Energy is generated uniformly in a 20cm thick wall the steady state temperature distribution of the wall is indicated on the table below; z (cm) T(C) 0 2 4 6 8 10 12 14 16 18 20 150 177 205 230 250 272 292 310 330 345| 360 If thermal conductivity of the wall is 15 W/m.K and the indicated temperatures are in °C, determine the average rate of heat generation in unit volume.

A 5-cm-diameter copper sphere is initially at a uniform temperature of 200◦C. Itis suddenly exposed to an environment at 20◦C having a heat-transfer coefficienth=28W/m2 · ◦C. Using the lumped-capacity method of analysis, calculate the timenecessary for the sphere temperature to reach 90◦C.

The exhaust duct from a heater has an inside diameter of 114.3 mm with ceramic walls 6.4 mm thick. The average k=1.52 W/m· K. Outside this wall, an insulation or rock wool 102 mm thick is installed. The thermal conductivity of the rock wool is k= 0.046+ 1.56 x 104 T°C (W/m · K). The inside surface * = temperature of the ceramic is T1 = 588.7 K, and the outside surface temperature of the insulation is 311 K. Calculate the heat loss for 1.5 m of duct and the interface temperature T2 between the ceramic and the insulation. [Hint: The correct value of km for the insulation is that evaluated at the mean temperature of (T2 + T3)/2. Hence, for the first trial assume a mean temperature of, say, 448 K. Then calculate the heat loss and T2 Using this new T2, calculate a new mean temperature and proceed as before.]

(a) What is the heat loss per unit length of the pipe?(b) The pipe material is switched to PTFE (k = 0.38 W/(m⋅K)). To maintain the same heat loss as theprevious question, if all other parameters are to remain the same as before, what is the required thicknessof the pipe wall in centimeters?

À wall of area 30 m² having a density of 1500 kg/m', thermal conductivity 30 W/m.K, and specific heat capacity 4 kJ/kg.K. The temperature distribution across a wall 0.5 m thick at a certain instant of time is given as T(x) = 30-5 x-7x The wall is generating a uniform heat (q.) of 1000 W. (1) Find the rate of heat transfer entering and leaving the wall (in W). (2) Find rate of energy stored in Watt. (3) Find (dFT/dx²) (4) Derive the change in temperature with respect to time equation (time rate of temperature change)- remember to substitute the value of (d T/dx²) from (part 3) and values of all other properties into final equation. %3D

.240mm steam main pipe, 210m long is covered with 50mm of high temperature insulation (k-0.092 W/m °C) and 40mm of low temperature insulation (k-0.062 W/m °C). The inner and the outer surface temperature as measured are 390 °C and 40 °C respectively. Calculate: 1- The total heat loss per hour. 2- The temperature between two layers of insulation.

A copper electric wire of radius R, = 1 mm is isolated by a layer of PVC so that the outer radius of the wire Rg = 2 mm, as shown in Figure below. The wire exchanges heat with the air at 20°C according to a heat transfer coefficient h=20 W/m2°c: Given that : k=copper electrical conductivity=4.0 × 1070hm-'m¯! kpvc= PVC thermal conductivity = 0.3- m°C kco = copper thermal conductivity = 100 m°C %3D (amp/m)² And that the electrical heating source is given by : S, amp²s /kgm³ If the temperature (T,) on the outer surface (r = RG) is 25°C, what is the electrical current C (amp) that passes through this wire? Dont forget to state your hypothesis clearly.     Hi, Could you please tell me what the book's name is? Thank you!

A large slab of aluminum has a thickness of 10 cm and is initially uniform in temperatureat 400◦C. It is then suddenly exposed to a convection environment at 90◦Cwith h=1400 W/m2 · ◦C. How long does it take the center to cool to 180◦C?

Problem 8. Energy is generated uniformly in a 20cm thick wall the steady state temperature distribution of the wall is indicated on the table below; z (cm) T (C) 8 10 12 14 16 18 20 0 2 4 6 150 177 205 230 250 272 292 310 330 345 360 If thermal conductivity of the wall is 15 W/m.K and the indicated temperatures are in °C, determine the average rate of heat generation in unit volume.