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- 2.15 Suppose that a pipe carrying a hot fluid with an external temperature of and outer radius is to be insulated with an insulation material of thermal conductivity k and outer radius . Show that if the convection heat transfer coefficient on the outside of the insulation is and the environmental temperature is , the addition of insulation actually increases the rate of heat loss if , and the maximum heat loss occurs when . This radius, is often called the critical radius.10B.4. Heat conduction in an annulus (Fig. 10B.4). (a) Heat is flowing through an annular wall of inside radius and outside radius ₁. The thermal conductivity varies linearly with temperature from ko at To to k₁ at T₁. Develop an ex- pression for the heat flow through the wall. (b) Show how the expression in (a) can be simplified when (r₁-ro)/ro is very small. Interpret the result physically. Answer: (a) Q = 2πL(T₁- To T₁ T₁) ›(ko + k) (in 7.) *'; 2 "'; (b) Q = 2mr_L (ko + ki ) ( 7 2 Problems 323 Fig. 10B.4. Temperature profile in an annular wall.Qi: (50 marks) Find the total heat flux of the composite wall when: B KA = KC = KF = 15 m. K KB = KD = 10 m. K KE = KG = 20 %3D m. K D. Height of B = C = D 4 cm 3 cm 4 cm 6 cm Height of F = G AT = 30 K
- An electric heater with a capacity P is used to heat air in a spherical chamber. The inside radius is r. outside radius r, and the conductivity is k. surface heat is exchanged by convection. Sur At the inside kh The inside heat transfer coefficient is h,. Heat loss from the outside surface is by +1 radiation. The surroundings temperature is Tur and the surface emissivity is ɛ. Assuming one-dimensional steady state conduction, use a simplified radiation model to determine: [a] The temperature distribution in the spherical wall. [b] The inside air temperatures for the following conditions: h-6.5 W/m-"C, P-1, 500 W, &=0.81, T 18°C. %3D sur k 2.4 W/m-°C. 1=10 cm. 1,= 14 cm.Create two problem solving about steady-state heat flow (Heat convection in fluids) and show your solutions. Thank you!The thermal conductivities of wood is kwood = 0.1W/(m°C)and air is kair = 0.0234W/(m°C). Part A If the temperature of the room is 20°C and outside is 10°C, find the rate of heat flow for a wall of wood with area = 10 m² and thickness of 5cm. O 60 W O 304 W O 34 W O 200 W O 100 W Submit Request Answer Part B The wall of wood with thickness of 5cm is now replaced with two layers of wood and a gap of air between the wood. Each layer of wood has a 2.5cm thickness and the gap is 1cm. The rate of heat flow will, decreases. increases. stay the same. Submit Request Answer Part C The temperature in the air gap will be, O 20°C, between 10°C and 20°C, O 10°C,
- solve step by step and correctly. A family enters a winter vacation cabin has been unheated for such a long time the interior temperature is the same as the outside temperature (00C). The cabin consists of a single room of floor area 4m by 4m and height 3m. The room contains one 2kW electric heater. Assuming that the room is perfectly airtight and that all the heat from the electric heater is absorbed by the air, none escaping through the walls or being absorbed by the furnishing, how long after the heater is turned on will the temperature reach the comfort level of 240C.5. An irregularly shaped solid made of a material with a density of 3200 kg/m³ has a volume of 0.003 m3 and a surface area of 0.07 m². The thermal conductivity of the material is 300 W/m K, and its specific heat is 500 J/kg K. Initially, there is a 100°C difference between the solid and its environment, what is the approximate time it will take for this system to have the difference between its temperature and the environment to be one-third of the initial difference? Use h- 60 W/m-K for the environment. Express your answer in minutes.Derive equation for heat transfer by conduction through hollow cylinder. Also mention assumptions made for it.
- To solve heat conduction equation, we have assumed Steady case O all of the above constant cross-sectional area one dimensional heat transfer O no thermal energy generation O none of the above3.15 The heating rate that a heat pump delivers to a living space of tempera- ture 20°C is 5 kW. The coefficient of performance of the heat pump is COP = 2. The temperature of the ambient is 0°C. (a) What is the electrical power required by the heat pump? (b) What is the rate at which the heat pump draws heat from the ambient? (c) What is the highest COP value that the heat pump may attain? (d) Is the operation of this heat pump violating the second law of thermodynamics?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