Question

(7 pts.) A metal plate of thickness L with a constant thermal conductivity of k W/m/k is insulated at x = L. The surface at x = 0 is kept at a constant temperature of T.. Within the plate, heat is generated at the rate of ġ W/m². Find an expression for steady-state temperature profile, T(x) and the x-location where the maximum temperature occurs. $$ \frac{d}{dx} \left( k \frac{dT}{dx} \right) + \frac{d}{dy} \left( k \frac{dT}{dy} \right) + \frac{d}{dz} \left( k \frac{dT}{dz} \right) + \dot{q} = \rho c \frac{dT}{dt} $$ Bq x=0 T:S BC2 x=L -KA $\frac{dT}{dx}|_{x=L}$ = 0 x=0 x=L

          (7 pts.) A metal plate of thickness L with a constant thermal conductivity of k W/m/k is insulated
at x = L. The surface at x = 0 is kept at a constant temperature of T.. Within the plate, heat is
generated at the rate of ġ W/m². Find an expression for steady-state temperature profile, T(x) and
the x-location where the maximum temperature occurs.
$$ \frac{d}{dx} \left( k \frac{dT}{dx} \right) + \frac{d}{dy} \left( k \frac{dT}{dy} \right) + \frac{d}{dz} \left( k \frac{dT}{dz} \right) + \dot{q} = \rho c \frac{dT}{dt} $$
Bq x=0 T:S
BC2 x=L -KA $\frac{dT}{dx}|_{x=L}$ = 0
x=0
x=L

Show more…

7 pts a metal plate of thickness l with a constant thermal conductivity of k wmk is insulated at x l the surface at x 0 is kept at a constant temperature of t within the plate heat is genera 54238

Added by Antonia C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

07/09/2024

Step 1

This means that there is no heat flow across the surface at x = L. Mathematically, this can be expressed as: $$-kA \frac{dT}{dx}|_{x=L} = 0$$ where k is the thermal conductivity, A is the cross-sectional area of the plate, and dT/dx is the temperature gradient at Show more…

Show all steps

lock

Thanks for your feedback!

(7 pts.) A metal plate of thickness L with a constant thermal conductivity of k W/m/k is insulated at x = L. The surface at x = 0 is kept at a constant temperature of T.. Within the plate, heat is generated at the rate of ġ W/m². Find an expression for steady-state temperature profile, T(x) and the x-location where the maximum temperature occurs. $$ \frac{d}{dx} \left( k \frac{dT}{dx} \right) + \frac{d}{dy} \left( k \frac{dT}{dy} \right) + \frac{d}{dz} \left( k \frac{dT}{dz} \right) + \dot{q} = \rho c \frac{dT}{dt} $$ Bq x=0 T:S BC2 x=L -KA $\frac{dT}{dx}|_{x=L}$ = 0 x=0 x=L

Play audio

Feedback

Powered by NumerAI

Adi S and 85 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later