## MEL242

## MEL242

## HEAT AND MASS TRANSFER

### Prabal Talukdar

### Associate Professor

### Department of Mechanical Engineering

### p

### g

### g

### IIT Delhi

Course Coordinator: Dr. Prabal Talukdar Room No: III, 368

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

Lectures: Tue, Wed, Fri: 9-9.50 a.m. (Room No: IV LT1)

Tut: 1-1.50 p.m. Course webpage:

http://web.iitd.ac.in/~prabal/courses.html

Pre-requisite: Fluid Mechanics (AML 160)

(Tentative Room no: III352

**MEL 242: Heat and Mass Transfer (3-1-0)**

•Syllabus (for total 42 lectures)

**Introduction and basics of to heat transfer: Modes of heat transfer, Fourier’s law, conductivity, diffusivity.**

**Heat conduction equation:q** 1D Heat conduction, General heat conduction equation, Boundary and initial, q , y

conditions, Heat generation.

**Steady heat conduction: Heat conduction in plane wall, cylinder, sphere, network analysis, critical radius of**

insulation, heat transfer from fins.

**Transient heat conduction: Lumped system analysis, transient heat conduction in large plane walls, long**

li d d h ith ti l ff t H i l d G b h t cylinders and spheres with spatial effect, Heisler and Grober charts

**Numerical methods of heat conduction: Finite difference formulation, numerical methods for 1D and 2D steady**

state heat conduction.

**(≈ 10 lectures)**

**Introduction to convection: Fundamentals, Velocity and thermal boundary layer, laminar, turbulent flows,**

conservation equations for mass, momentum and energy, solution of boundary layer equations, Analogy between heat and momentum transfer, Non-dimensional numbers

**External heat transfer: Drag and heat transfer, parallel flow over flat plates, flow across cylinders and spheres**
**Internal heat transfer: Mean velocity and mean temperature, entrance region, constant heat flux and temperature**

condition in pipe flow Hagen Poiseuille flow Turbulent flow and heat transfer condition in pipe flow, Hagen–Poiseuille flow, Turbulent flow and heat transfer

**Boiling and condensation: Boiling heat transfer, pool boiling, flow boiling, condensation heat transfer, film **

condensation, heat transfer correlations.

**(≈ 4 lectures)****( 4 lectures)**

**Heat Exchangers: Types of heat exchangers, overall heat transfer coefficient, analysis of heat exchangers, the **

log mean temperature method, ε-NTU method.

**(≈ 4 lectures)**

**Introduction to radiation: Fundamentals, radiative properties of opaque surfaces, Intensity, emissive power, **

di i Pl k’ l Wi ’ di l l Bl k d G f E i i i b i i S l d radiosity, Planck’s law, Wien’s displacement law, Black and Gray surfaces, Emissivity, absorptivity, Spectral and directional variations, Stephan Boltzmann law, Kirchhoff’s law

**View factors: Definitions and relations, radiation heat transfer between two black surfaces, between diffuse gray **

surfaces, network method above two surfaces, re-radiating surface, radiation shield, radiation effects on temperature measurements. p

**(≈ 7 lectures)**

**Mass Transfer: Introduction, analogy between heat and mass transfer, mass diffusion, Fick’s Law, boundary **

conditions, steady mass diffusion through a wall, cylinder and sphere, water vapour migration in buildings, transient mass diffusion, mass transfer in a moving medium, diffusion of vapor through a stationary gas: Stefan Flow

Flow

**(≈ 4 lectures)**

Quiz Quiz 1 Quiz 2 Tentative Date August 27 November 5

**Evaluation:**

Tuts and Quiz (2 nos): 20% (Closed note, book)

Minor Test I: 20% (Open note closed book) Tentative Date August 27 November 5 Minor Test I: 20% (Open note, closed book)

Minor Test II: 25% (Open note, closed book) Major Test: 35% (Open note, closed book) Total: 100%

**Textbook: Fundamental of Heat and Mass Transfer: F. P.**

Incropera and D. P. Dewitt

## Heat Transfer as a Course

• Has a “reputation” for being one of the most challenging, fundamental, conceptual courses in ME. It is the “heart” of

h l i i

thermal engineering • Why??

*– Physically diverse: thermodynamics material science diffusionPhysically diverse: thermodynamics, material science, diffusion *

theory, fluid mechanics, radiation theory

*– Higher-level math: vector calculus, ODEs, PDEs, numerical *
methods

methods

*– Physically elusive: heat is invisible; developing intuition takes *
time

i d i lif d l

*– Appropriate assumptions: required to simplify and solve most *
problems

*• However, Heat Transfer is interesting, fun, and readily *
applicable to the real world

### Heat Transfer Applications

• Heat transfer is commonly encountered in engineering systems and other aspects of life, and one does not need to go very far to see some application areas of heat transfer

### Heat Transfer -

### Thermodynamics

### y

• Thermodynamics is concerned with the amount of heat transfer as a system undergoes a process from one equilibrium state to another, y g p q and it gives no indication about how long the process will take. • A thermodynamic analysis simply tells us how much heat must be

transferred to realize a specified change of state to satisfy the transferred to realize a specified change of state to satisfy the conservation of energy principle.

We are normally interested in how long it takes for the hot coffee in a thermos to cool to a certain

temperature, which cannot be determined from a thermodynamic analysis alone

thermodynamic analysis alone.

• Determining the rates of heat transfer to or from a

system and thus the times of cooling or heating as well as the
system and thus the times of cooling or heating, as well as the
*variation of the temperature, is the subject of heat transfer*

## Definition

• Heat transfer is energy transfer due to a temperature difference in a medium or between two or more media

• Different types of heat transfer processes are called different modes of heat transfer

**• Conduction heat transfer is due to a temperature gradient in a **
stationary medium or media

**• Convection heat transfer occurs between a surface and a movingConvection heat transfer occurs between a surface and a moving **

fluid at different temperatures

**• Radiation heat transfer occurs due to emission of energy in the **

f f ele t eti e b ll b die b e b l te e

form of electromagnetic waves by all bodies above absolute zero temperature

**– Net radiation heat transfer occurs when there exists a temperature **
difference between two or more surfaces emitting radiation energy

## Conduction

• Conduction heat transfer is due to random molecular and atomic vibrational, rotational and translational motions

– High temperature and more energetic molecules vibrate more and transfer energy to less energetic particles as a result of molecular collisions or interactions

• The heat flux (a vector)

### Q ′′

### &

(W / m2_{)}

• The heat flux (a vector) (W / m2_{)}

is characterized by a transport property know as the

**– Thermal Conductivity, k (W / m · K)**
x

### Q

**y** **(** **)**

**• Conduction is the transfer of energy from the more energetic**
**• Conduction is the transfer of energy from the more energetic **

**particles of a substance to the adjacent less energetic ones as a **

result of interactions between the particles.

• Conduction can take place in solids, liquids, or gases. In gases and liquids, conduction is due to the collisions and diffusion of the

molecules during their random motion. In solids, it is due to the combination of vibrations of the molecules in a lattice and the energy transport by free electrons

• The rate of heat conduction through a medium depends on theThe rate of heat conduction through a medium depends on the geometry of the medium, its thickness, and the material of the medium, as well as the temperature difference across the medium

## Fourier’s Law

### (W)

### x

### T

### kA

### x

### T

### T

### kA

### Q

_{cond}2 1

### Δ

### Δ

### −

### =

### Δ

### −

### −

### =

### &

• In the limiting case of x →0, the equation above reduces to the

differential form _{Fourier’s law of heat }

### x

### x

### Δ

### Δ

• The negative sign ensures that heat

**conduction after J. Fourier, **
**who expressed **it first in his

heat transfer text in 1822

### (W)

### dx

### dT

### kA

### Q

### &

_{cond}

### =

### −

• The negative sign ensures that heat transfer in the positive x direction is a positive quantity

T_{1}=

## Thermal Conductivityy

• Specific heat C_{p} is a measure of a material’s ability to store thermal
energy.gy For example, Cp , _{p}_{p} = 4.18 kJ/kg·°C for water and Cg _{p}_{p} = 0.45
kJ/kg·°C for iron at room temperature, which indicates that water
can store almost 10 times the energy that iron can per unit mass.
• Likewise the thermal conductivity k is a measure of a material’s
• Likewise, the thermal conductivity k is a measure of a material s

ability to conduct heat. For example, k = 0.608 W/m·°C for water and k = 80.2 W/m·°C for iron at room temperature, which indicates that iron cond cts heat more than 100 times faster than ater can that iron conducts heat more than 100 times faster than water can.

**• Thus water is a poor heat conductor relative to iron, although **

### Range of Thermal Conductivity

### g

### y

• The thermal conductivities of gases such as air vary by a factor of 104

from those of pure metals such as copper.

• Note that pure crystals and metals have the highest thermal

conductivities and gases and conductivities, and gases and insulating materials the lowest.

A simple experimental setup to determine the thermal conductivity of a material

The range of

thermal conductivity thermal conductivity of various materials at room temperature

• The thermal conductivity of a substance is normally highest in the solid phase and lowest normally highest in the solid phase and lowest in the gas phase.

• Unlike gases, the thermal conductivities of

li id d i h i i

most liquids decrease with increasing temperature, with water being a notable exception.

• In solids, heat conduction is due to two

effects: the lattice vibrational waves induced by the vibrational motions of the molecules by t e v b at o a ot o s o t e o ecu es positioned at relatively fixed positions in a periodic manner called a lattice, and the energy transported via the free flow of energy transported via the free flow of electrons in the solid .

The thermal conductivity of a solid is obtained by adding the lattice and electronic components The relatively high thermal conductivities and electronic components. The relatively high thermal conductivities

• The lattice component of thermal conductivity strongly depends onThe lattice component of thermal conductivity strongly depends on the way the molecules are arranged

• Unlike metals, which are good electrical and heat conductors,

lli lid h di d d i d h

crystalline solids such as diamond and semiconductors such as

silicon are good heat conductors but poor electrical conductors. As a result, such materials find widespread use in the electronics industry. For example, diamond, which is a highly ordered crystalline solid, has the highest known thermal conductivity at room temperature.

**Even small amounts in a pure metal of “foreign” **
**molecules that are good conductors themselves**

**i** **l di** **t th fl** **f h** **t i th t** **t l**
**seriously disrupt the flow of heat in that metal. **
**For example, the thermal conductivity** **of steel **
**containing just 1 percent of chrome is 62 W/m·°C, **
**while the thermal conductivities of iron**

• The variation of the thermal

the thermal

conductivity of various solids, liquids and gases liquids, and gases with temperature (from White)

## Thermal Diffusivityy

• The product ρC_{p}, which is frequently encountered in heat transfer
**analysis, is called the heat capacity of a material. Both the **y **p** **y**

**specific heat C _{p}**

**and the heat capacity**ρC

_{p}represent the heat

storage capability of a material.

• But C expresses it per unit mass whereas ρC expresses it per unit
• But C_{p }expresses it per unit mass whereas ρC_{p} expresses it per unit

volume, as can be noticed from their units J/kg·°C and J/m3_{·°C, }

respectively.

• Another material property that appears in the transient heat

**conduction analysis is the thermal diffusivity, which represents **

**how fast heat diffuses through a material and **

is defined as The larger the thermal diffusivity,

the faster the propagation of heat into the medium. A small value of thermal diffusivity means that heat t e a d us v ty ea s t at eat is mostly absorbed by the material and a small amount of heat will be

• Note that the thermal diffusivity
ranges from 0.14 x 10-6 _{m}2_{/s for }

water to 174 x 10-6 _{m}2_{/s for silver, }

which is a difference of more than a thousand times.

• Also note that the thermal

diffusivities of beef and water are the diffusivities of beef and water are the same. This is not surprising, since meat as well as fresh vegetables and fruits are mostly water and thus they fruits are mostly water, and thus they possess the thermal properties of

Forced Convection Natural Convection

B ili C d i

## Convection

• Convection heat transfer involves both energy transfer due to random molecular motions and by bulk motion of the fluid

molecular motions and by bulk motion of the fluid

– Convection heat transfer includes both forced convection and natural convection

I i h f h f f h i b f

• In convection heat transfer, the transfer of heat is between a surface and a moving fluid (liquid or gas), when they are at different

**temperatures. The rate of transfer is given by Newton’s Law of **

**Cooling.**

### )

### T

### T

### (

### h

### q

''### =

_{s}

### −

_{∞}Moving fluid T

_{∞}T

_{s}q’’ T > T

## Typical values of convection

## h t t

## f

## ffi i t

## heat transfer coefficient

**Process** **h (W / m2** _{K)}**Process** **h (W / m2** ** _{K)}**
Free Convection
Gases 2-25
Liquids 50 -1000
Forced Convection
Gases 35 -250
Gases 35 250
Liquids 50 -20,000

with Phase Change

Boiling or Condensation

## Radiation

• All surfaces of finite temperature emit energy in the form of electromagnetic waves

• In the absence of an intervening medium, there is a heat transfer by radiation between two surfaces at different temperatures

• The maximum flux, E (W / m2_{), at which radiation may be emitted from a }

bl kb d f i i b

blackbody surface is given by:

– Stefan Boltzmann Law

E where 4 s b

### T

### E

### =

### σ

Eb T_{s}E

_{b}or E = Surface emissive power (W / m2

_{)}

• For a real surface:

4

• For a surface with absorptivity α, the incident radiation (G, W/m2_{) }

4 s

### T

### E

### =

### εσ

p y , ( , )

that is absorbed by the surface is given by:
G
G_{abs} = α⋅ G
where
G
G_{abs} α
G_{abs}
G = incident radiation (W / m2_{)}
T = absolute temperature (K)
ε = surface emissivity (0 ≤ ε ≤ 1)
α = surface absorptivity (0 ≤ α ≤ 1)
α surface absorptivity (0 ≤ α ≤ 1)

• For a gray surface α = ε

• When radiant energy is incident on a transparent surface, it can be absorbed, reflected, or transmitted through the material. Hence,

### (

### )

GG G

G

G = _{absorbed} + _{transmitte}_{d} + _{reflected} = α + τ + ρ
1
=
ρ
+
τ
+
α
where

ρ = materials surface reflectivity 1 = ρ + τ + α τ = materials transmissivity

• Consider a small gray surface at temperature T_{s} that is completely
enclosed by the surroundings at temperature T_{sur}.

• The net rate of radiation heat transfer from the surface is:

T

### (

### )

4 4 '' q_{T}

_{T}

_{h}

_{T}

_{T}q εσ ασ q

_{sur}’’ T

_{sur}

_{4}sur 4 s sur s '' rad E G T T q = −α = εσ −ασ

### (

_{s}

_{sur}

### )

r sur s rad T T h T T A q = = εσ −ασ = − q_{s}’’ T

_{s}

• Where h_{r} is the radiation heat transfer coefficient, W / m2 _{K}

### (

### )

## (

2## )

sur 2 s sur s r T T T T h_{r}= ε ⋅σ

### (

T_{s}+ T

_{sur}

### )

## (

T_{s}+ T

_{sur}

## )

h ε σ + +## Convection example

Calculate the heat flux Calculate the heat flux from your hand when it is exposed to moving air and water, assuming the surface temperature of your hand is 30°C.

## Radiation ex.

An instrumentation package has a spherical outer surface of diameter D = 100 mm and emissivity ε = 0 25 The

emissivity ε = 0.25. The

package is placed in a large space simulation chamber whose walls are maintained

f f

at 77 K. If the operation of the electronic components is restricted to the temperature range of 40 ≤ T ≤ 85°C, what range of 40 ≤ T ≤ 85 C, what is the range of acceptable power dissipation for the package?