Find the generalized solution to the following heat equation ди a(x)- at = д дх a1u(0, 1) + βι ди (T(x) out) - B(x)u, 0 < x 0, дх ди azu(l, t) + 2(l,t) = 0, t > 0, дх 0 < x 0, (x) > 0, and ß(x) > 0 for 0 < x 0,

The wall (thickness L) of a furnace is comprised of brick material (thermal conductivity, k = 0.2 Wm¯' K'). Given that the atmospheric temperature is 0°C at both sides of wall, the density (p) and heat capacity (c) of the brick material are 1.6 gm cm³ and 5.0 J kg K¯l respectively. du Solve pc = k- subject to initial conditions as u(x,0) = x²(L – x). ốt Consider the case 2=- p² only.

1. A spring mass system serving as a shock absorber under a car's suspension, supports the M=1000kgmass of the car. For this shock absorber,k=1000N/m and c=2000N s/m. The car drives over a corrugated road with force F=2000sin(wt)N. Use your notes to model the second order differential equation suited to thisapplication. Simplify the equation with the coefficient of x'' as one. Solve x (the general solution) interms of using the complimentary and particular solution method. In determining the coefficients ofyour particular solution, it will be required that you assume w2 -1=w or . Do not 1-w2=-wuse Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w.You must indicate in your solution:1. The simplified differential equation in terms of the displacement x you will be solving2. The m equation and complimentary solution3. The choice for the particular solution and the actual particular solution xp4. Express the solution x as a piecewise…

Q3: Consider evaluation of different temperatures of solar photovoltaic/thermal system (PVT) as shown in Figure 1(a). The following set of differential equations represent energy balance equations to be solve using matrices and eigenvalues using MATLAB: dTglass = -0.75Tgtass + 0.75TpvT (1) dt - 1.187glass – 22Tpyr + 23Twax (2) dt dTwax 12Tglass + 18TpyT – 19 Twax (3) dt Where, Tgtass , TPVT, and Twax, are temperatures illustrated in Figure 1(b). At time t-0 the initial conditions are Tglass = 35 , Tpyr = 33, and Twax = 31 °C. Cold suppty In frem water Tank Glass PVT Espann Nane-PCMPVT Collector Wax Tubes Sterg Tank Nanofluid Heat Exchanger Contalner Tepe Teek oe Pump for drain

ng/19:HupCeX-7fb1 TjKjAnHHIrQ7-ussXeH9Kbx8 lo-gK_PM1@thread.tacv2 R Search WODOGA Vote 40000 00 Brushes Color Color Edit colors Edit with Paint 30 Shapes Colors Steam is generated at 4.1O MPa and 440C and condensation occurs at 0.105 MPa. Find the thermal efficiency of the cycl the T-S diagram. Draw the schematic diagram and

Consider the following linear equations,

A fire has been happened near a wall in a building, suppose the heat transfer f(x, y) = y²-K(x² + equation in the wall will be according to the equation: 2x - xy) a- Compute the constant (K) if you know that the heat transfer equation satisfy the following differential equation a²fa²f + = 0 дх2 т дуг b- Find the location of extreme heat value in the wall 4 2.

Specific Heat, Cp Water Thermal Thermal Content, Temperature, T Density, p Conductivity, k Ibm/ft3 Diffusivity, a ft2/s Food %(mass) °F Btu/h-ft.°F Btu/lbm-R Fruits/Vegetables Apple juice Apples Apples, dried Apricots, dried Bananas, fresh 1.51 x 10-6 1.47 x 10-6 87 68 62.4 0.323 0.922 85 32-86 52.4 0.242 0.910 41.6 73 53.4 0.127 1.03 x 10-6 0.650 1.22 x 10-6 1.51 × 10-6 43.6 73 82.4 0.217 0.662 76 41 61.2 0.278 0.856 Broccoli 21 35.0 0.223 | 1.42 x 10-6 Cherries, fresh Figs Grape juice 92 32-86 65.5 0.315 0.952 40.4 73 77.5 0.179 1.03 x 10-6 0.642 1.51 × 10-6 1.51 × 10-6 89 68 62.4 0.328 0.934 Peaches 36-90 2-32 59.9 0.304 0.934 Plums 3 38.1 0.143 | Potatoes 32-158 0-70 65.7 0.288 1.40 x 10-6 0.868 Raisins 32 73 86.2 0.217 1.18 x 10-6 0.592 Meats Beef, ground Beef, lean 67 43 59.3 0.235 1.40 x 10-6 0.802 74 37 68.0 0.272 1.40 x 10-6 0.844 Beef fat 95 50.5 0.110 72 95 73 Beef liver 0.259 0.832 1.18 x 10-6 1.40 x 10-6 Cat food 39.7 71.2 0.188 0.638 Chicken breast 75 32 65.5 0.275 0.850

Question 2: Air at the temperature of T1 is being heated with the help of a cylindrical cooling fin shown in the figure below. A hot fluid at temperature To passes through the pipe with radius Rc. a) Derive the mathematical model that gives the variation of the temperature inside the fin at the dynamic conditions. b) Determine the initial and boundary conditions to solve the equation derived in (a). air To Re Assumptions: 1. Temperature is a function of only r direction 2. There is no heat loss from the surface of A 3. Convective heat transfer coefficient is constant

= Consider 1D transient conduction in a bar with c² = 1. Let the left end be subjected to a temperature To 10, and the right end be held at temperature T 0. The bar is initially at a constant temperature T(x, 0) = T. = Compute the solution u(x, t) using the Fourier series solution for finite bars found earlier in the semester (see HW 5, Problem 4 for an example). Compare the solution with the semi-infinite solution. Use 100 terms in the partial sums of the Fourier series. Compare the solutions for various lengths of the rod: (a) L = 10 (b) L= 100 (c) L = 500