inertial force viscosity force V 2 L VL 2 char char VL char Gr volume expansivity viscosity g 2 ( s 2 f ) L char

24 11.8 Natural convection over surfaces ΔE Q - W Average h, in an natural convection - he value of C and n depend on the geometry and on the flow regime. (show able 12-3) Nu L Ra hl n CRa C( Gr 2 g ( s f ) Lchar 2 Pr) n Pr

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Table of contents Task... 2 Calculation of heat loss of storage tanks... 3 Properties ambient air Properties of air... 7 Heat transfer outside, roof Heat transfer in flow past a plane wall... 8 Properties