Project details: Consider the ceramic plate whose cross section is shown in below figure. Small diameter electrical heating elements dissipating 50 W/m (length normal to the sketch) are used to heat a ceramic plate of thermal conductivity k=2 W/m.K. The upper surface of the plate is exposed to ambient air at 30C with a convection coefficient of 100W/m2 .K, while the lower surface is well insulated. - Discretize the body using x= 6 mm and y= 2 mm and use the energy balance approach to obtain finite difference formulation of the heat conduction in the body for the nodes. - Determine the temperatures at nodes by solving the generated system of equations by using an appropriate technique (e.g. Gauss-Seidel, matrix inversion etc.). Use a programming language or a computer tool (e.g. FORTRAN, MATLAB, EES etc.) for solving the system. - Use a graphing tool (e.g. MATLAB graphing tools) to plot temperature contours in the cross section. Hint: Utilize symmetry; thus consider only the 12 mm section (see figure below). Also aware that the heat generation term will be halved when you consider the symmetry element. In addition note that the heat generation term is per unit length not per unit volume meaning that the heat generation term exists at that particular node only (no need for multiplying with volume element).

1) Project details Consider the ceramic plate whose cross section is shown in below figure. Small diameter electrical heating elements dissipating 50 W/m (length normal to the sketch) are used to heat a ceramic plate of thermal conductivity k-2 W/m.K. The upper surface of the plate is exposed to ambient air at 30C with a convection coefficient of 100W/m2.K, while the lower surface is well insulated. Air To, h Ceramic plate Heating element 6 mm 2 mm 24 mm- Discretize the body using -6 mm and obtain finite difference formulation of the heat conduction in the body for the nodes. Determine the temperatures at nodes by solving the generated system of equations by using an appropriate technique (e.g. Gauss-Seidel, matrix inversion etc.). Use a programming language or a computer tool (e.g. FORTRAN, MATLAB, EES etc.) for solving the system. 2 mm and use the energy balance approach to . Use a graphing tool (e.g. MATLAB graphing tools) to plot temperature contours in the cross section Hint: Utilize symmetry; thus consider only the 12 mm section (see figure below). Also aware that the heat generation term will be halved when you consider the symmetry element. In addition note that the heat generation term is per unit length not per unit volume meaning that the heat generation term exists at that particular node only (no need for multiplying with volume element). Heating element 50 Wim Symmetry line1 Symmetry line 2 12 mm h= 100 W/m2-K Symmetry element Ceramic plate, k=2W/mK 24 mm 6 mm 1) Project details Consider the ceramic plate whose cross section is shown in below figure. Small diameter electrical heating elements dissipating 50 W/m (length normal to the sketch) are used to heat a ceramic plate of thermal conductivity k-2 W/m.K. The upper surface of the plate is exposed to ambient air at 30C with a convection coefficient of 100W/m2.K, while the lower surface is well insulated. Air To, h Ceramic plate Heating element 6 mm 2 mm 24 mm- Discretize the body using -6 mm and obtain finite difference formulation of the heat conduction in the body for the nodes. Determine the temperatures at nodes by solving the generated system of equations by using an appropriate technique (e.g. Gauss-Seidel, matrix inversion etc.). Use a programming language or a computer tool (e.g. FORTRAN, MATLAB, EES etc.) for solving the system. 2 mm and use the energy balance approach to . Use a graphing tool (e.g. MATLAB graphing tools) to plot temperature contours in the cross section Hint: Utilize symmetry; thus consider only the 12 mm section (see figure below). Also aware that the heat generation term will be halved when you consider the symmetry element. In addition note that the heat generation term is per unit length not per unit volume meaning that the heat generation term exists at that particular node only (no need for multiplying with volume element). Heating element 50 Wim Symmetry line1 Symmetry line 2 12 mm h= 100 W/m2-K Symmetry element Ceramic plate, k=2W/mK 24 mm 6 mm