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1. Homework Statement

1. Homework Statement

Calculate the distribution of the temperature of the inner part of the model.

Thermal conductivity:

*λ*= 47 W/(m*K)

Specific heat capacity:

*cp*= 465 J/(kg*K)

Density:

*ρ*= 7,85 kg/m^3

Length of one side of a cell:

*L*= 0,05 m

Starting temperature of model:

*T*0 = 0 °C

__A:__

Wall temperature:

*Tw*= 500 °C

__B:__

Fluid temperature:

*Tf*= 20 °C

Heat transfer coefficient:

*α*= 500 W/(m^2*K)

Image of the model:

## Homework Equations

Here T_i,j is supposed to be the temperature of the cell in question, whereas the T_{i+1,j} should be known.

## The Attempt at a Solution

Yes I know it's a rather weak attempt, as I stated earlier, I'm new to programming in general, any further attempts would look like the work of a chimpanzee, ergo pointless.

Code:

```
% Given variables
lambda = 47 % Thermal conductivity [W/(m*K)]
cp = 465 % Specific heat capacity [J/(kg*K)]
rho = 7.85 % Density [kg/m^3]
L = 0.05 % Length of one side of a cell [m]
T0 = 0 % Starting temperature of the model [°C]
%Boundary condition A
Tw = 500 % Wall temperature [°C]
%Boundary condition B
Tf = 20 % Fluid temperature [°C]
alfa = 500 % Heat transfer coefficient [W/(m^2*K)]
model = [0 0 Tf 0 Tf 0 Tf 0 0 0 % model matrix, an attempt
0 Tf T0 Tf T0 Tf T0 Tf 0 0
Tw T0 T0 Tf T0 Tf T0 Tf Tf 0
Tw T0 T0 T0 T0 T0 T0 T0 T0 Tf
0 Tf T0 T0 T0 T0 Tf Tf Tf 0
0 Tf T0 T0 T0 T0 Tf Tf Tf 0
Tw T0 T0 T0 T0 T0 T0 T0 T0 Tf
Tw T0 T0 Tf T0 Tf T0 Tf Tf 0
0 Tf T0 Tf T0 Tf T0 Tf 0 0
0 0 Tf 0 Tf 0 Tf 0 0 0];
mean = ( ... %Should I use something like this for the equation?
sum ( ) ...
+ sum ( ) ...
+ sum ( ) ...
+ sum ( ) ) ...
/ ( 2 * m + 2 * n - 4 );
```