A plane wall has thickness of 5 cm, thermal conductivity of 2 W/mK and generates heat....

A plane wall has thickness of 5 cm, thermal conductivity of 2 W/mK and generates heat. The left face of the wall (x=0) has a surface temp. of 80C and has air at 20C flowing past it with a heat transfer coefficient of 50 W/m^2K. If the right face is insulated then the temperature distribution through the wall has a general format T(x)=A+B*x+C*x^2

(a) Draw a properly labeled diagram (including a representative temperature distribution), state all assumptions and calculate the volumetric energy generation in the wall.

(b) Apply appropriate boundary conditions to determine the coefficients A, B, and C for the temperature distribution through the wall.

(c) Where will the maximum temperature be located in the wall?

Expert Solution

samet mamat answered 2 years ago

A composite cylindrical wall is composed of 2 materials of thermal conductivity ka = 240 W/mK...

A composite cylindrical wall is composed of 2 materials of thermal conductivity ka = 240 W/mK and kb = 20 W/mK, where interfacial contact resistance is negligible. - Liquid pumped through the tube is at a temperature Tinf, i = 200 F and provides a convection coefficient hi = 450 W/m^2K at the inner surface of the composite pipe -The outer surface is exposed to Tinf, o and provides a convection coefficient of ho = 20 W/m^2K -A thermocouple between...

Heat is generated uniformly at a rate of 2x105 W/m3 in a wall of thermal conductivity...

Heat is generated uniformly at a rate of 2x105 W/m3 in a wall of thermal conductivity 25W/m K and thickness 60 mm. The wall is exposed to convection on both sides, with a fluid temperature of 30C and h = 50W/m2 K on the left side, a fluid temperature of 15C and h = 12 W/m2 K on the right side. (a) Determine surface temperature on each side of the wall, and (b) the maximum temperature in the wall.

In a slab of material 0.25 m thick and having a thermal conductivity of 45 W/mK,...

In a slab of material 0.25 m thick and having a thermal conductivity of 45 W/mK, the temperature °C at x under steady state is given by T = 100 + 200x – 400x2 when x is measured from one face in m. Determine the heat flow at x = 0, x = 0.125 and x = 0.25 m and also the temperatures and temperature gradients at these planes. If the difference in heat flow at these sections is due...

Consider a large plate of thickness 50 mm and thermal conductivity of k= 69 W/m.C in...

Consider a large plate of thickness 50 mm and thermal conductivity of k= 69 W/m.C in which heat is generated uniformly at a constant rate of 600 kW/m3. One side of the plate is insulated while the other side is subjected to convection to the environment at 30oC with a heat transfer coefficient of h= 94 W/m^2.C. considering six equal spaced nodes with a nodal spacing of 10 mm: (a) obtain the Finite Difference formulation of this problem, (b) determine...

Convert: a. Thermal conductivity value of 0.3 Btu/(h ft oF) to W/(m oC). b. Surface heat...

Convert: a. Thermal conductivity value of 0.3 Btu/(h ft oF) to W/(m oC). b. Surface heat transfer coefficient value of 105 Btu/(h ft^2 oF) to W/(m^2 oC)

i need the solution with comsol Consider a large plane wall of thickness L 5 0.4...

i need the solution with comsol Consider a large plane wall of thickness L 5 0.4 m, ther- mal conductivity k 5 2.3 W/m·K, and surface area A 5 20 m 2 . The left side of the wall is maintained at a constant temperature of 95°C, while the right side loses heat by convection to the surrounding air at T ` 5 15°C with a heat transfer coefficient of h 5 18 W/m 2 ·K. Assuming steady one-dimensional heat...

A spherical shell of wood with thermal conductivity of 0.13 W/m.K and an inner and outer...

A spherical shell of wood with thermal conductivity of 0.13 W/m.K and an inner and outer radius of 10 cm and 20 cm respectively contains a mixture of water and water vapor(100 C) inside the shell which is undergoing a phase change at atmospheric pressure. The shell is suspended in a large room with an ambient air temperature of 25 C Determine the temperature on the outer surface of the spherical shell and rate of heat loss from the fluid...

3. A stainless steel sphere of thermal conductivity 16 W/m · K with a diameter of...

3. A stainless steel sphere of thermal conductivity 16 W/m · K with a diameter of 4 cm is exposed to a convective environment of 15 W/m2 · K, 20?C. Heat is generated uniformly in the sphere at a rate of 1.0 MW/m3 . Determine the steady-state temperature of the sphere at its center and its surface. Also determine the heat flux at a radius of 1.5 cm.

A rod of diameter D = 25 mm and thermal conductivity of 60 W/m·K protrudes from...

A rod of diameter D = 25 mm and thermal conductivity of 60 W/m·K protrudes from a furnace with a wall temperature of 200ºC. The rod is welded to the furnace wall and is used as a hangar for instrumentation cables. To avoid damaging the cables, the surface temperature of last 100 mm of the rod must be kept below 100ºC. The ambient air temperature is 25ºC and the convection coefficient is 15 W/m2K. (a) Write the finite-difference equation for...

Q1. Suppose a hollow cylinder made of SS 316 with the thermal conductivity of 16.26 W/m...

Q1. Suppose a hollow cylinder made of SS 316 with the thermal conductivity of 16.26 W/m K, has inner diameter and thickness of 0.4 and 0.03 m, respectively and length of 1 m. Find the outer diameter of the cylinder (in meter) Q2. Calculate the thermal energy generation, if the volumetric heat generation inside the cylinder equal to 2.2 x 10^5 W/m^3 Q3. If the outer diameter of cylinder is changed to 0.46 m and the cylinder is cooled by...

Question