Pindah Panas 8/24/2011

(1)

Pindah Pindah Panas Panas Pindah Pindah Panas Panas Panas Panas Panas Panas

Lecture Note Lecture Note Principles of Food

Principles of Food EngineeringEngineering (ITP 330)(ITP 330)

Dept of Food

Dept of Food Science & Science & TechnologyTechnology Faculty of Agricultural Technology Faculty of Agricultural Technology Bogor Agricultural University Bogor Agricultural University BOGOR

BOGOR

Pindah Panas Pindah Panas

Tujuan Pembelajaran Tujuan Pembelajaran

Pindah Panas Pindah Panas

Tujuan Pembelajaran Tujuan Pembelajaran

•• Mengerti prinsip dasar pindah panasMengerti prinsip dasar pindah panas

•• Mengerti prinsip dasar pindah panasMengerti prinsip dasar pindah panasMengerti prinsip dasar pindah panasMengerti prinsip dasar pindah panas

–

– untuk mengetahui bagaimana bahan pangan untuk mengetahui bagaimana bahan pangan dipanaskan dan/atau didinginkan

dipanaskan dan/atau didinginkan

•• mengerti bagaimana pindah panas diukurmengerti bagaimana pindah panas diukur

–

– menentukan laju pemanasan dan pendinginan bahan menentukan laju pemanasan dan pendinginan bahan pangan

pangan

•• Mengerti faktorMengerti faktor--faktor apa saja yang faktor apa saja yang Mengerti prinsip dasar pindah panas Mengerti prinsip dasar pindah panas

–

– untuk mengetahui bagaimana bahan pangan untuk mengetahui bagaimana bahan pangan dipanaskan dan/atau didinginkan

dipanaskan dan/atau didinginkan

•• mengerti bagaimana pindah panas diukurmengerti bagaimana pindah panas diukur

–

– menentukan laju pemanasan dan pendinginan bahan menentukan laju pemanasan dan pendinginan bahan pangan

pangan

•• Mengerti faktorMengerti faktor--faktor apa saja yang gg faktor apa saja yang pp j yj y gg

mempengaruhi (dan bagaimana pengaruhnya) mempengaruhi (dan bagaimana pengaruhnya) aplikasi pindah panas dalam proses penanganan, aplikasi pindah panas dalam proses penanganan, pengolahan, distribusi dan pemanfaatan pangan pengolahan, distribusi dan pemanfaatan pangan

g

g pp j yj y gg

mempengaruhi (dan bagaimana pengaruhnya) mempengaruhi (dan bagaimana pengaruhnya) aplikasi pindah panas dalam proses penanganan, aplikasi pindah panas dalam proses penanganan, pengolahan, distribusi dan pemanfaatan pangan pengolahan, distribusi dan pemanfaatan pangan

Purwiyatno

Purwiyatno HariyadiHariyadi/ITP//ITP/FatetaFateta/IPB/IPB Purwiyatno

Purwiyatno HariyadiHariyadi/ITP//ITP/FatetaFateta/IPB/IPB

(2)

Pindah Panas Pindah Panas Pindah Panas Pindah Panas

•• Heat transferHeat transfer -- movement of energy due to amovement of energy due to a

•• Heat transferHeat transfer -- movement of energy due to aHeat transfer Heat transfer movement of energy due to a movement of energy due to amovement of energy due to a temperature difference

temperature difference

•• Can only occur if a temperature difference existsCan only occur if a temperature difference exists

•• Occurs through:Occurs through:

1. conduction, 1. conduction, 2. convection, and 2. convection, and Heat transfer

Heat transfer movement of energy due to a movement of energy due to a temperature difference

temperature difference

•• Can only occur if a temperature difference existsCan only occur if a temperature difference exists

•• Occurs through:Occurs through:

1. conduction, 1. conduction, 2. convection, and 2. convection, and 3. radiation, or 3. radiation, or

4. combination of above 4. combination of above 3. radiation, or

3. radiation, or

4. combination of above 4. combination of above

Purwiyatno

•• May be indicated as total transfer May be indicated as total transfer

Identified by total heat flow (Q) with units of Btu Identified by total heat flow (Q) with units of Btu

•• May be indicated as total transfer May be indicated as total transfer

Identified by total heat flow (Q) with units of Btu Identified by total heat flow (Q) with units of Btu

Heat Transfer (1)

•• Identified by total heat flow (Q) with units of BtuIdentified by total heat flow (Q) with units of Btu

•• Identified by rate of heat flow (q) or Identified by rate of heat flow (q) or ΔΔQ/Q/ΔΔt with units t with units of watts ot Btu/hr

of watts ot Btu/hr

•• Also, may be expressed as heat transfer per unit Also, may be expressed as heat transfer per unit

•• Identified by total heat flow (Q) with units of BtuIdentified by total heat flow (Q) with units of Btu

•• Identified by rate of heat flow (q) or Identified by rate of heat flow (q) or ΔΔQ/Q/ΔΔt with units t with units of watts ot Btu/hr

of watts ot Btu/hr

•• Also, may be expressed as heat transfer per unit Also, may be expressed as heat transfer per unit ,, yy pp pp area =

area = heat fluxheat fluxor q/Aor q/A

, y p p

area =

area = heat fluxheat fluxor q/Aor q/A

(3)

•• Heat transfer can be classified as:Heat transfer can be classified as:

1. Steady

1. Steady--state:state:

o all factors are stabilized with respect to time o all factors are stabilized with respect to time

•• Heat transfer can be classified as:Heat transfer can be classified as:

1. Steady

1. Steady--state:state:

o all factors are stabilized with respect to time o all factors are stabilized with respect to time

Heat Transfer (2)

Heat Transfer (2) Heat Transfer (2) Heat Transfer (2)

o temperatures are constant at all locations o temperatures are constant at all locations o steady

o steady--state is sometimes assumed if little error state is sometimes assumed if little error results

results 2. Unsteady

2. Unsteady--state (transient)state (transient)heat transfer occurs when:heat transfer occurs when:

o temperature changes with time o temperature changes with time

o thermal processing of foods is an important o thermal processing of foods is an important o temperatures are constant at all locations o temperatures are constant at all locations o steady

o steady--state is sometimes assumed if little error state is sometimes assumed if little error results

results 2. Unsteady

2. Unsteady--state (transient)state (transient)heat transfer occurs when:heat transfer occurs when:

o temperature changes with time o temperature changes with time

o thermal processing of foods is an important o thermal processing of foods is an important o thermal processing of foods is an important o thermal processing of foods is an important

example example

o must know time required for the coldest spot in o must know time required for the coldest spot in

can to reach set temperature can to reach set temperature

o thermal processing of foods is an important o thermal processing of foods is an important

example example

o must know time required for the coldest spot in o must know time required for the coldest spot in

can to reach set temperature can to reach set temperature

Purwiyatno

•• Occurs when heat moves through a material Occurs when heat moves through a material (usually solid or viscous liquid) due to molecular (usually solid or viscous liquid) due to molecular action only

action only

•• Occurs when heat moves through a material Occurs when heat moves through a material (usually solid or viscous liquid) due to molecular (usually solid or viscous liquid) due to molecular action only

action only

CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER

HEAT HEAT HEAT HEAT

•• Heat/energy is transferred at molecular levelHeat/energy is transferred at molecular level

•• No physical movement of materialNo physical movement of material

•• Heat/energy is transferred at molecular levelHeat/energy is transferred at molecular level

•• No physical movement of materialNo physical movement of material

•• Heating/cooling of solidHeating/cooling of solid

•• Heat flux is directly proportional to the temperature Heat flux is directly proportional to the temperature gradient, and inversely proportional to distance gradient, and inversely proportional to distance (thickness of material).

(thickness of material).

•• Heating/cooling of solidHeating/cooling of solid

•• Heat flux is directly proportional to the temperature Heat flux is directly proportional to the temperature gradient, and inversely proportional to distance gradient, and inversely proportional to distance (thickness of material).

(thickness of material).

Purwiyatno

(4)

••

May occur simultaneously in one, or two, or three May occur simultaneously in one, or two, or three directions

directions

••

May occur simultaneously in one, or two, or three May occur simultaneously in one, or two, or three directions

directions

CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER

••

Many practical problems involve heat flow in only one Many practical problems involve heat flow in only one or two directions

or two directions

••

Conduction along a rod heated at one end is an Conduction along a rod heated at one end is an example of two dimensional conduction

example of two dimensional conduction

••

Heat flows along the length of the rod to the cooler Heat flows along the length of the rod to the cooler end (one direction)

end (one direction)

••

Many practical problems involve heat flow in only one Many practical problems involve heat flow in only one or two directions

or two directions

••

Conduction along a rod heated at one end is an Conduction along a rod heated at one end is an example of two dimensional conduction

example of two dimensional conduction

••

Heat flows along the length of the rod to the cooler Heat flows along the length of the rod to the cooler end (one direction)

end (one direction)(( ))

••

If rod is not insulated, heat is also lost to If rod is not insulated, heat is also lost to surroundings

surroundings

••

Center warmer than outer surfaceCenter warmer than outer surface

( )

••

If rod is not insulated, heat is also lost to If rod is not insulated, heat is also lost to surroundings

surroundings

••

Center warmer than outer surfaceCenter warmer than outer surface

Purwiyatno

Purwiyatno HariyadiHariyadi/ITP//ITP/FatetaFateta/IPB/IPB Purwiyatno

Purwiyatno HariyadiHariyadi/ITP//ITP/FatetaFateta/IPB/IPB

•• One dimensional conduction heat transfer is a One dimensional conduction heat transfer is a

•• One dimensional conduction heat transfer is a One dimensional conduction heat transfer is a -- one dimensional one dimensional (unidirectional)(unidirectional)

-- one dimensional one dimensional (unidirectional)(unidirectional)

CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER

function of:

1. temperature difference 1. temperature difference 2. material thickness 2. material thickness

3. area through which heat flows 3. area through which heat flows

4. resistance of the material to heat flow 4. resistance of the material to heat flow function of:

function of:

1. temperature difference 1. temperature difference 2. material thickness 2. material thickness

3. area through which heat flows 3. area through which heat flows

4. resistance of the material to heat flow 4. resistance of the material to heat flow

(5)

CONDUCTION HEAT TRANSFER

-- one dimensionalone dimensional

CONDUCTION HEAT TRANSFER

-- one dimensionalone dimensional Fourier’s Law Of Heat Conduction:

Fourier’s Law Of Heat Conduction:

XX₁₁

XX₁₁ XXXX₂₂₂₂

qq_xx qq_xx

ΔΔQ = Total heat flowQ = Total heat flow q

q = rate of heat flow in x direction by conduction W= rate of heat flow in x direction by conduction W ΔΔQ = Total heat flowQ = Total heat flow

q

q = rate of heat flow in x direction by conduction W= rate of heat flow in x direction by conduction W

dx dx dx dx dT dT dT kA dT kA kA ---- kA

=

= q = q

_xx

q q

_xx

Δ

ΔQ Q Δ Δtt Δ ΔQ Q

Δ Δtt = = = =

q

q_x_x= rate of heat flow in x direction by conduction, W= rate of heat flow in x direction by conduction, W k = thermal conductivity, W/mC

k = thermal conductivity, W/mC A= area (normal to x

A= area (normal to x--direction) through which heat flows, mdirection) through which heat flows, m²² T = temperature, C

T = temperature, C

x = distance increment, variable, m x = distance increment, variable, m q

q_x_x= rate of heat flow in x direction by conduction, W= rate of heat flow in x direction by conduction, W k = thermal conductivity, W/mC

k = thermal conductivity, W/mC A= area (normal to x

A= area (normal to x--direction) through which heat flows, mdirection) through which heat flows, m²² T = temperature, C

T = temperature, C

x = distance increment, variable, m x = distance increment, variable, m

Purwiyatno

SIGN CONVENTION SIGN CONVENTION SIGN CONVENTION SIGN CONVENTION

direction of heat flow direction of heat flow direction of heat flow direction of heat flow Δ

ΔTT Δ ΔTT

Δ Δ xx Δ Δ xx

TEMPERATURETEMPERATURETEMPERATURETEMPERATURE

dx dx dx dx dT dT dT ----dT slope slope slope slope====

Temperature profile Temperature profile Temperature profile Temperature profile

DISTANCE DISTANCE DISTANCE DISTANCE

Purwiyatno

(6)

PH/TPG/Fateta/IPB

USING FOURIER’S LAW USING FOURIER’S LAW

∫∫

^T^T

X X₁₁

x

d d kdT kdT

q q

Integrating : Integrating :

qq_xx qq_xx

T1

T2

dx dx dT -- k A k A dT q

q

xx

= =

∫∫

∫∫ ⁼⁼

_T_T

X X

x x

1 2 1

2

kdT kdT --

dx dx A A q q

XX₁₁

XX₁₁ XXXX₂₂₂₂

qq_xx qq_xx

)) x x -- x x

₁₁

q ((

T q T T T

₁₁

2 2 1

1 2

2

−−

==

)) T T -- k(T k(T

₁₁

))

x x -- x x

₁₁

q ((

q

_x_x

A

22

== −−

22

X = X

X = X₁₁......> T = T> T = T₁₁ X = X

X = X₂₂......>> T = TT = T₂₂

--kdT kdT dx

A dx A q q

_x_x

=

1

)) ((

1

kA

1

kA

1 ₂₂ ₂₂

)) X X -- (X (X

₁₁

)) T T -- (T (T

₁₁

kA kA q

q

2 2 2 2 x

x

== −−

(7)

qq

Composite Rectangular Wall (In Series) Composite Rectangular Wall (In Series)

kk_A_A kk_B_B kk_C_C

qq

HEAT CONDUCTION IN MULTILAYERED SYSTEMS HEAT CONDUCTION IN MULTILAYERED SYSTEMS

qq

xx_A_A xx_B_B xx_C_C

qq

Temperature profile in Temperature profile in

TT₁₁

eratureerature Temperature profile in Temperature profile in

a multilayered system a multilayered system

TT₂₂ XX

TempeTempe

Purwiyatno

qq

dT --kA kA dT qq ==

USING FOURIER’S LAW :

k k A A

x --q q x T

T

A A

A A A

A

== ΔΔ ΔΔ

x --q q x T

T

^B^B

B B

== ΔΔ dX ΔΔ

dX kA kA x --q q x T

T Δ Δ

==

Δ Δ

A A k k q q

B B B

B

Purwiyatno

A A k k

x --q q x T

T

C C

C C C

C

== ΔΔ Δ

Δ

(8)

qq

T1 T2

A A k k

x --q q x T

T

A A

A A A

A

== ΔΔ ΔΔ

x --q q x T

T

^B^B

B B

== ΔΔ ΔΔ

Δ Δ ++

Δ Δ

==

ΔΔTT TT_A_A TT_B_B TT_C_C

−−

==

ΔΔTT TT₁₁ TT₂₂

Purwiyatno

A A k k q q

B B B

B

A A k k

x --q q x T

T

C C

C C C

C

== ΔΔ

⎟⎟⎟⎟

ΔΔ

⎠⎠

⎞⎞

⎜⎜⎜⎜⎝⎝

⎛⎛ ΔΔ

Δ ++

++ Δ Δ

== Δ

−−

C C C C

B B B B

A A A A 2

2 1

1 kk

X X k

k X X k

k X X A A q -- q T T T T

C C B

B A

A

CONDUCTION IN CYLINDRICAL OBJECTS CONDUCTION IN CYLINDRICAL OBJECTS

Fourier’s law in cylindrical coordinates Fourier’s law in cylindrical coordinates

dT kA dT

kA

Integrating :Integrating :

rr_ii rr_o_o

dr dr

dr -- kA kA dr qq

_rr

==

dr dr dT r L dT 2 r L --k k 2 ππ qq

_rr

==

Boundary Conditions : Boundary Conditions :

∫∫

⁼⁼ ⁻⁻ ^o^o

ii T T T T

dT dT k

k rr

dr dr 22ππLL

q q rr_o_o

rr_ii

T T kT kT Ln r

Ln r 22ππLL

q q

−−

==

rr_oo TT_oo

g g

Boundary Conditions : Boundary Conditions : TT = T = T

_ii

at at r = r r = r

_ii

T = T

_oo

at at r = r r = r

_oo

== ii −− oo rr

⎟⎟⎟⎟⎠⎠

⎜⎜⎜⎜ ⎞⎞

⎝⎝

⎛⎛

ii o o ln rr ln

)) T T Lk(T Lk(T 22ππ q q

Tii 2 T

2ππLL rr_ii

(9)

COMPOSITE CYLINDRICAL TUBE COMPOSITE CYLINDRICAL TUBE

rr₂₂

rr₃₃ rr₁₁

TT_ii

TT_oo

FROM FOURIER’S LAW:

⎟⎟⎟⎟ ⎠⎠

⎜⎜⎜⎜ ⎞⎞

⎝⎝

⎛⎛

== −−

ii oo

oo rr ii

rr ln rr ln

)) TT Lk(T 22ππ Lk(T qq

Purwiyatno

A =?

Let us define logarithmic mean area A Let us define logarithmic mean area A_m_m such that

such that

o o ii m m

rr

(r (r rr ))

)) T T T T kA ((

kA q

q == −−

rr₁₁ rr₂₂ rr₃₃ TT_ii

TT_oo

ii o o

rr )) (r (r −−

)) rr (r (r −−

ii o o ii o o m

m

rr ln rr ln L L 2 2ππ A

A

⎟⎟⎟⎟ ⎠⎠

⎜⎜⎜⎜ ⎞⎞

⎝⎝

== ⎛⎛

where where

ii o o rr

(( rr rr )) q

T q T T

T −−

^m^m ²³²³

2 2 3 3 rr 3 3 2

2 (kA(kA ))

)) rr (r (r q T q T T

T −−

==

−−

12 12 m m

1 1 2 2 rr 2 2 1

1 (kA(kA ))

)) rr (r (r q T q T T

T −−

==

−−

Purwiyatno

Purwiyatno HariyadiHariyadi/ITP//ITP/FatetaFateta/IPB/IPB m

m o

o

ii

T T kA kA

T

T −− ==

adding above two equationsadding above two equations

⎟⎟⎟⎟⎠⎠

⎞⎞

⎜⎜⎜⎜⎝⎝

⎛⎛ ΔΔ

⎟⎟⎟⎟ ++

⎠⎠

⎞⎞

⎜⎜⎜⎜⎝⎝

⎛⎛ ΔΔ

== −−

m 12 m

3 3 1 1 rr

kA kA rr kA

kA rr

)) T T T T q ((

q

23 23

(10)

Convection Heat Transfer Convection Heat Transfer

•• Transfer of energy due to the movement of a heated Transfer of energy due to the movement of a heated fluid

fluid

•• Movement of the fluid (liquid or gas) causes transfer of Movement of the fluid (liquid or gas) causes transfer of heat from regions of warm fluid to cooler regions in the heat from regions of warm fluid to cooler regions in the fluid

fluid

•• Natural ConvectionNatural Convection occurs when a fluid is heated and occurs when a fluid is heated and moves due to the change in density of the heated fluid moves due to the change in density of the heated fluid

•• Forced ConvectionForced Convection occurs when the fluid is moved by occurs when the fluid is moved by other methods (pumps, fans, etc.)

other methods (pumps, fans, etc.)

Purwiyatno Hariyadi/ITP/Fateta/IPB

CONVECTIVE HEAT TRANSFER : heat transfer to fluid CONVECTIVE HEAT TRANSFER : heat transfer to fluid

qqTT_aa< T< T_ss Surface area = ASurface area = A

q = h A(T q = h A(T

_ss

-- TT

_aa

))

TT_ss

q = rate of heat transfer q = rate of heat transfer

h = convective heat transfer coefficient, W/m h = convective heat transfer coefficient, W/m²²..^ooCC TT_ss= surface temperature= surface temperature

TT_aa= surrounding fluid temperature= surrounding fluid temperature

(11)

Colder fluid (hi h d it )

Fluid absorbs heat (higher density) Natural

Convection

(temperature increase:

density decrease)

PH/TPG/Fateta/IPB

FLUID FLOW IN A PIPE FLUID FLOW IN A PIPE

HEAT TRANSFER TO FLUID (Forced Convection) HEAT TRANSFER TO FLUID (Forced Convection)

Fluid flow can occur as Fluid flow can occur as -- laminar flowlaminar flow

-- turbulent flowturbulent flow

-- transition between laminar and turbulent flowtransition between laminar and turbulent flow

-- direction of flow direction of flow ^…..^…..> parallel or perpendicular to the solid > parallel or perpendicular to the solid object

object object object

Purwiyatno

(12)

q = h A (T q = h A (T_ss-- TT_aa))

h = f (density, velocity, diameter, viscosity, specific h = f (density, velocity, diameter, viscosity, specific

HEAT TRANSFER TO FLUID

^………^………

> h? > h?

( y, y, , y, p

heat, thermal conductivity, viscosity of fluid at heat, thermal conductivity, viscosity of fluid at wall temperature

wall temperature

The convective heat transfer coefficient is The convective heat transfer coefficient is determined by dimensional analysis.

determined by dimensional analysis.

A series of experiment are conducted to determine A series of experiment are conducted to determine

A series of experiment are conducted to determine A series of experiment are conducted to determine relationships between following dimensionless relationships between following dimensionless numbers.

numbers.

Purwiyatno

Dimensionless Numbers In Convective Heat Dimensionless Numbers In Convective Heat Transfer

Transfer

HEAT TRANSFER TO FLUID

^………^………

> h? > h?

Nusselt Number =

Nusselt Number = NN_nu_nu= (hD)/k= (hD)/k Prandtl Number = N

Prandtl Number = N_Pr_Pr= = μμCC_p_p/k/k Reynolds Number = Re = (

Reynolds Number = Re = (ρρvD)/vD)/μμ Where

Where

D = characteristic dimension D = characteristic dimension k th l d ti it f fl id k th l d ti it f fl id k = thermal conductivity of fluid k = thermal conductivity of fluid v = velocity of fluid

v = velocity of fluid C

C_p_p= specific heat of fluid= specific heat of fluid ρρ= density of fluid= density of fluid

μμ= viscosity of fluid= viscosity of fluid

(13)

N

_nu_nu

= f (N = f (N

_Re_Re

, N , N

_Pr_Pr

))

Laminar flow in pipes: If N

Laminar flow in pipes: If N_Re_Re<2100<2100 For

For (N(N_R_R x Nx N_P_P x D/L) < 100x D/L) < 100

⎞⎞

⎛⎛

HEAT TRANSFER TO FLUID

^….^….

> >

FORCED CONVECTIONFORCED CONVECTION

For

For (N(N_Re_Rex Nx N_Pr_Prx D/L) < 100x D/L) < 100

14 14 ..

0 0

66 66 ..

0 0

Pr Pr Re Re

045 045 ..

0 0 1 1

085 085 ..

0 0 66

66 ..

3 3 ⎟⎟⎟⎟ ⎠⎠

⎜⎜⎜⎜ ⎞⎞

⎝⎝

⎛⎛

⎟⎟ ⎠⎠

⎜⎜ ⎞⎞

⎝⎝

++ ⎛⎛

⎟⎟ ⎠⎠

⎜⎜ ⎞⎞

⎝⎝

⎛⎛

++

==

w w b b Nu

Nu

L L D x D x xN xN N N

L L D x D x xN xN N N N

N μμ

μμ

For (N

For (N_Re_Rex Nx N_PR_PRx D/L) > 100x D/L) > 100 ₀₀₃₃₃₃ ₀₀_..₁₄₁₄

⎞⎞

⎞⎞ ⎛⎛

⎛⎛

⁰⁰^..³³³³

PR PR RE RE Nu

Nu

L L w w

D x D x xN xN N N 86 86 ..

1 1 N

N ⎟⎟⎟⎟

⎠⎠

⎜⎜⎜⎜ ⎞⎞

⎝⎝

⎟⎟ ⎛⎛

⎠⎠

⎜⎜ ⎞⎞

⎝⎝

== ⎛⎛

μμ μμ

Purwiyatno

All physical properties are evaluated at bulk fluid All physical properties are evaluated at bulk fluid temperature, except

temperature, except μμ_w_w(viscosity at the wall)(viscosity at the wall)

Transition Flow in Pipes

Transition Flow in Pipes ÆÆ NN_RE_REbetween 2100 and 10,000: between 2100 and 10,000:

Æ

Æ use chart to determine h : use chart to determine h : Æ

Æ diagram diagram J Colburn factor (J) vs Re.

HEAT TRANSFER TO FLUID

^….^….

> >

14 . 0

3 2 h ⎞⎛Cpμ⎞ ⎛ μ ⎞

Æ ^J⁼⎛^⎜⎜_⎝^⎛_ρ_CpV^h ^⎟⎟_⎠^⎞^⎜_⎝^⎛^Cp._k^μ^⎟_⎠^⎞ ³^⎜⎜_⎝^⎛^μ_μ^w^⎟⎟_⎠^⎞

Purwiyatno

(14)

HEAT TRANSFER TO FLUID

^….^….

> >

Turbulent Flow in Pipes:

Turbulent Flow in Pipes: ^{………….}^{………….}> N> N_RE_RE> 10,000:> 10,000:

14 14 ..

0 0 0.33

0.33 Pr Pr NU

NU

0 0 .. 023 023 N N x x

N

N ⎟⎟⎟⎟

⎠⎠

⎜⎜⎜⎜ ⎞⎞

⎝⎝

== ⎛⎛ _μμ ^μμ

_w_w

Purwiyatno

⎠⎠

⎝⎝

Free convection involves the dimensionless Free convection involves the dimensionless number called Grashof Number, N

number called Grashof Number, N_Gr_Gr

((

^d^d ³³^ρρ ²²^g^gββ ^Δ^Δ^T^T

))

HEAT TRANSFER TO FLUID

^….^….

> >

FREE CONVECTIONFREE CONVECTION

((

_{G r}_{G r}

))

^m^m

Nu Nu

N N N N a a k k h D h D N

N

Pr

= Pr

=

(( ))

G r G r

N N

2 2

=

µ µ

ggββ ρρ

d= Dimension of the system;

d= Dimension of the system; ρρ= density; = density; ββ = koeff ekspansi volumetrik = koeff ekspansi volumetrik (koef muai volumetrik; 1/K);

(koef muai volumetrik; 1/K); µ=µ=viscosity; g= gravityviscosity; g= gravity a and m = constant

a and m = constant

(15)

V l f d f( h i l fi ti )

HEAT TRANSFER TO FLUID

^….^….

> >

FREE CONVECTIONFREE CONVECTION

((

_{G r}_{G r}

))

^m^m

Nu

a a N N N N

k k h D N h D

N = = = =

PrPr

Value of a and m =f(physical configuration) Value of a and m =f(physical configuration) Vertical surface

Vertical surface D=vertical dim. < 1

D=vertical dim. < 1 mNmN_Gr_GrNN_Pr_Pr<10<10⁴⁴ a=1.36a=1.36 m=1/5m=1/5 Horizontal cylinder

Horizontal cylinder D = dia < 20 cm

D = dia < 20 cm NN_Gr_GrNN_Pr_Pr<10<10^--5⁵ a=0.49a=0.49 m=0m=0 10

10^--5<^5<NN_Gr_GrNN_Pr_Pr<1<1 a=0.71a=0.71 m=1/25m=1/25 1<N

1<N_Gr_GrNN_Pr_Pr<10<10⁴⁴ a=1,09a=1,09 m=1/10m=1/10 Horizontal flat surface

Horizontal flat surface Facing Upward

Facing Upward 1010⁵⁵< N< N_Gr_GrNN_Pr_Pr<2x10<2x10⁷⁷ a=0.54a=0.54 m=1/4m=1/4 2x10

2x10⁷⁷< N< N_Gr_GrNN_Pr_Pr<3x10<3x10¹⁰¹⁰a=0.14a=0.14 m=1/3m=1/3 Facing downward

Facing downward 3x103x10⁵⁵< N< N_Gr_GrNN_Pr_Pr<3x10<3x10¹⁰¹⁰a=0.27a=0.27 m=1/4m=1/4

Purwiyatno

Equations for calculating heat transfer coefficient (h) in free convection from water to air (Toledo, p. 271, Table 7.3)

Kondisi permukaan Persamaan Nilai untuk C p

Udara/Uap Air

Silinder horisontal yang

dipanaskan/didinginkan

h = C(ΔT/D)^0.25 1.3196 291.1

Fluida di atas plate horizontal yang dipanaskan

h = C(ΔT)^0.25 2.4492 d t

…. dst

(16)

Temperature profile : conductive and convective heat transfer Temperature profile : conductive and convective heat transfer through a slab

through a slab

TT

₁₁

HEAT TRANSFER TO FLUID

^………^………

> U? > U?

TT

_aa

TT

_bb

hh

_ii

hh

TT

₁₁

TT

₂₂

hh

_ii

hh

_oo

Q = UA(T

_aa

--TT

_bb

)) where

where

U = Overall heat transfer coefficient [=] W/m U = Overall heat transfer coefficient [=] W/m

²²

C C

Purwiyatno

Steady State : Steady State : q

q_ii= q= q_x_x=q=q_o_o=q=q q = UA(T q = UA(T_a_a--TT_b_b) )

TT

_aa

TT

₁₁ HEAT TRANSFER TO FLUID

HEAT TRANSFER TO FLUID^………^………> U?> U?

q q x x q q q q q

q ΔΔ ++

+ +

=

= q

q_ii=q=h=q=h_iiA(TA(T_a_a--TT₁₁)) q

q_x_x=q=kA(T1=q=kA(T1--T2)/T2)/ΔΔxx q

q_o_o=q=h=q=h_o_oA(TA(T₂₂--TT_b_b)) T

T_a_a--TT_b_b= (T= (T_a_a--TT₁₁)+(T)+(T₁₁--TT₂₂)+(T)+(T₂₂--TT_b_b))

TT

_bb

hh

_ii

hh

_oo

TT

₂₂

O O O O lm lm ii

ii ii

ii hh AA

1 1 kA

kA x x A

A h h

1 1 A

A U U 1

1 ΔΔ ++

+ +

=

O O

ii hh

1 1 k k x x h

h 1 1 U U 1

1 ΔΔ ++

+ +

=

O O

ii hh AA

q q kA kA q q A A h h q q A A U U q

q == ++ ++

Atau, Atau, umum : umum :

A

A_ii=A=A_lm_lm=A=A_o_o=A=A

(17)

HEAT TRANSFER TO FLUID

^………^………

> U? > U?

TT

_aa

TT

₁₁

rr₂₂ T T_a_a

TT

_bb

hh

_ii

hh

_oo

TT

₂₂ rr₁₁

Surrounding fluid temp; T Surrounding fluid temp; T_b_b< T< T_a_a

1 1 rr

1 1 1

1 ΔΔ

O O O O lm lm ii

ii ii

ii hh AA

1 1 kA

kA rr A

A h h

1 1 A

A U U 1

1 ΔΔ ++

+ +

=

O O

ii hh

1 1 k k rr h h 1 1 U U 1

1 ΔΔ ++

+ +

=

= Atau,Atau,

umum : umum :

A A_ii A A_o_o ln ln

A A_ii -- A A_o_o A

A_lm_lm ==

Purwiyatno

HEAT TRANSFER TO FLUID

^………^………

> U? > U?

rr₁₁ rr₂₂ rr₃₃ TT

ri= r1= inside radius of cylinder r_o= r₃= outside radius of cylinder h_i= inside heat transfer coefficient TT_ii 11

TT_oo

i

ho= outside heat transfer coefficient

Calculating U based on outside radius of cylinder:

rr_o_oln(rln(r₂₂/r/r₁₁)) 1

1 1

1 ++ ++ rr_o_oln(rln(r₃₃/r/r₂₂)) rr_o_oln(rln(r_n_n/r/r_n_{n 1}₁)) rr_o_o

Purwiyatno

Purwiyatno HariyadiHariyadi/ITP//ITP/FatetaFateta/IPB/IPB o

o kk₁₁

rr_o_oln(rln(r₂₂/r/r₁₁)) h

h 1 1 U

U 1

1 == ++ ++

k k₂₂ rr_o_oln(rln(r₃₃/r/r₂₂))

K K_n_n--1₁ rr_o_oln(rln(r_n_n/r/r_n_n--1₁)) + …+

+ …+ rr_iihh_ii rr_o_o + +

(18)

Contoh soal

• Hitung heat flux (q/A) yang melewati glass pane

• Hitung heat flux (q/A) yang melewati glass pane yang terbuat dari lapisan gelas dengan ketebalan 1.6 mm yang dipisahkan oleh 0.8 mm lapisan insulator. Koefisien pindah panas pada sisi yang satu pada 21

^o

C adalah 2.84 W/m

²

K dan pada sisi yang lain bersuhu -15

^o

C adalah 11.4 W/m

²

K. y g

Konduktivitas panas gelas adalah 0.52 W/mK dan pada lapisan udara adalah 0.031 W/mK.

1.6mm 0.8mm 1.6mm T1 = 21^oC

T2= -15^oC

h1 = 2.84 W/m²K h2 = 11.4 W/m².K k1 = 0.52 W/mK k2 = 0.031 W/mK

h1 h2

Jawab:

k1 k2 k1 Heat flow

Terdapat 5 hambatan yang dialami selama proses pindah panas: 2 konveksi, 3 konduksi

1/U 1/h1 + x1/k1 + x2/k2 + x3/k3 + 1/h2 1/U = 1/h1 + x1/k1 + x2/k2 + x3/k3 + 1/h2

1/U = 1/2.84 + 1.6 x 10^-3/0.52 + 0.8x10^-3/0.031 + 1.6x10^-3/0.52 + 1/11.4

= 0.352 + 0.0031 + 0.0258 + 0.0031 + 0.0877 = 0.4718 U = 2.12 W/m²K

q/A = U ΔT = 2.12 (21-(-15) = 76.32 W/m²

(19)

Soal 2

• Hitung overall heat transfer coefficient (U) untuk

• Hitung overall heat transfer coefficient (U) untuk heat exchanger dengan koefisien pindah panas 568/m

²

K di bagian dalam dan 5678 W/m

²

K di bagian luar. Dinding tube mempunyai

konduktivitas panas (k) 55.6 W/mK. Tube

mempunyai diameter dalam 2.21 cm dan ketebalan p y 1.65 mm. Jika suhu fluida di dalam tube 80

^o

C dan di luar 120

^o

C, hitung juga suhu pada dinding tube sebelah dalam.

rr_ii= 1.105 cm= 1.105 cm

rr_oo= 1.2701 cm= 1.2701 cm T1 =

T1 = 80 80^ooCC

T2 = 120 T2 = 120^ooCC

hi= 568 W/m²K ho= 5678 W/m².K k = 55.6 W/mK

(a) Menghitung U:

ri = 2.21/2 = 1.105 cm

r_o= 1.105 + 0.1651 = 1.2701 cm

Terdapat 3 hambatan yang dialami selama proses pindah panas melalui heat exchanger: 2 konveksi, 1 konduksi

1/U = r /rihi+ + r ln(r /r1)/k + 1/h 1/U ro/rihi+ + roln(ro/r1)/k + 1/ho

1/U = 1.2701x10^-2/[(1.105x10^-2)(568)] + 1.2701x10^-2ln(1.2701x10^-2/1.105x10^-2)/55.6 + 1/5678

= 20.236x10^-4+ 0.318x10^-4+ 1.76x10-4 = 22.315x10^-4 U = 448 W/m²K

Pindah Panas 8/24/2011

Pindah Pindah Panas Panas Pindah Pindah Panas Panas Panas Panas Panas Panas

Pindah Panas Pindah Panas

Tujuan Pembelajaran Tujuan Pembelajaran

Pindah Panas Pindah Panas

Tujuan Pembelajaran Tujuan Pembelajaran

Pindah Panas Pindah Panas Pindah Panas Pindah Panas

Heat Transfer (1)

Heat Transfer (1)

Heat Transfer (2)

Heat Transfer (2) Heat Transfer (2) Heat Transfer (2)

CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER

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CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER

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CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER CONDUCTION HEAT TRANSFER

CONDUCTION HEAT TRANSFER

CONDUCTION HEAT TRANSFER

CONDUCTION HEAT TRANSFER

CONDUCTION HEAT TRANSFER

dx dx dx dx dT dT dT kA dT kA kA ---- kA

=

=

= q = q

q q

Δ

ΔQ Q Δ Δtt Δ ΔQ Q

Δ Δtt = = = =

SIGN CONVENTION SIGN CONVENTION SIGN CONVENTION SIGN CONVENTION

direction of heat flow direction of heat flow direction of heat flow direction of heat flow Δ

ΔTT Δ ΔTT

Δ Δ xx Δ Δ xx

DISTANCE DISTANCE DISTANCE DISTANCE

∫∫

∫∫

d d kdT kdT

q q

dx dx dT -- k A k A dT q

q

= =

∫∫

∫∫ ==

kdT kdT --

dx dx A A q q

)) x x -- x x

q ((

T q T T T

−−

==

)) T T -- k(T k(T

))

x x -- x x

q ((

q

A

A

== −−

--kdT kdT dx

A dx A q q

=

=

)) ((

kA

kA

)) X X -- (X (X

)) T T -- (T (T

kA kA q

q

== −−

HEAT CONDUCTION IN MULTILAYERED SYSTEMS HEAT CONDUCTION IN MULTILAYERED SYSTEMS

∫∫ ⁼⁼