Steady state heat transfer, Cheat Sheet of Physical Chemistry

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Steady State Heat Transfer

Absolute heat capacity: Q = m c T

Gain (loss) of heat DQ = m c DT

Plate heat exchanger http://www.youtube.com/watch?v=DmE91qjZ-3Q

Heat can be transferred

◼ Through walls of a structure (loss of energy)

◼ Utilized in unit operations in processing

◼ Pasteurization of milk, juices ◼ Freezing of foods ◼ Cooling of fruits and vegetables (transportation and storage purposes) ◼ Thermal sterilization of canned food ◼ Fermentation (heat must be removed) ◼ To support bacteria growth in cottage-cheese making

One-dimensional heat transfer by conduction (diffusion of energy) ◼ Conduction heat transfer described by Fourier’s law

q = - k A

T

2

• T 1

L

q = heat flow, J/s or W A = cross-section area, m 2 T = temperature o C k = thermal conductivity, W/(m o C) L = wall thickness, m Building industry uses R value to classify performance of insulation: q T 2

– T

1

DT

A L R

k

R= thermal resistance (m 2 K)/W; (ft 2 F h)/Btu RSI=3.5 R= q T 1 T 2 T(x) L T x https://www.youtube.com/watch?v=fXjzqbRdR8g

Thermal resistance RSI of selected materials

Windows RSI R Single pane 0.16 0. Double pane (6 mm sealed air space) 0.27 1. Triple pane (6 mm sealed air space) 0.38 2. Storm windows (20 to 100 mm unsealed air space) 0.31 1. Cold Outdoors 10 °C Gypsum board (9.5 mm thick)............... 0.056 0. Plane concrete (10 mm thick)............... 0.004 0. https://www.youtube.com/watch ?v=JWO_msMieQU

Example 1

• The wall of an industrial furnace is constructed from 0.15 m thick fireclay brick having a thermal conductivity of 1.7 W/(m K).
• Measurements made during steady-state operation reveal temperatures of 560 and 120°C at the inner and outer surfaces, respectively.
• What is the rate of heat loss through a wall that is 0.5 m by 3 m on one side?

Mechanisms of convective heat transfer

Forced convection Forced flow (a) Air q (c) Boiling Vapor bubbles Hot plate Water q (d) Condensation Water droplets Moist air Cold Water q (b) Natural convection Buoyancy-driven flow Air q Hot components on printed circuit board

Example 2 ◼ The heat flux from a metal plate of a kitchen ranger is 1000 W/m 2 . ◼ The surface temperature of the plate is 120°C, and the ambient temperature is 20°C. ◼ Estimate the convection heat transfer coefficient. ◼ Also, determine the heat flow from the plate which has a 20 cm diameter and is 2 cm thick.

Multilayer composite wall

Determination of temperatures of intermediate surfaces

q=A

T

1

– T

5

SR

i

q

1

= q

2

= q

3

= q

4 Cold fluid Hot fluid T 1 TS T 2 T 3 TS T 4 x LA LB LC kA kB kC q 1 q 2 q 3 q 4