MET 214 Module 3
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- Heat exchangers transfer heat between fluids through solid surfaces. Heat is transferred by convection between the fluid and solid surface. - The rate of heat transfer depends on the convection heat transfer coefficient (h), which depends on fluid properties and velocities. - Dimensionless numbers like Reynolds, Prandtl, and Nusselt relate fluid flow regime (laminar or turbulent) to heat transfer rate. - Empirical relationships using these numbers predict heat transfer for forced and natural convection in different geometries. - The overall heat transfer coefficient (U) accounts for resistances of conductive and convective boundaries in composite systems.
MET 214 Module 3
- 2. INTRODUCTION • When a fluid flows past a stationary solid surface ,a thin film of fluid is postulated as existing between the flowing fluid and the stationary surface • It is also assumed that all the resistance to transmission of heat between the flowing fluid and the body containing the fluid is due to the film at the stationary surface.
- 3. Increasing Advection U , T T u Ts T(y) U(y)
- 4. Heat transfer co-efficient(h): ability of the fluid carry away heat from the surfaces which in turn depends upon velocities and other thermal properties. unit :w/m2 k or w/m2oC Fluid motion induced by external means
- 5. Chilled water pipes Hot air rising Qout Qin Cool air falling
- 6. • The amount of heat transferred Q across this film is given by the convection equation Where h: film co-efficient of convective heat transfer,W/m2K A: area of heat transfer parallel to the direction of fluid flow, m2. T1:solid surface temperature, 0C or K T2: flowing fluid temperature, 0C or K ∆t: temperature difference ,K
- 7. • Laminar flow of the fluid is encountered at Re<2100.Turbulent flow is normally at Re>4000.Sometimes when Re>2100 the fluid flow regime is considered to be turbulent • Reynolds number= • Prandtl number= • Nusselt number= • Peclet number=
- 8. • Grashof number= • Where in SI system • D: pipe diameter,m • V :fluid velocity,m/s • :fluid density,kg/m3 • μ :fluid dynamic viscosity N.s/m2 or kg/m.s • ᵧfluid kinematic viscosity, m2/s :
- 9. • K:fluid thermal conductivity,w/mK • h: convective heat transfer coefficient,w/m2.K • Cp:fluid specific heat transfer,J/Kg.K • g:acceleration of gravity m/s2 • β:cubical coefficient of expansion of fluid= • ∆t:temperature difference between surface and fluid ,K
- 10. Functional Relation Between Dimensionless Groups in Convective Heat Transfer • For fluids flowing without a change of phase(i.e without boiling or condensation),it has been found that Nusselt number (Nu) is a function of Prandtl number(Pr) and Reynolds number(Re) or Grashof number(Gr). • Thus for natural convection • And for forced convection
- 11. Empirical relationships for Force Convection • Laminar Flow in tubes: • Turbulent Flow in Tubes: For fluids with a Prandtl number near unity ,Dittus and Boelter recommend: • Turbulent Flow among flat plates: • Problem:
- 12. Empirical Relationships for natural convection • Where a and b are constants. Laminar and turbulent flow regimes have been observed in natural convection,10<7<GrPr<109 depending on the geometry. • Horizontal Cylinders: when 104<GrPr<109(laminar flow)and Nu=0.129(GrPr)0.33
- 13. when 109<GrPr<1012 (turbulent flow) Problem: Vertical surfaces: Nu=0.59(GrPr)0.25 4 When 10 <GrPr<109(laminar flow) Nu=0.129(GrPr)0.33 9 When 10 <GrPr<1012 (turbulent flow) Horizontal flat surfaces:fluid flow is most restricted in the case of horizontal surfaces. Nu=0.54(GrPr)0.25
- 14. 5 When 10 <GrPr<108(laminar flow) Nu=0.14(GrPr)0.33 8 whenGrPrᵧ10 (turbulent flow) Problem:
- 15. Laminar and Turbulent Flow 1Viscous sublayer Buffer Layer 2 3 Turbulent region 2 1 Laminar Transition Turbulent
- 16. Velocity profiles in the laminar and turbulent areas are very different U U y y 0, Lam y y 0,Turb Which means that the convective coefficient must be different Laminar Transition Turbulent
- 17. OVERALL HEAT TRANSFER CO-EFFICIENT FOR CONDUCTIVE –CONVECTIVE SYSTEMS • One of the common process heat transfer applications consists of heat flow from a hot fluid, through a solid wall, to a cooler fluid on the other side. The fluid flowing from one fluid to another fluid may pass through several resistances, to overcome all these resistance we use overall heat transfer • Newton's Law may be conveniently re-written as Where h=convective heat transfer co- efficient,W/m2-k
- 18. • A=area normal to the direction of heat flux,m2 • ∆T=temperature difference between the solid surface and the fluid,K. • It is often convenient to express the heat transfer rate for a combined conductive convective problem in the form(1),with h replaced by an overall heat transfer coefficient U.We now determine U for plane and cylindrical wall systems.
- 19. Figure 1 • Plane wall Or 1/Ahi and 1/Ah0 are known as thermal resistances due to convective boundaries or the convective resistances(K/W) Conductive heat flow Q=kAdt/dx=KA(T1-T2)/x
- 20. • Comparing the equations we get
- 21. problems • Radial Systems The Fourier law gives