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Required Concepts: Solving heat diffusion equation in Cartesian and Polar Co-ordinates Problem 1 A long electric...
(1) A sphere of decaying radioactive material of radius ro produces heat at a rate of q"" (W/m3)....
(1) A sphere of decaying radioactive material of radius ro produces heat at a rate of q"" (W/m3). The sphere is contained in a spherical shell of graphite of outside radius r1. The outside surface of the graphite is cooled uniformly by flowing air of temperature To. The heat transfer coefficient at the outside surface is h. The constant thermal conductivities of the radioactive material and the graphite are ko and ki, respectively. Densities and heat capacities are ρο, co...
Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C...
Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C and 100°C, respectively. Determine the rate of heal transfer by radiation between the plates in Wim and the radiative heat transfer coefficient in W/m K ) 12 Write down the one-dimensional sent heal conduction equation for a plane wall with constant thermal conductivity and heat generation in its simplest form, and indicate what each variable represents 13 Write down the one-dimensional transient heat conduction...
FIGURE P2-101 2-102 A long home r.= 0.6 cm and thermal cond used to boil water...
FIGURE P2-101 2-102 A long home r.= 0.6 cm and thermal cond used to boil water at atmosph electric current. Heat is gener result of resistance heating a generated is transferred to water at 10 an average heat transfer coe Assuming steady one-dir the differential equation and the boundary COI ong homogeneous resistance wire of radius rmal conductivity k = 15.2 W/m.K is being it atmospheric pressure by the passage of at is generated in the wire uniformly as a...
Chenical reaction, Figure 1: Two end of the rods are maintained at different temperatures A chemically...
Chenical reaction, Figure 1: Two end of the rods are maintained at different temperatures A chemically reacting mixture is stored in a thin-walled spherical container of radius 1 200 mm, and the exothermic reaction generates heat at a uniform, but temperature-dependent volumetric rate of q exp( A/T ), where如= 500 W/m3. A = 75 K. and To IS the mixture teinperature in kelvins. The vessel is enclosed by an insulating material of outer radius r2, thermal conductivity k, and emissivity...
finite element method The equation for the heat diffusion of a one-dimensional system widh heat generation in a Car...
finite element method
The equation for the heat diffusion of a one-dimensional system widh heat generation in a Cartesian coordinate system is 4. d'T dx2 The rate of thermal energy generation q represents the convessice of enery os electrical, chemical, nuclear, or electromagnetic forms to thermal energy witin the volume of a given system. Derive the contribution of á to the load matrix. Consider a strip of heating elements embedded within the rear glass of a car peoducing a uniform...
In a food processing facility, a spherical container of inner radius n = 40 cm, outer...
In a food processing facility, a spherical container of inner radius n = 40 cm, outer radius r2 = 41 cm, and thermal conductivity k = 1.5 W/m 'C is used to store hot water and to keep it at 100°C at all times (see Figure Q2). To accomplish this, the outer surface of the container is wrapped with a 500-W electric strip heater and then insulated. The temperature of the inner surface of the container is observed to be...
Problem 3 Using Fourier series expansion, solve the heat conduction equation in one dimension a?т ат...
Problem 3 Using Fourier series expansion, solve the heat conduction equation in one dimension a?т ат ax2 де with the Dirichlet boundary conditions: T T, if x 0, and T temperature distribution is given by: T(x, 0) -f(x) T, if x L. The initial 0 = *First find the steady state temperature distribution under the given boundary conditions. The steady form solution has the form (x)-C+C2x *Then write for the full solution T(x,t)=To(x)+u(x,t) with u(x,t) obeying the boundary contions U(0,t)...
A large plane wall has a constant thermal conductivity of 8.5W/(m·K), a surface area of 15...
A large plane wall has a constant thermal conductivity of 8.5W/(m·K), a surface area of 15 m² and a thickness L=25 cm. The temperature on the leftside of the wall (T0) is constant and measured at 0.0°C. A constant heat flux(푞̇H)of 450.0 W/m² entersthe rightside of the wall.a.Express the differential equation and the boundary conditions(mathematical formulation)for steady one-dimensional heat conduction through the wall.b.Obtain a numerical equationfor the variation of temperature in the wall by solving the differential equation. c.Evaluate the...
QUESTION FOUR Consider the base plate of an 900-W household iron with a thickness of L-0.6...
QUESTION FOUR Consider the base plate of an 900-W household iron with a thickness of L-0.6 cm, base area of A-160 cm2, and the thermal conductivity of k-60 W/m.K. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When stea dy operating itions are reached, the outer surface temperature of the plate is measured to be 112 C. Disregarding any heat loss through the upper part of the iron, (a)...
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...
(1) A sphere of decaying radioactive material of radius ro produces heat at a rate of q"" (W/m3). The sphere is contained in a spherical shell of graphite of outside radius r1. The outside surface of the graphite is cooled uniformly by flowing air of temperature To. The heat transfer coefficient at the outside surface is h. The constant thermal conductivities of the radioactive material and the graphite are ko and ki, respectively. Densities and heat capacities are ρο, co...
Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C and 100°C, respectively. Determine the rate of heal transfer by radiation between the plates in Wim and the radiative heat transfer coefficient in W/m K ) 12 Write down the one-dimensional sent heal conduction equation for a plane wall with constant thermal conductivity and heat generation in its simplest form, and indicate what each variable represents 13 Write down the one-dimensional transient heat conduction...
FIGURE P2-101 2-102 A long home r.= 0.6 cm and thermal cond used to boil water at atmosph electric current. Heat is gener result of resistance heating a generated is transferred to water at 10 an average heat transfer coe Assuming steady one-dir the differential equation and the boundary COI ong homogeneous resistance wire of radius rmal conductivity k = 15.2 W/m.K is being it atmospheric pressure by the passage of at is generated in the wire uniformly as a...
Chenical reaction, Figure 1: Two end of the rods are maintained at different temperatures A chemically reacting mixture is stored in a thin-walled spherical container of radius 1 200 mm, and the exothermic reaction generates heat at a uniform, but temperature-dependent volumetric rate of q exp( A/T ), where如= 500 W/m3. A = 75 K. and To IS the mixture teinperature in kelvins. The vessel is enclosed by an insulating material of outer radius r2, thermal conductivity k, and emissivity...
finite element method
The equation for the heat diffusion of a one-dimensional system widh heat generation in a Cartesian coordinate system is 4. d'T dx2 The rate of thermal energy generation q represents the convessice of enery os electrical, chemical, nuclear, or electromagnetic forms to thermal energy witin the volume of a given system. Derive the contribution of á to the load matrix. Consider a strip of heating elements embedded within the rear glass of a car peoducing a uniform...
In a food processing facility, a spherical container of inner radius n = 40 cm, outer radius r2 = 41 cm, and thermal conductivity k = 1.5 W/m 'C is used to store hot water and to keep it at 100°C at all times (see Figure Q2). To accomplish this, the outer surface of the container is wrapped with a 500-W electric strip heater and then insulated. The temperature of the inner surface of the container is observed to be...
Problem 3 Using Fourier series expansion, solve the heat conduction equation in one dimension a?т ат ax2 де with the Dirichlet boundary conditions: T T, if x 0, and T temperature distribution is given by: T(x, 0) -f(x) T, if x L. The initial 0 = *First find the steady state temperature distribution under the given boundary conditions. The steady form solution has the form (x)-C+C2x *Then write for the full solution T(x,t)=To(x)+u(x,t) with u(x,t) obeying the boundary contions U(0,t)...
QUESTION FOUR Consider the base plate of an 900-W household iron with a thickness of L-0.6 cm, base area of A-160 cm2, and the thermal conductivity of k-60 W/m.K. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When stea dy operating itions are reached, the outer surface temperature of the plate is measured to be 112 C. Disregarding any heat loss through the upper part of the iron, (a)...
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...
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