INTRODUCTION TO CONVECTIVE HEAT TRANSFERHEAT TRANSFER

Prabal TalukdarPrabal TalukdarAssociate Professor

Department of Mechanical EngineeringDepartment of Mechanical EngineeringIIT Delhi

E-mail: prabal@mech.iitd.ac.inp

P.Talukdar/Mech-IITD

Introduction to ConvectionHeat transfer through a fluid is by convection in the presence of bulk fluid pmotion and by conduction in the absence of it. Therefore, conduction in a fluid can be viewed as the limiting case of convection,corresponding to the case of quiescentcorresponding to the case of quiescent fluid

)TT(hq& 2m/W)TT(hq sconv ∞−= m/W

)TT(hAQ ssconv ∞−=& W

P.Talukdar/Mech-IITD

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 thethat heat transfer from the solid surface to the fluid layer adjacent to the surface is by pure conduction, since the fluid layer is motionless, and can be expressed as

)m/W(Tkqq 2∂&& )m/W(

ykqq

0yfluidcondconv

=∂−==

conduction heat transfer from theconduction heat transfer from the solid surface to the fluid layer adjacent to the surface

Convection heat transfer from a solid surface to a fluid =

Heat is then convected away from the surface as a result of fluid motionTk ∂ result of fluid motion.

)C.m/W(TTy

kh 2

s

0yfluid

∞

=

−

∂−

=

P.Talukdar/Mech-IITD

Nusselt NumberNusselt NumberThq Δ=& Thqconv Δ

LTkqcond

Δ=&

Nusselt number represents the enhancement

L

Nuk

hLTk

Thqq

d

conv ==ΔΔ

=&

&

pof heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid layer.

hL

kL

kqcond

The larger the Nusselt number, the more effective the convection.

khLNu c=

P.Talukdar/Mech-IITD

Nu = 1 for a fluid layer represents heat transfer across the layer by pure conduction

Nusselt NumberNusselt NumberWilhelm Nusselt, a German engineer, was born November 25, 1882, at Nurnberg, Germany.

Nusselt studied mechanical engineering at the Munich Technical University where he got his doctorate in 1907 He taught in DresdenTechnical University, where he got his doctorate in 1907. He taught in Dresden from 1913 to 1917.

He completed his doctoral thesis on the "Conductivity of Insulating Materials" in 1907, using the "Nusselt Sphere" for his experiments.

In 1915, Nusselt published his pioneering paper: The Basic Laws of Heat Transfer, in which he first proposed the dimensionless groups nowTransfer, in which he first proposed the dimensionless groups now known as the principal parameters in the similarity theory of heat transfer.

P.Talukdar/Mech-IITD

Different types of flowDifferent types of flow

P.Talukdar/Mech-IITD

Velocity Boundary Layer

P.Talukdar/Mech-IITD

)m/N(u 2s ∂

∂μ=τ

Surface shear stress

where the constant of proportionality μ is called the dynamic viscosity of the fluid, whose unit is

)(y 0y

s=∂

μ

y ykg/m . s (or equivalently, N .s/m2, or Pa.s, or poise = 0.1 Pa.s).The ratio of dynamic viscosity to density appears frequently. For

i thi ti i i th ki ti i it d iconvenience, this ratio is given the name kinematic viscosity and is expressed as μ /ρ. Two common units of kinematic viscosity are m2/s and stoke (1 stoke = 1 cm2/s = 0.0001 m2/s).)

)m/N(2VC 2

2

fsρ

=τ

The viscosity of a fluid is a measure of its resistance to flow, and it is a strong function of temperature

P.Talukdar/Mech-IITD

Experimentally determined2 function of temperature

P.Talukdar/Mech-IITD

Thermal Boundary Layer

The thickness of the thermal boundary layer δt at any location along the surface is defined as the distance from the surface at which the temperature difference T Tdefined as the distance from the surface at which the temperature difference T -Tsequals 0.99(T∞ -Ts).

Note that for the special case of Ts = 0, we have T = 0.99T∞ at the outer edge of the

P.Talukdar/Mech-IITD

p s ∞ gthermal boundary layer, which is analogous to u = 0.99u∞ for the velocity boundarylayer.

The thickness of the thermal boundary layer increases in the flow direction

The convection heat transfer rate anywhere along the surface is directly related to the temperature gradient at that location. T

Therefore, the shape of the temperature profile in the thermal boundary layer dictates the convection heat transfer

Noting that the fluid velocity 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

P.Talukdar/Mech-IITD

thermal boundary layer will have a strong effect on the convection heat transfer.

Prandtl numberPrandtl number

It is named after Ludwig Prandtl, who introduced the concept of boundary layer inconcept of boundary layer in 1904 and made significant contributions to boundary layer theory.

The Prandtl numbers of gases are about 1, which indicates that both momentum and heat dissipate through the fluid at about the same rate. Heat diffuses very quickly in liquid metals (Pr <<1) and very

Consequently the thermal boundary layer is much thicker for liquid metals and much

P.Talukdar/Mech-IITD

liquid metals (Pr <<1) and very slowly in oils (Pr >> 1) relativeto momentum

thinner for oils relative to the velocity boundary layer.

Ludwig PrandtlLudwig Prandtl(1875-1953)

Prandtl was born in Freising, near Munich, g, ,in 1875.He entered the Technische Hochschule Munich in 1894 and graduated with a Ph.D. under guidance of Professor Augustunder guidance of Professor August Foeppl in six years

In 1901 Prandtl became a professor of fluid mechanics at the Technical school in Hannover, now the Technical University Hannover

Doctoral students: Ackeret, Heinrich Blasius, Busemann, Nikuradse, Pohlhausen, Schlichting, Tietjens, Tollmien,

P.Talukdar/Mech-IITD

von Kármán, and many others (85 in total)

Laminar / Turbulent FlowLaminar / Turbulent Flow

The intense mixing of the fluid in turbulent flow as a result of rapid fluctuationsenhances heat and momentum transfer e a ces ea a d o e u a s ebetween fluid particles, whichincreases the friction force on the surface and the convection heat transferrate

P.Talukdar/Mech-IITD

rate.

Reynolds numberReynolds numberBritish scientist Osborn Reynolds (1842–1912)

The transition from laminar to turbulentThe transition from laminar to turbulent flow depends on the surface geometry,surface roughness, free-stream velocity, surface temperature, and type of fluid, p ypamong other things.

After exhaustive experiments in the 1880s, Osborn Reynolds discovered that the flowNote that kinematic viscosity Osborn Reynolds discovered that the flow regime depends mainly on the ratio of theinertia forces to viscous forces in the fluid

Note that kinematic viscosity has the unit m2/s, which is identical to the unit of thermal diffusivity, and can be viewed

P.Talukdar/Mech-IITD

as viscous diffusivity or diffusivity for momentum.

At large Reynolds numbers, the inertia forces, which areinertia forces, which are proportional to the density and the velocity of the fluid, are large relative to the viscous forces,and thus the viscous forces cannot prevent the random and rapid fluctuations of the fluid.

At small Reynolds numbers, however, the viscous forces are large eno gh to o ercome thelarge enough to overcome the inertia forces and to keep the fluid “in line.” Thus the flow is turbulent in the first case and laminar in the

The Reynolds number at which the flow becomes turbulent is called thecritical Reynolds number

in the first case and laminar in the second.

For flow over a flat plate, the generally accepted value of the critical Reynolds number is Re = Vx /ν = u x / ν = 5 x 105 where x is the distance from the

P.Talukdar/Mech-IITD

number is Recr Vxcr/ν u∞xcr/ ν 5 x 10 , where xcr is the distance from the leading edge of the plate at which transition from laminar to turbulent flow occurs