The efficiency of a single cylindrical cross-section fin is 85%. The diameter of the fin is 13 mm and it extends 32 mm from the base. The base is 65 K hotter than the surrounding fluid, and the heat transfer coefficient is 32 W/m2K. How many fins would be required to increase heat transfer from the base by 50 W? Give your answer as an integer.

Consider a large plane wall of thickness L = 0.2 m, thermal conductivity k = 1.2 W/mK, and surface area A = 15 m². Internally, the wall is assumed to generate heat at 500 W/m³. The left and right surfaces of the walls are exposed to convective heat transfer. On the left side (at x = 0 m), the wall temperature is maintained at 60°C. On the right surface side (at x = 0.2 m), the surface is exposed to convective heat transfer with an ambient temperature of 20°C. The convective heat transfer coefficient on the right side is assumed to be 200 W/m²K. Please answer the following questions: 1. What are the given material properties and boundary conditions? 2. What is the coordinate system used here? Please draw a schematic with proper coordinates to represent the problem 3. What are the assumptions associated with the problem? 1D, steady state, etc.? 4. Show the full heat conduction equation associated with the problem (including the unsteady term) 5. Show how to reduce it (based on…

Consider one-dimensional, steady-state conditions for the plane composite wall shown be- low. The left surface of wall A is well-insulated with a constant surface temperature of T₁ = 160°C. Heat is generated within wall A at a rate of 5,000 W/m³. The right surface of wall C is maintained at a temperature of T4 = 19°C due to environmental conditions. Assume negligible contact resistance between all interfaces. The thermal conductivity for each wall is listed be- low and the figure indicates the thickness of each wall. (60 points) (a) Find the temperature at interface between wall A and B (x = 20 mm). (b) Find the temperature at interface between wall B and C (x = 85 mm). (c) Sketch the temperature distribution as a function of x for the composite wall. (d) Sketch the heat flux as a function of x for the composite wall. KA = 0.11 W/m.K KB = 0.05 W/m.K kc 0.72 W/m.K T₁ ف A B TA 15 mm 65 mm 20 mm

Calculate the overall heat transfer coefficient of the steel pipe based on the inner surface. The inner diameter of the pipe is 12.7 cm, and the thickness of the pipe is 2.4 cm. The convection heat transfer coefficient in the pipe is 350 W / (m² ° C), the convective heat transfer coefficient outside the pipe is 25 W / (m² ° C), the thermal conductivity of the steel pipe is 15 W / (m ° C). If the pipe is used to deliver steam at 110 ° C and the ambient temperature is 20 ° C, determine the heat transfer rate of the pipe per meter. q = Watt / m

A furnace of 0.3m by 0.3m by 0.6m inside dimensions is constructed of a material having a thermal conductivity of 0.894 W/m.K. The wall thickness is 10cm. The inner and outer surface temperatures are 600 degree Celcius and 100 degree Celcius respectively. Calculate the heat loss through the furnace wall by using (i) Conduction shape factor. (ii) Thermal resistance.

​​​​​​​can you please please do this one and please show all the work please step by step

Consider a power transistor encapsulated in an aluminum case that is attached at its base to a square aluminum plate of thermal conductivity k= 240W/m.K, thickness L= 6mm, and width W= 20mm. The case is joined to the plate by screws that maintain a contact pressure of 1 bar, and the back surface of the plate transfers heat by natural convection and radiation to ambient air and large surroundings at T∞ =Tsur -25°C. The surface has an emissivity of ε=0.9, and the convection coefficient is h=4 W/m².K. The case is completely enclosed such that heat transfer may be assumed to occur exclusively through the base plate. a) If the air-filled aluminum-to-aluminum interface is characterized by an area of A₁=2×10-4 m² and contact resistance of R+c= 1.375 K/W, what is the maximum allowable power dissipation if the surface temperature of the case, Ts,c, is not to exceed 85°C? S,C' Transistor case Ts. Pelec S,C' Enclosure W Isur Base plate, (k,ε) Interface, Ac Air Th 801 b) How much should the h be…

A steel pipe with heat transfer coefficient of 42 W/mK contains flowing water. The outer diameter of the pipe is 90 mm and the wall thickness is 3mm. Calculate: i. The heat loss by convection and conduction per meter length of un-insulated pipe when the water temperature is 14°C, the outside air temperature is -10°C, the water side heat transfer coefficient is 30 KW/m^2K and the outside heat transfer coefficient is 20 KW/m^2K. ii. Calculate the corresponding heat loss when the pipe is lagged with insulation having an outer diameter of 200 mm, and thermal conductivity of K = 0.05 W/mK