To create a steady-state heat transfer model with conduction on the left side of the wall and convection from air on the right, top, and bottom sides in MATLAB, you can follow these steps:
Define the properties of the wall and the air, such as thermal conductivity (k), thickness (L), and temperature (T_air) of the air.
Set up a finite difference grid to discretize the wall into smaller nodes. Define the number of nodes and the grid spacing (dx) according to your requirements.
Initialize the temperature distribution across the wall. For simplicity, you can assume an initial uniform temperature.
Implement the heat conduction equation using finite difference method for the interior nodes of the wall. The equation is given by:
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Where T_center is the temperature at the current node, T_left and T_right are the temperatures at the adjacent nodes, and alpha is the thermal diffusivity calculated as:
Here, rho is the density of the wall material and Cp is the specific heat capacity.
Apply the boundary conditions for the left side of the wall, which is the conduction boundary condition:
This means the temperature gradient at the left boundary is zero.
Apply the boundary conditions for the right, top, and bottom sides of the wall, which are the convection boundary conditions:
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Here, h is the convective heat transfer coefficient, and T_air is the temperature of the air.
Solve the system of equations using MATLAB's built-in solvers such as fsolve or ode45.
Plot the temperature distribution across the wall using MATLAB's plotting functions.
It is important to note that the specific implementation details may vary depending on the specific requirements of your problem. The above steps provide a general guideline for creating a steady-state heat transfer model with conduction and convection in MATLAB.
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