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 дуг b- Find the location of extreme heat value in the wall

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 dTglass = -0.75Tglass + 0.75TPVT (1) dt - 1.18Tglass – 22TpyT + 237wax (2) dt dTwax 12Tglass + 18TpyT – 19 Twax (3) dt Where, Tptass, 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 sappty In frem water Tank Glass PVT Enpann Nane-PCMPVT Collector Wax Tubes Sterg Tank Mat Nanofluid Heat Exchanger Tepe Contalner Tuek et Pump for drain

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The temperature on a sheet of metal is known to vary according to the following function: T(z,9) – 4z - 2ry We are interested to find the maximum temperature at the intersection of this sheet with a cylindrical pipe of negligible thickness. The equation of the intersection curve can be approximated as: 2+-4 Find the coordinates for the location of maximum temperature, the Lagrangian multiplier and the value of temperature at the optimum point. Wnite your answer with two decimal places of accuracy. HINT: IF there are more than one critical point, you can use substitution in the objective function to select the maximum. Enter your results here: Optimum value of z Optimum value of y Optimum value of A Optimum value of T

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An air conditioner supplies cold air at the same temperature to each room on the fourth floor of the building shownin Fig. The floor plan is shown in Fig. The cold air flow produces an equal amount of heat flow ݍ out of each room. Write a set ofdifferential equations governing the temperature in each room, where To= temperature outside the building, Ro= resistance to heatflow through the outer walls, Ri= resistance to heat flow through the inner walls. Thermal capacitance of each room is C. Assumethat (1) all rooms are perfect squares, (2) there is no heat flow through the floors or ceilings, and (3) the temperature in each roomis uniform throughout the room. Take advantage of symmetry to reduce the number of differential equations to three.

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