6. A semi-infinite plate initially at a temperature 20℃ is subjected to forced convection (h) at x = 0 with air flow at 80℃ at t = 0. The thermal conductivity of the plate is 0.25 W/mK and the thermal diffusivity of the plate is 10−7 𝑚2𝑠⁄. A small area at the surface (x = 0) subjected to convection reaches 45℃ at t = 10 seconds, find the convective heat transfer coefficient (h) acting at the small area at x = 0. The plate thickness (L) is 12 mm and the temperature at x = L remains at the plate’s initial temperature, i.e., 20℃.
Given the thermal properties of the plate considered here, a one-dimensional heat conduction into the thickness (x-direction) of the solid should be modeled. Obtain the solution through explicit and implicit formulations of finite-difference equations via energy balance method. Show detailed derivation for each method, heat transfer coefficient calculation procedure, and present a well-commented code.

Question

6.	A semi-infinite plate initially at a temperature 20℃ is subjected to forced convection (h) at x = 0 with air flow at 80℃ at t = 0. The thermal conductivity of the plate is 0.25 W/mK and the thermal diffusivity of the plate is 10−7 𝑚2𝑠⁄. A small area at the surface (x = 0) subjected to convection reaches 45℃ at t = 10 seconds, find the convective heat transfer coefficient (h) acting at the small area at x = 0. The plate thickness (L) is 12 mm and the temperature at x = L remains at the plate’s initial temperature, i.e., 20℃.
Given the thermal properties of the plate considered here, a one-dimensional heat conduction into the thickness (x-direction) of the solid should be modeled. Obtain the solution through explicit and implicit formulations of finite-difference equations via energy balance method. Show detailed derivation for each method, heat transfer coefficient calculation procedure, and present a well-commented code.

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Question Text	6. A semi-infinite plate initially at a temperature 20℃ is subjected to forced convection (h) at x = 0 with air flow at 80℃ at t = 0. The thermal conductivity of the plate is 0.25 W/mK and the thermal diffusivity of the plate is 10−7 𝑚2𝑠⁄. A small area at the surface (x = 0) subjected to convection reaches 45℃ at t = 10 seconds, find the convective heat transfer coefficient (h) acting at the small area at x = 0. The plate thickness (L) is 12 mm and the temperature at x = L remains at the plate’s initial temperature, i.e., 20℃. Given the thermal properties of the plate considered here, a one-dimensional heat conduction into the thickness (x-direction) of the solid should be modeled. Obtain the solution through explicit and implicit formulations of finite-difference equations via energy balance method. Show detailed derivation for each method, heat transfer coefficient calculation procedure, and present a well-commented code.
Topic	All topics
Subject	Physics
Class	Class 11

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