Question

Can you please help me with this question. Much appreciated. So I have a sample code, but we need to change the code in a way that fits the problem.

A planar slab of material is initially at a temperature of 300 K. At the time t=0, microwave radiation is directed at the material, leading to internal heat generation that is uniform within the material. The sides of the slab experience negligible heat losses and a water bath maintains the top and bottom surfaces of the slab at 300 K. Material properties for the slab are as follows: k 0.57 W/( mK), p = 1987 kg/m², and c = 1200 J/(kg K). In addition, 9 = 5.7 x 106 W/m2 from application of the microwave radiation. Assuming one-dimensional planar heat transfer, calculate and plot the peak temperature in the slab as a function of time for the slab thickness L = 2 cm (L is the distance between the bottom and top surfaces of the slab). How long does it take for the peak slab temperature to be within 2 K of the steady-state peak slab temperature? Calculate the peak steady-state temperature using an exact analytical solution. Repeat the calculations for L = 4 cm and determine whether the times you calculated scale with L, L², or some other power of L. What power of L would you expect based on physical grounds, i.e., considering the physical interpretation of thermal diffusivity? Matlab code to calculate and plot the peak temperature in a plane wall as a function of time, including heat generation, is included. This code uses an implicit formulation. Modify this code to include the appropriate properties as well as to vary the grid spacing, the integration time, and the Fourier number. You should demonstrate that your results can be considered to be grid and time step independent.

Answer 1

Answetro clear L=2; % slab thicknesem N =51; % number of nodes t-max - Os To integration time, s FO = 1; %Fourier number K=0.57W/mK; Itheormal conductivity W/(m^2K) lobo=1987; %density , kg/m^3 C=1200)/(kg k); % Specific heat , JI (Kg K) edot = 5.78106; % W/m^3 alph = K / Gho*c )3 % themal diffusivity 2 m^z/s Ti = 300; % in Hol temperature its 5300 3 % surface temperature Idx = LICN-3) 3 % node spucing x = -1/2: dx:L/275% hoce locations dt = Fo*dy* dxlalphas 7. physical time steps Pmax = Ceil (t-maxld b); %total number of time steps Tmax = Zexas (Pmaxel) ; % vector to hold the maximum temperature values t = Zeros (Pmare, t); Blector to hold the time valuess 6 = Zeros (NL) % vedor to hold the heat generation terms.

% set the values for the smatra DC12 = 0; for m=2:(N-12 0 (m) = qdet* del Lobot c); end OWN) = 0; % set the A matrix Values A = Zexas (N). Told = Zeros CNL 1 ; Tnew zeros (ND; for n = 2:00-01 A= (m,m=1=1 Almim) -2; Almimtu) = 1 end % impláct solution Told C = TE for 2: N- Told (m)=ti end Told Ni) Toga for PP): pmax Thew = leye(n)-Fo*A) \(toldto); % gauss elimination told Tnews Tmax (P)= max (Thew);_% % save the maximum temperature

P*dt to end Timplicit و بیامTn trew "lo plot the results Plot (ty Tmax Luxlabel ('t ()y label compor (ks);