## Solution Library

# Find the Thermal Conductivity of an Infinitely Long Horizontal Plate

**Question**

A plate of thickness t is subjected to the imposed surface flux q," on its top surface with a pitch of 2L as shown in the figure. The plate is infinitely long in the horizontal direction. The in-depth width of the plate is w. The thermal conductivity of the plate is k. The unheated area on the top surface is thermally insulated. The bottom surface faces an air at T∞. The convective motion of the air gives rise to the heat transfer coefficient h. If the thermal conductivity k is very large and the thickness t is small, you can assume that it is an ID steady-state heat conduction problem in the horizontal direction.

(a) Sketch the temperature distribution along the plate.

(b) Describe all the boundary conditions.

(c) Derive the governing equations and obtain the mathematical expressions for the local temperature.

Now, consider poor thermal conductivity and a large thickness for the plate. You need to treat it as a 2D steady-state heat conduction problem this time. Considering the temperature distribution in the both horizontal and vertical direction,

(d) Describe all the boundary conditions.

(e) Obtain the mathematical expression for the local temperature T(x, y).

Plate subjected to heat flux with spatial period on its top and to air convection on its bottom.

**Summary**

The question belongs to Mechanical Engineering and it is about thermal conductivity of a plate which has infinitely long in the horizontal direction. The questions are about finding the temperature distribution along the plate, describe the boundaries of the plate and to find the governing equations for the plate.

Note: The solution is in handwritten format.

## Comments

Rashathis is a very good website

maaniI have 50 questions for the same test your page is showing only 28

joeannehi can you please help or guide me to answer my assignments. thanks

joeannehi can anyone help or guide me to my assignments. thanks

MonikCristinaThis solution is perfect ...thanks

JaneteHello Allison,I love the 2nd image that you did! I also, had never heard of SumoPaint, is something that I will have to exolpre a bit! I understand completely the 52 (or so) youtube videos that you probably watched. Sometimes they have what you want, sometimes they don't! However, it is always satisfying when you are able to produce something that you have taught yourself. Great job!Debra 0 likes

SandeepPerfect bank of solution.

Oxanagreat !

Paul Brandon-Fritziusthanks for the quick response. the solution looks good. :)

tina Johnsonthnx for the answer. it was perfect. just the way i wanted it.

Giuseppeworks fine.