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Anna,” I corrected, and held out my hand. It was 10am on a Saturday. Houston, a filmmaker and director of the "Crash Pad Series," looked a little confused, but invited me in. She told me to help myself to some coffee, strawberries, pita chips and cookies laid out on the kitchen counter.
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Mechanical Engineering Dept. CEME NUST 2
Steady State Heat Conduction
Considerable Temperature Difference between the inner and the outer surfaces
of the wall (significant temperature gradient in the x-direction)
Steady Heat Conduction in Plane Walls
The wall surface is nearly isothermal
Steady 1-dimensional modeling approach is justified
Assuming heat transfer is the only energy
interaction and there is no heat generation, the
energy balance is:
Mechanical Engineering Dept. CEME NUST 3
Steady State Heat Conduction
Steady Heat Conduction in Plane Walls
rate of heat transfer through the wall must be
constant, Qcond,wall = constant
⇒ ⇒
Temperature Distribution
general heat conduction equation in Cartesian
coordinates
⇒
⇒
no change in temperature of wall with time at any point
Mechanical Engineering Dept. CEME NUST 4
Steady State Heat Conduction
Steady Heat Conduction in Plane Walls
Temperature Distribution —contd--
⇒
⇒
→
temperature distribution across a wall is
linear and is independent of thermal
conductivity ⇒
heat through the plane wall using Fourier’s Eq.
Mechanical Engineering Dept. CEME NUST 5
Steady State Heat Conduction
Steady Heat Conduction in Plane Walls
Temperature Distribution —contd--
⇒
once the rate of heat conduction is available,
temperature T(x) at any location x can be
determined by replacing T2 in above Eq. by T,
and L by x
Mechanical Engineering Dept. CEME NUST 6
Steady State Heat Conduction
Steady Heat Conduction in Plane Walls
Thermal Resistance Concept
Heat Conduction through a plane wall can be rearranged as:
Where Rwall is the conduction resistance
⇒ Thermal Resistance of a medium depends on the geometry and the
thermal properties of the medium
Mechanical Engineering Dept. CEME NUST 7
Steady State Heat Conduction
Steady Heat Conduction in Plane Walls
Analogy to Electrical Current Flow
Above Eq. is analogous to the relation for electric current flow I, expressed as:
Heat Transfer
Rate of heat transfer
Thermal resistance
Temperature difference
Electrical current flow
←→ Electrical resistance
Electric current
Voltage difference
←→
←→
Thermal Resistance Concept – contd--
Mechanical Engineering Dept. CEME NUST 8
Steady State Heat Conduction
Steady Heat Conduction in Plane Walls
Thermal Resistance Concept – contd--
Convection Resistance
Thermal resistance can also be applied to convection processes
Newton’s Law of Cooling for convection heat transfer rate (Qconv = hAs (Ts-T ))
can be rearranged as:
Rconv is the convection resistance
Mechanical Engineering Dept. CEME NUST 9
Steady State Heat Conduction
Steady Heat Conduction in Plane Walls
Thermal Resistance Concept – contd--
Radiation Resistance
Rate of Radiation Heat Transfer between a surface and the surrounding
Mechanical Engineering Dept. CEME NUST 10
Steady State Heat Conduction
Steady Heat Conduction in Plane Walls
Thermal Resistance Concept – contd--
Radiation and Convection Resistance
A surface exposed to the surrounding might involves convection and radiation
simultaneously
Convection and Radiation Resistances
are parallel to each other
When Tsurr ≈ T∞, radiation effect can
properly be accounted for by replacing h in
the convection resistance relation by
Mechanical Engineering Dept. CEME NUST 11
Steady State Heat Conduction
Heat Conduction Through a Composite Wall
Quantity of heat transmitted per unit
time through each slab/layer is same
Assuming a perfect contact between the
layers and no temperature drop occurs
across the interface between the materials
Mechanical Engineering Dept. CEME NUST 12
Steady State Heat Conduction
Heat Conduction Through a Composite Wall
For composite wall
consists of n layers
Mechanical Engineering Dept. CEME NUST 13
Steady State Heat Conduction
Heat Conduction Through a Composite Wall
Parallel Arrangement
total heat transfer is the sum of the heat
transfers through each layer
⇒
Mechanical Engineering Dept. CEME NUST 14
Steady State Heat Conduction
Heat Conduction Through a Composite Wall
Combined Parallel-Series Arrangement
Total rate of heat transfer through the
composite system
Mechanical Engineering Dept. CEME NUST 15
Steady State Heat Conduction
The Overall Heat-transfer Coefficient
While dealing with the problems of fluid to fluid heat transfer across a metal
boundary, it is usual to adopt an overall heat transfer coefficient U
⇒