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The diffusion equations
Ɏ2t + q g = (1/α) (d t/d r)
Governs the temperature distribution under unsteady heat flow through a homogenous and isotropic material. The Fourier equation follows from this expression when
Ɏ2t + q g = (1/α) (d t/d r)
Governs the temperature distribution under unsteady heat flow through a homogenous and isotropic material. The Fourier equation follows from this expression when
- a)Temperature doesn’t depends on time
- b)There is no internal heat generation
- c)Steady state conditions prevail
- d)There is no internal heat generation but unsteady state condition prevails
Correct answer is option 'D'. Can you explain this answer?
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The diffusion equationsɎ2t + qg= (1/α) (d t/d r)Governs the...
In unsteady state condition, there is no internal heat generation.
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The diffusion equationsɎ2t + qg= (1/α) (d t/d r)Governs the...
The diffusion equation is commonly written as:
∂u/∂t = D∇²u
where u is the concentration or density of the diffusing species, t is time, D is the diffusion coefficient, and ∇² is the Laplacian operator.
To solve this equation for a one-dimensional case (assuming u is only a function of position x), we can rewrite it as:
∂u/∂t = D∂²u/∂x²
where ∂²u/∂x² represents the second derivative of u with respect to x.
To solve this equation numerically, we can use a finite difference method. We divide the spatial domain into a grid of points, with each point representing a discrete location. We can then approximate the second derivative using finite difference approximations.
For example, using the central difference approximation, we can write the equation as:
∂u/∂t ≈ D(u(x+Δx, t) - 2u(x, t) + u(x-Δx, t))/Δx²
where Δx is the spacing between grid points.
We can discretize the time domain as well, using a time step Δt. Using an explicit finite difference scheme, we can update the concentration at each grid point at each time step using the above equation:
u(x, t+Δt) = u(x, t) + (DΔt/Δx²)(u(x+Δx, t) - 2u(x, t) + u(x-Δx, t))
This equation allows us to simulate the diffusion of a species over time in a one-dimensional system. However, it should be noted that this is a simplified version and there may be additional terms or considerations depending on the specific problem being studied.
∂u/∂t = D∇²u
where u is the concentration or density of the diffusing species, t is time, D is the diffusion coefficient, and ∇² is the Laplacian operator.
To solve this equation for a one-dimensional case (assuming u is only a function of position x), we can rewrite it as:
∂u/∂t = D∂²u/∂x²
where ∂²u/∂x² represents the second derivative of u with respect to x.
To solve this equation numerically, we can use a finite difference method. We divide the spatial domain into a grid of points, with each point representing a discrete location. We can then approximate the second derivative using finite difference approximations.
For example, using the central difference approximation, we can write the equation as:
∂u/∂t ≈ D(u(x+Δx, t) - 2u(x, t) + u(x-Δx, t))/Δx²
where Δx is the spacing between grid points.
We can discretize the time domain as well, using a time step Δt. Using an explicit finite difference scheme, we can update the concentration at each grid point at each time step using the above equation:
u(x, t+Δt) = u(x, t) + (DΔt/Δx²)(u(x+Δx, t) - 2u(x, t) + u(x-Δx, t))
This equation allows us to simulate the diffusion of a species over time in a one-dimensional system. However, it should be noted that this is a simplified version and there may be additional terms or considerations depending on the specific problem being studied.
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The diffusion equationsɎ2t + qg= (1/α) (d t/d r)Governs the temperature distribution under unsteady heat flow through a homogenous and isotropic material. The Fourier equation follows from this expression whena)Temperature doesn’t depends on timeb)There is no internal heat generationc)Steady state conditions prevaild)There is no internal heat generation but unsteady state condition prevailsCorrect answer is option 'D'. Can you explain this answer?
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The diffusion equationsɎ2t + qg= (1/α) (d t/d r)Governs the temperature distribution under unsteady heat flow through a homogenous and isotropic material. The Fourier equation follows from this expression whena)Temperature doesn’t depends on timeb)There is no internal heat generationc)Steady state conditions prevaild)There is no internal heat generation but unsteady state condition prevailsCorrect answer is option 'D'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about The diffusion equationsɎ2t + qg= (1/α) (d t/d r)Governs the temperature distribution under unsteady heat flow through a homogenous and isotropic material. The Fourier equation follows from this expression whena)Temperature doesn’t depends on timeb)There is no internal heat generationc)Steady state conditions prevaild)There is no internal heat generation but unsteady state condition prevailsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diffusion equationsɎ2t + qg= (1/α) (d t/d r)Governs the temperature distribution under unsteady heat flow through a homogenous and isotropic material. The Fourier equation follows from this expression whena)Temperature doesn’t depends on timeb)There is no internal heat generationc)Steady state conditions prevaild)There is no internal heat generation but unsteady state condition prevailsCorrect answer is option 'D'. Can you explain this answer?.
The diffusion equationsɎ2t + qg= (1/α) (d t/d r)Governs the temperature distribution under unsteady heat flow through a homogenous and isotropic material. The Fourier equation follows from this expression whena)Temperature doesn’t depends on timeb)There is no internal heat generationc)Steady state conditions prevaild)There is no internal heat generation but unsteady state condition prevailsCorrect answer is option 'D'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about The diffusion equationsɎ2t + qg= (1/α) (d t/d r)Governs the temperature distribution under unsteady heat flow through a homogenous and isotropic material. The Fourier equation follows from this expression whena)Temperature doesn’t depends on timeb)There is no internal heat generationc)Steady state conditions prevaild)There is no internal heat generation but unsteady state condition prevailsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diffusion equationsɎ2t + qg= (1/α) (d t/d r)Governs the temperature distribution under unsteady heat flow through a homogenous and isotropic material. The Fourier equation follows from this expression whena)Temperature doesn’t depends on timeb)There is no internal heat generationc)Steady state conditions prevaild)There is no internal heat generation but unsteady state condition prevailsCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The diffusion equationsɎ2t + qg= (1/α) (d t/d r)Governs the temperature distribution under unsteady heat flow through a homogenous and isotropic material. The Fourier equation follows from this expression whena)Temperature doesn’t depends on timeb)There is no internal heat generationc)Steady state conditions prevaild)There is no internal heat generation but unsteady state condition prevailsCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Chemical Engineering.
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