Basic Heat transfer for buildings

Asst. Prof. Dr. Channarong Asavatesanupap

Department of Mechanical Engineering

Faculty of Engineering

Outline

1. Introduction to Heat Transfer

2. Conduction Heat Transfer

3. Convection Heat Transfer

4. Radiation Heat Transfer

Introduction to Heat Transfer

Heat transfer is the exchange of thermal energy between physical systems. The rate of heat transfer is dependent on the temperatures of the systems and the properties of the intervening medium through which the heat is transferred.

System 1 System 2

medium

T1 T2

Thermal energy

Introduction to Heat Transfer (cont.)

The transfer of heat is the principal mechanism by which environmental effects are manifested within buildings.

Examples of Heat transfer

Conduction of heat through a building’s envelope,

Cooling of occupants by ventilation,

Transmission of solar radiation through windows.

There are three mechanisms that heat is transferred between substances or objects

(1) Conduction(2) Convection(3) Radiation

Heat Transfer Mechanisms

What is the driving force of Heat transfer?Answer: Temperature difference or Temperature gradient

Source: http://www.studentsoftheworld.info/sites/science/img/31368_heat-transmittance-means.jpg

Hot ColdHeat

Conduction heat transfer is a result of molecular-level kinetic energy transfers in solids, liquids, and gases. Conduction heat flows occur in the direction of decreasing temperature.

(1) Heat Conduction

An example of the flow of heat by conduction is the heat gain through the opaque walls of buildings

Outside inside

T1 T2

Transfer of heat within a substance by molecular interaction

The rate of heat transfer by conduction is proportional to the temperature difference and the heat flow area, whereas is inversely proportional to the distance through which conduction occurs.

Heat Conduction (cont.)

Fourier’s law

where k is the thermal conductivity in units of W/(m.K)

condQ

dx

dTkAQcond (W)

Thermal conductivityis the property of a material to conduct heat

Conductor

Material with high k value

Insulator

Material with low k value

Thermal properties for common building materials

Heat Conduction (cont.)

1 2 (W)cond

T T TQ kA kA

x x

Fourier’s law

Steady conduction in plane walls

R

TT

kAx

TTQcond

2121

/

Rearrange the equation as,

where R is the resistance to heat transfer (absolute thermal resistance) in unit of K/W

Thermal Resistance,is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow.

W

KmRA

k

xRth

2

thR

tyconductiviThermal

ThicknessvalueRRth

Thermal conductance, “U” valueAnother convenient measure of thermal conductance is called the unit conductance. It is the inverse of the Rth value:

Therefore,

The use of R, Rth or U to solve a given problem depends on which is more convenient.

thRU

1

TUAR

TA

R

TQ

th

cond

Analogous concept between thermal and electrical resistancesLike electrical resistors, “thermal resistors” can be connected in series and in parallel or in combinations.

Electric-resistance analog

Series connection

Parallel connection

Example 1 R-value calculation for a building wallThe outside wall of a home consists essentially of a 10-cm layer of common brick [k= 0.68 W/(m.K)], a 15-cm layer of fiberglass insulation [k= 0.038 W/(m.K)], and a 1-cm layer of gypsum board [k= 0.48 W/(m.K)], What is the overall R value? What is the heat flux through this wall if the interior surface temperature is 22C and the exterior surface is 5 C

Note: Heat flux is defined as the heat rate per unit area: ]/[ 2mWA

Qq

Example 1 R-value calculation for a building wallSoln:

WKmRR brickthbrick /).(147.068.0

10.0 2

,

WKmRR fiberthfiber /).(947.3038.0

15.0 2

,

WKmRR gypsumthgypsum /).(021.048.0

01.0 2

,

Since, a unit wall area is used, to find the heat flux, R and Rth are the same numerically (but not dimensionally)

Then, thth RARR /

Example 1 R-value calculation for a building wallSoln:

The heat flux is

2

2

,

/13.4/).(115.4

)522(mW

WKm

K

R

Tq

totth

WKmRRRRR gypsumthfiberfibertottotth /)(115.4 2

,,

Example 2 Effect of studs on wall heat lossFor structural reasons the wall described in Example 1 must have studs placed every 60 cm. The studs are fabricated from wood [k= 0.10 W/(m.K)] and are 5 cm wide and 15 cm deep. Find the R value and heat flux through this wall compare with the results of Example 1 to quantify the effect of framing with studs ignoring the brick and gypsum board.

Heat losses from piping in building HVAC systemsThe heat transfer through a cylindrical solid wall is given by

)2/()/ln( kLrr

T

R

TQ

io

cond

Heat losses from piping in building HVAC systems

Multi-layer conduction in a pipe with electric-resistance analogy circuit

Convection heat transfer is the transfer of heat when a moving fluid contacts a surface at a different temperature. It is always associated with large scale motion of a fluid over a warmer or cooler surface.

(2) Heat convection

Newton’s law of cooling

where h is the convection coefficient [W/(m2.K)]

( ) (W)conv s sQ hA T T

T

T s

Convection is classified as natural and forced convection. Natural (Free) convection results from density differences in the fluid whereas forced convection occurs when a force external to the problem move a fluid past a warmer or cooler surface.

(2) Heat convection (cont.)

Convection coefficients is a quantitative characteristic of convective heat transfer between a fluid medium (a fluid) and the surface (wall) flowed over by the fluid.

Convection heat transfer is expressed by

from which the resistance to heat transfer for convection is

The thermal resistance value Rth and its reciprocal, the U value, are given by

and

Convection thermal resistance and R Value

R

TQconv

hAR

1

hRth

1 h

RU

th

1

Flows which occur in unconfined geometries are called external flows, e.g. the air flow over the wall of a building.

For free convectionHorizontal surface: (Flat roofs of buildings warmed by the sun)

External flow equations for buildings

4/1/32.1 LThlam

Type of flow – Laminar or Turbulent

3/152.1 Thtur

2/)( baL 0.1/3 TL

a

b 0.1/3 TL

y

Tilt surface:

External flow equations for buildings

4/1/sin42.1 LThlam

3/1sin33.1 Thtur

L

y

“L” is the length of the surface in the direction of flow.

For force convectionForce convection over planes does not depend on their orientation

External flow equations for buildings

2/1/0.2 Lvhlam

5/14 /2.6 LvhTur

4.1vL

4.1vL

“L” is the length of the surface in the direction of flow.

Radiation heat transfer is the transfer of heat across a system boundary due to a T, by the mechanism of photon emission or electromagnetic wave emission.

(3) Heat radiation

where e is the emissivity

s is the Stefan–Boltzmann [=5.670X108 W/m2·K4]

Stefan-Boltzmann law

for black body, e =1, for grey body, 0< e <1

)(4 WTAQ ssemit se

Heat transferred through wave energy

Radiation properties:

(3) Heat radiation (cont.)

Incoming radiation (=1)

Reflectivity (=r)

Transmissivity (=t)

absorptivity (=a)a t r 1

Conservation of energy,

For gray surfaces,

a e Kirchhoff’s identity

The rate of heat transport between small object (1) and much large environment (2) is given by

(3) Heat radiation (cont.)

4

2

4

11121 TTAQ se

A1 << A2

A1

T1

A2

T2

As a rule of thumb, the emissivity of most building materials is approximately 0.9

Nearly all heat transfer situations in building include more than one mode of heat transfer.

Combined-mode heat transfer

Example 3 Effect of convection on wall R value.Repeat Example 2 for a stud wall to include the effect of inner and out surface convection coefficients. The inner and outer surface coefficients are 1.0 and 4.0 (m2.K)/W, respectively. Find the overall wall R value.

End.