Plaster Insulation Brick Inside Air Outside Air le ra A particular house wall consists of three layers and has a surface area A. The inside layer is made of plaster board, the middle layer is made of fiberglass insulation, and the outside layer is made of brick. The thermal conductivity of all three layers is known, and the thickness of the plaster board and siding are also known. The convection coefficient for the inside and outside wall surfaces are known: System Parameters - (h; = 40.0 h,= 60.0 kị = 0.2 k,= 0.04 kz = 0.3 A = 30.0) System_Parameters - (L = 10.0 L½= unknown Lz= 100.0 c„ = 950.0 cp2 = 10.0 cp3=800.0 pi = 700.0 p2= 0.5 P3 = 2000.0) L ~ mm; A ~ m²; k~ _W m °C , kg ; T ~ °C m² °C kg °C a) If the thermal capacitances of the walls is ignored, How thíck must the insulation layer be so that the heat loss is no greater than 400W if the outside temperature is -15-C? b) Now consider the situation where the thermal capacitance is also considered. Develop the state variable model of the temperatures at the midpoints of each of the materials. Assume perfect conduction at the interfaces. Write the state equations in terms of the variables provided (not numbers). c) Consider the following situation: This wall represents the external wall of a small room. Throughout the night, there is no heat source turned on in the room, so the air temperature in the room is nearly the same as the temperature outside, which is 17 •C. Just before 7:00 am an air handling system is turned on which quickly stabilizes the room temperature at a constant 21 •C. At 7:00 am, the sun begins to rise and warms the outside air at a fairly constant rate, so that by 3:00 pm, the outside air temperatures is 30 ·C. Plot the thermal response of each of the layers of the wall throughout this time period. What can you identify about the thermal behavior of each of the layers in the wall?

A flat wall is formed by connecting layers A, [B and E parallel] and C in series. The thicknesses of A, B and E layers are equal and are 40 mm. There is a uniformly distributed heat generation of 9.0x105 W/m3 in layer A; There is no heat generation in layers B, E and C. The surface of the A surface open to the atmosphere is completely insulated. In order to keep the temperature of the C layer below 75 oC, water at 20 oC is continuously supplied from its outer surface (h= 900 W/m2. K) to cool it. a) Calculate the outer surface temperatures of layers A and C and the interface temperatures between the layers. b) Calculate the thickness of layer C. The TB and TE interface temperatures and heat transfer surface areas (AB=AE= A/2) are equal. Thermal conductivities: KA (W/m K) 62 a) b) A B E KB (W/m K) 96 B E kc (W/m K) 160 Yükseklik 2 m Genişlik 80 cm KE (W/m K) 130 Prove whether or not the C-layer temperature changes when the same flat wall (choice a) heat generation is replaced by the B…

The following graph shows the thermal behavior of 2 kg of a material called Uniandesato undergoing a solid-liquid phase transition. In a container, thermally insulated from the outside, 20 kg of liquid water at a temperature of 80°C are placed. In addition to this, an unknown amount of Uniandesato in a 100% solid state at its melting temperature (10°C) is added. The specific heat of water is 4186 J/kg°C. a) If the system reaches an equilibrium temperature of 60°C, calculate the initial amount of Uniandesato added to the container. b) Calculate the change in entropy during this process and show that it is consistent with the Second Law of Thermodynamics. Hint: Extract the necessary information to solve this problem from the graph.

A composite wall of a refrigerator consists of three different materials; A, B, and C. Two of the used materials have known thermal conductivity, KA = 30 W/m. K and kc-45 W/m. K, and known thickness, LA=0.20 m and Lc = 0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, LB = 0.15 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,o= 20°C, an inner surface temperature of Ts,i = 600°C, and a refrigerator air temperature of Too = 800°C. The inside convection coefficient h is known to be 25 W/m².K. (a) First, draw the thermal circuit for this wall. (b) What is the value of thermal conductivity for material B? Tsi Air To, h KA K₂ kc Lg Lc Figure 2: Composite wall configuration described in problem 3.