In: Mechanical Engineering

**Develop** and explain each step the
**general equation of heat transfer by conduction** in
a constructive way starting from an element general differential in
the cartesian coordinate system and then reduce to get:

1) Laplace's equation (in R3)

Δ? = 0

2) The Poisson equation (with constant thermal conductivity
?)

Δ? + ? '''= 0

Δ is the Laplacian operator and ? ''' is a source term.

Note: start the analysis from a differential element with volume
??????. Make a energy balance over this volume considering that it
can increase if temperature in time according to its thermal
capacity. Give more generality to the model assuming there is a
source term ? ''' which can be a source that produces thermal
energy or consume it.

what is the three forms of heat transfer?
(explain with each type with equations)
give equation for net rate of heat transfer by radiation &
explain terms used.

Conduction is a transfer of heat energy that requires direct
contact requires actual motion of substance it does not require
matter all of the above

Conduction is a transfer of heat energy that
requires direct contact
requires actual motion of substance
it does not require matter
all of the above

Match the types of heat transfer to the example.
Natural Convection
Forced Convection
Conduction
Radiation
A.
You burn your hand touching a hot pot in the kitchen.
B.
Frost forming during a cold clear night, with an outdoor
temperature of 2 degrees Celsius.
C.
Cold wind blowing on your face.
D.
Water heating up in a pot on a stove top.

Write the heat conduction equation (without flow in and out) in
cartesian coordinates for the following case:
1. Steady-state, 1-D, without heat generation (2 points)
2.Transient, 1-D, without heat generation (2 points)
3.Transient, 3-D, with heat generation (3 points)
3. Write the three types of boundary conditions. (3 points)

Write a function to solve the two-dimensional in Matlab,
unsteady heat conduction equation with no internal heat generation
on a square domain. The length of each side of the square is 1 m.
The function will have the following 4 inputs:
npts
number of grid points in each coordinate direction
nt
number of time steps to take
dt
size of time step (s)
alpha
thermal diffusivity (m2/s)
Use the following initial and boundary conditions:
Initialize the body to T =...

This is a heat transfer problem.
Question is the following;
You had been assigned, at General Motors, as design engineer to
design a radiator ( Heat exchanger) for a new model car . It is
necessary the the heat exchanger will be compact to fit within 2
feet by 3 feet space available in front of the car. IF the
temperature of the incoming engine coolant is 150 degree Centigrade
and outside temperature of air is about 38 C, what...

There are three heat transfer mechanisms. Define each type and
briefly explain how they work. Additionally define insulation and
how it contrasts against these transfer mechanisms

Explain heat transfer, latent heat and change in temperature for
the following case: Ice kept at -10 degrees C temperature turns
into water at +10 degrees C temperature upon heating.

(a) Perform Von-Neumann stability analysis for 1-D transient
heat conduction equation and establish the limiting condition for
time step.
(b) Compare hybrid differencing scheme and QUICK schemes in finite
volume formulation of fluid flows.
(c) Explain the steps needed to understand the flow and heat
transfer analysis in a typical problem.

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