Homework Answers
a) Governing Equation with Boundary condition:
This is a basis of classical theory of laminar boundary layes
please find the full equation for 2D in the attachment,
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heat transfer
Consider a long solid rod of constant thermal conductivity k whose cross section is...
A long solid rod of constant thermophysical properties and radius ro is initially at a uniform...
A long solid rod of constant thermophysical properties and radius ro is initially at a uniform temperature Tj. At time t = 0, the temperature of the peripheral surface at r=r, is changed to Tw and is subsequently maintained constant at this value for t> 0. (a) Show the governing equation with the boundary conditions. (b) Redefine the temperature for the homogeneous boundary conditions. (c) Show the separation of variables. (d) Show how to obtain the eigenvalues. (e) Obtain an...
A plane wall with thermal conductivity of k, is insulated on one side and is exposed...
A plane wall with thermal conductivity of k, is insulated on one side and is exposed to ambient air at To and convection coefficient of h, on the other side. A heat source in the 3) wall is generating a uniform heat rate per unit volume of For one-dimensional steady-state conduction in the wall, derive a proper differential equation for the temperature by either using the heat equations or doing the energy balance. Identify proper boundary conditions and find the...
A very long rod of 5-mm diameter and uniform thermal conductivity k = 25 W/m-K is subjected to a heat treatment process
A very long rod of 5-mm diameter and uniform thermal conductivity k = 25 W/m-K is subjected to a heat treatment process. The center, 30-mm-long portion of the rod within the induction heating coil experiences uniform volumetric heat generation of 7.5 x 106 W/m3. The unheated portions of the rod, which protrude from the heating coil on either side, experience convection with the ambient air at T∞ = 20 °C and h = 10 W/m2K. Assume that there is no convection...
Consider a large plane wall with a thickness of L and a constant thermal conductivity k....
Consider a large plane wall with a thickness of L and a constant thermal conductivity k. The left surface of the plane is exposed to a uniform heat flux, ?̇?. The right face is exposed air at uniform ?∞ with h. The emissivity on the right surface is ε. a. Write an appropriate form of heat conduction equation for the plane. b. Express the boundary conditions.
3/5 25 pts.J A slab of thickness L, made of material with constant thermal conductivity k,...
3/5 25 pts.J A slab of thickness L, made of material with constant thermal conductivity k, is undergoing a 1-D, steady heat transfer. Its boundary surface at x 0 is insulated while the boundary surface at x= 1 is kept at constant temperature T= oc. Heat energy is generated within the slab at a rate of 2. qx)o cos(rx/2L) is the energy generation rate per unit volume (Wm) at x= 0. where qo a. Develop an expression for the steady-state...
2-157 A long electrical resistance wire of radius r.-0.25 cm has a thermal conductivity kwire-15 W/m-K. Heat is gene...
2-157 A long electrical resistance wire of radius r.-0.25 cm has a thermal conductivity kwire-15 W/m-K. Heat is generated uniformly in the wire as a result of resistance heating at a constant rate of 0.5 W/cm3. The wire is covered with polyethylene insulation with a thickness of 0.25 cm and thermal conductivity of ks 0.4 W/m K. The outer surface of the insulation is subjected to free convection in air at 20°C and a convection heat transfer coefficient of 2...
The heat that is conducted through a body must frequently be removed by other heat transfer...
The heat that is conducted through a body must frequently be removed by other heat transfer processes. For example, the heat generated in an electronic device must be dissipated to the surroundings through convection by means of fins. Consider the one-dimensional aluminum fin (thickness t 3.0 mm, width 20 cm, length L) shown in Figure 1, that is exposed to a surrounding fluid at a temperature T. The conductivity of the aluminum fin (k) and coefficient of heat convection of...
A plane wall of thickness 2L= 30 mm and thermal conductivity k= 3 W/m·K experiences uniform...
A plane wall of thickness 2L= 30 mm and thermal conductivity k= 3 W/m·K experiences uniform volumetric heat generation at a rate q˙, while convection heat transfer occurs at both of its surfaces (x=-L, +L), each of which is exposed to a fluid of temperature ∞T∞= 20°C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x)=a+bx+cx2 where a= 82.0°C, b= -210°C/m, c= -2 × 104°C/m2, and x is in meters. The origin of the x-coordinate...
Question You are studying heat transfer through a spherical shell container with a thermal conductivity k....
Question You are studying heat transfer through a spherical shell container with a thermal conductivity k. The inner and outer radii are identified as a and b, respectively. The inside surface of the shell is exposed to a constant heat flux in the outward direction. The outside surface temperature of the container is measured at Note that only the variables values provided in the problem statement are known. Assume steady one-dimensional radial heat transfer a. Give the mathematical formulation of...
Problem 3. A plane wall of thickness 2L = 40 mm and thermal conductivity k =...
Problem 3. A plane wall of thickness 2L = 40 mm and thermal conductivity k = 5 W/m.K experiences uniform volumetric heat generation at a rate ġ, while convection heat transfer occurs at both of its surfaces (x = -1, + L), each of which is exposed to a fluid of temperature Too = 20 °C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x) = a + bx + cx? where a = 82.0°C,...
A long solid rod of constant thermophysical properties and radius ro is initially at a uniform temperature Tj. At time t = 0, the temperature of the peripheral surface at r=r, is changed to Tw and is subsequently maintained constant at this value for t> 0. (a) Show the governing equation with the boundary conditions. (b) Redefine the temperature for the homogeneous boundary conditions. (c) Show the separation of variables. (d) Show how to obtain the eigenvalues. (e) Obtain an...
A plane wall with thermal conductivity of k, is insulated on one side and is exposed to ambient air at To and convection coefficient of h, on the other side. A heat source in the 3) wall is generating a uniform heat rate per unit volume of For one-dimensional steady-state conduction in the wall, derive a proper differential equation for the temperature by either using the heat equations or doing the energy balance. Identify proper boundary conditions and find the...
3/5 25 pts.J A slab of thickness L, made of material with constant thermal conductivity k, is undergoing a 1-D, steady heat transfer. Its boundary surface at x 0 is insulated while the boundary surface at x= 1 is kept at constant temperature T= oc. Heat energy is generated within the slab at a rate of 2. qx)o cos(rx/2L) is the energy generation rate per unit volume (Wm) at x= 0. where qo a. Develop an expression for the steady-state...
2-157 A long electrical resistance wire of radius r.-0.25 cm has a thermal conductivity kwire-15 W/m-K. Heat is generated uniformly in the wire as a result of resistance heating at a constant rate of 0.5 W/cm3. The wire is covered with polyethylene insulation with a thickness of 0.25 cm and thermal conductivity of ks 0.4 W/m K. The outer surface of the insulation is subjected to free convection in air at 20°C and a convection heat transfer coefficient of 2...
The heat that is conducted through a body must frequently be removed by other heat transfer processes. For example, the heat generated in an electronic device must be dissipated to the surroundings through convection by means of fins. Consider the one-dimensional aluminum fin (thickness t 3.0 mm, width 20 cm, length L) shown in Figure 1, that is exposed to a surrounding fluid at a temperature T. The conductivity of the aluminum fin (k) and coefficient of heat convection of...
Question You are studying heat transfer through a spherical shell container with a thermal conductivity k. The inner and outer radii are identified as a and b, respectively. The inside surface of the shell is exposed to a constant heat flux in the outward direction. The outside surface temperature of the container is measured at Note that only the variables values provided in the problem statement are known. Assume steady one-dimensional radial heat transfer a. Give the mathematical formulation of...
Problem 3. A plane wall of thickness 2L = 40 mm and thermal conductivity k = 5 W/m.K experiences uniform volumetric heat generation at a rate ġ, while convection heat transfer occurs at both of its surfaces (x = -1, + L), each of which is exposed to a fluid of temperature Too = 20 °C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x) = a + bx + cx? where a = 82.0°C,...
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