THUMBS UP GUARANTEE IF YOU SOLVE ACCORDING TO THE HINT AND STEP BY STEP! IT IS A PARTIAL D.E. QUESTION IF YOU ARE NOT EXPERT IN THIS AREA PLS DO NOT SOLVE IT.
Consider an electrical heater made from a solid rod of thermal conductivity, k and rectangular cross- section (2Lx2H) as shown in the figure. The internal energy generation per unit volume, g0, in the heater is uniform. The temperature variation along the rod may be neglected. The rod is placed in an environment of temperature T[infinity] and the heat transfer coefficient between the rod and the environment is h and is assumed to be same for all surfaces. The model equation is given as differential equation below.
8²0
ax²
8²0
Əy²
80
kwhere θ= T-T[infinity]
Write the boundary conditions and find the two-dimensional temperature profile in the rod assuming that the heat transfer coefficient h is large.
hint: you should write 4 boundary conditions at origin (x=0,y=0) and at L,H. you should apply the partial differential equation solution method which is separation of variables. obtain 2 differential equations (second-order, non-homogenous ) to solve. (both the homogenous and particular solutions should be determined.) In doing this, assume that the particular solution is only a function of x and the general solution is in the following form: θ (x, y)= ψ(x, y) + φ (x) where ψ is the homogenous solution and φ is the particular solution.