Prof. Eduardo Cabrera Ruiz
Class Problems
Heat Transfer / Homework #3
Fouriers law of heat conduction
1.- Consider a solid cylindrical rod of length 0.15 m and
diameter 0.05 m. The top and bottom surfaces of the rod are
maintained at constant temperatures

Class' Problems
Prof. Eduardo Cabrera Ruiz
1.- A cylinder of radius r0, length L, and thermal conductivity k is immersed in fluid of convection coefficient h and
unknown temperature T. At a certain instant the temperature distribution in the cylinder is T

I Pmﬁ Edam Cabrera: Ruiz Class’ Problems.
1.- The resistance wire of a lOOO—W iron is 15 in long and has a diameter ofD' = 0.08 in. Determine the rate of heat generation in the wire per unit volume, in
Btwh - ﬂ}, the heat ﬂux on the outer surface ofthe wi

Drilling Problems
Prof. Eduardo Cabrera Ruiz
1.- A surface whose temperature is maintained at 400 C is separated from airflow by a layer of vermiculite (expanded)
insulation of 25 mm thick. If the air temperature is 35C and the convection coefficient betw

Prof. Eduardo Cabrera Ruiz
Class Problems
Heat Transfer / Homework #1
Heat
1.- A cylindrical resistor element on a circuit board dissipates
0.8 W of power. The resistor is 2 cm long, and has a diameter of
0.4 cm. Assuming heat to be transferred uniformly

Prof. Eduardo Cabrera Ruiz
Class Problems
Heat Transfer / Homework #2
1.- The resistance wire of a 1000-W iron is 15 in long and has a diameter of D
(d) Is the thermal conductivity of the medium constant or variable?
= 0.08 in. Determine the rate of heat

Prof. Eduardo Cabrera Ruiz
Heat Transfer
Department of Mechanical Engineering \ Heat Transfer
Prof. Eduardo Cabrera Ruiz (PRINT SIDE BY SIDE)
Heat Transfer Nomenclature
Quantity of Heat
Q
Q ,
Heat Rate (Power)
(
Heat Flux
Q A
)
Heat Rate per unit Volume
J

Prof. Eduardo Cabrera Ruiz
Drilling Problems
Drilling Problems for Heat Conduction Equation
1.- Heat is generated at a rate egen in a spherical shell with inner radius ri and outer radius ro Heat is added at the outer
surface at a uniform flux q0 . The in

Drilling Problems
Prof. Eduardo Cabrera Ruiz
1.- Heat is generated at a rate in a spherical shell with inner radius and outer radius Heat is added at the outer surface at a
uniform flux . The inside surface is maintained at uniform temperature Ti. Draw a

Prof. Eduardo Cabrera Ruiz
Drilling Problems
Drilling Problems for Fourier Law
1.- A cylinder of radius r0, length L, and thermal conductivity k is immersed in fluid of convection coefficient h and
unknown temperature T. At a certain instant the temperatu

Mechanical Engineering Department - Prof. Eduardo Cabrera Ruiz-
CONDUCTION
Although heat transfer and temperature are closely related, they are of a different nature.
Temperature has only magnitude it is a scalar quantity.
Heat transfer has direction as w

Prof. Eduardo Cabrera Ruiz
Drilling Problems
Drilling Problems for Heat Transfer Mechanisms
1.- A surface whose temperature is maintained at 400 C is separated from airflow by a layer of vermiculite (expanded)
insulation of 25 mm thick. If the air tempera

Prof. Eduardo Cabrera Ruiz
Drilling Problems
Drilling Problems for One Dimension Heat Conduction
1. Consider a steam pipe of stainless steel AISI-316 of length L = 60 ft, inner radius r1 = 2.6 in, outer radius r2 = 3.0 in.
Steam is flowing through the pip

Drilling Problems
Prof. Eduardo Cabrera Ruiz
1.- A cylinder of radius r0, length L, and thermal conductivity k is immersed in fluid of convection coefficient h and
unknown temperature T. At a certain instant the temperature distribution in the cylinder is

Drilling Problems
Prof. Eduardo Cabrera Ruiz
1. Consider a steam pipe of stainless steel AISI-316 of length L = 60 ft, inner radius r1 = 2.6 in, outer radius r2 = 3.0 in. Steam
is flowing through the pipe at an average temperature of 250F, and the average

Prof. Eduardo Cabrera Ruiz
Drilling Problems
Drilling Problems for Fourier Law
1.- A cylinder of radius r0, length L, and thermal conductivity k is immersed in fluid of convection coefficient h and
unknown temperature T. At a certain instant the temperatu

Prof. Eduardo Cabrera Ruiz
Drilling Problems
Drilling Problems for Heat Transfer Mechanisms
1.- A surface whose temperature is maintained at 400 C is separated from airflow by a layer of vermiculite (expanded)
insulation of 25 mm thick. If the air tempera

Prof. Eduardo Cabrera Ruiz
Class Problems
Heat Transfer / Homework #4
Steady Heat Conduction in Plane Walls
1.- Consider a 3-m-high, 6-m-wide, and 0.3-m-thick brick wall whose
thermal conductivity is k = 0.8 W/mC . On a certain day, the
temperatures of th

Prof. Eduardo Cabrera Ruiz
Class Problems
Heat Transfer / Homework #5
Heat Transfer from Finned Surface
1.- Obtain a relation for the fin efficiency for a fin of constant crosssectional area AC, perimeter p, length L, and thermal conductivity k
exposed to

Prof. Eduardo Cabrera Ruiz
Class Problems
Heat Transfer / Homework #7
Electromagnetic
1.- The speed of light in vacuum is given to be 3.0108 m/s.
Determine the speed of light in air (n = 1), in water (n = 1.33), and in
glass (n = 1.5) cfw_3.0,2.26.2.0 108

Prof. Eduardo Cabrera Ruiz
Class Problems
Heat Transfer / Homework #6
Lumped System Analysis
1.- Obtain relations for the characteristic lengths of a large plane wall
of thickness 2L, a very long cylinder of radius ro , and a sphere of
radius ro.
2.- The

| Pmﬁ Edward; Cabrera Ruiz {Has-3’ Pmiviems.
1_- A cylindrical resistor element on a circuit board dissipates 0.8 W ofperwer. The resistor is 2 cm long, and has a diameter of {1.4
cm. Assuming heat to he transferred uniformly ﬁom all surfaces. determine (

Mechanical Engineering Department - Prof. Eduardo Cabrera Ruiz-
Transient Heat Conduction
Lumped System Analysis
In heat transfer analysis, some bodies are essentially isothermal and can be
treated as a lump system.
An energy balance of an isothermal soli

Mechanical Engineering Department \ Prof. Eduardo Cabrera Ruiz
HEAT TRANSFER
Thermodynamics deals with the amount of heat transfer as a system undergoes a process from one equilibrium
state to another, and makes no reference to how long the process will t

Mechanical Engineering Department - Prof. Eduardo Cabrera Ruiz-
Heat Transfer from Finned Surfaces
Newtons law of cooling
Qconv
= hAs (Ts T )
Two ways to increase the rate of heat transfer:
increasing the heat transfer coefficient,
increase the surface ar

Mechanical Engineering Department - Prof. Eduardo Cabrera Ruiz-
CONDUCTION
Although heat transfer and temperature are closely related, they are of a different nature.
Temperature has only magnitude it is a scalar quantity.
Heat transfer has direction as w

Mechanical Engineering Department - Prof. Eduardo Cabrera Ruiz-
Steady Heat Conduction
Steady Heat Conduction in Plane Walls
1) Considerable temperature difference between the inner and the
outer surfaces of the wall (significant temperature radient in th

Mechanical Engineering Department - Prof. Eduardo Cabrera Ruiz-
Two Dimensional Steady State Conduction
2T 2T
0
x 2 y 2
Method of Separation of Variables
Introduce the transformation
T T1
T2 T1
Differential Equation
2T 2T
0
x 2 y 2
Boundary Conditions

Mechanical Engineering Department - Prof. Eduardo Cabrera Ruiz-
Transient Heat Conduction in Semi-Infinite Solids
A semi-infinite solid is an idealized body that has a single plane
surface and extends to infinity in all directions
Assumptions:
constant t

Mechanical Engineering Department - Prof. Eduardo Cabrera Ruiz-
Thermal Radiation
Unlike conduction and convection, radiation does not require the presence of a material medium to take place.
Electromagnetic waves or electromagnetic radiation represent th