Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions Solution

STEP 0: Pre-Calculation Summary
Formula Used
Maximum Temperature = Surface Temperature+(Internal Heat Generation*Wall Thickness^2)/(8*Thermal Conductivity)
Tmax = T1+(qG*b^2)/(8*k)
This formula uses 5 Variables
Variables Used
Maximum Temperature - (Measured in Kelvin) - Maximum Temperature is defined as the highest possible or permissible value of temperature.
Surface Temperature - (Measured in Kelvin) - Surface Temperature is the temperature at or near a surface. Specifically, it may refer to as Surface air temperature, the temperature of the air near the surface of the earth.
Internal Heat Generation - (Measured in Watt Per Cubic Meter) - Internal Heat Generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium.
Wall Thickness - (Measured in Meter) - Wall Thickness is simply the width of the wall that we are taking under consideration.
Thermal Conductivity - (Measured in Watt per Meter per K) - Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
STEP 1: Convert Input(s) to Base Unit
Surface Temperature: 305 Kelvin --> 305 Kelvin No Conversion Required
Internal Heat Generation: 100 Watt Per Cubic Meter --> 100 Watt Per Cubic Meter No Conversion Required
Wall Thickness: 12.601905 Meter --> 12.601905 Meter No Conversion Required
Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tmax = T1+(qG*b^2)/(8*k) --> 305+(100*12.601905^2)/(8*10.18)
Evaluating ... ...
Tmax = 500.000011823459
STEP 3: Convert Result to Output's Unit
500.000011823459 Kelvin --> No Conversion Required
FINAL ANSWER
500.000011823459 500 Kelvin <-- Maximum Temperature
(Calculation completed in 00.004 seconds)

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14 Steady State Heat Conduction with Heat Generation Calculators

Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius
Go Temperature = Internal Heat Generation/(4*Thermal Conductivity)*(Outer Radius of Cylinder^2-Radius^2)+Outer Surface Temperature+ln(Radius/Outer Radius of Cylinder)/ln(Outer Radius of Cylinder/Inner Radius of Cylinder)*(Internal Heat Generation/(4*Thermal Conductivity)*(Outer Radius of Cylinder^2-Inner Radius of Cylinder^2)+(Outer Surface Temperature-Inner Surface Temperature))
Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius
Go Temperature = Surface Temperature of wall+Internal Heat Generation/(6*Thermal Conductivity)*(Outer Radius of Sphere^2-Radius^2)+(Internal Heat Generation*Inner Radius of Sphere^3)/(3*Thermal Conductivity)*(1/Outer Radius of Sphere-1/Radius)
Temperature Inside Solid Cylinder at given Radius Immersed in Fluid
Go Temperature Solid Cylinder = Internal Heat Generation/(4*Thermal Conductivity)*(Radius of Cylinder^2-Radius^2)+Fluid Temperature+(Internal Heat Generation*Radius of Cylinder)/(2*Convection Heat Transfer Coefficient)
Temperature at given Thickness x Inside Plane Wall Surrounded by Fluid
Go Temperature = Internal Heat Generation/(8*Thermal Conductivity)*(Wall Thickness^2-4*Thickness^2)+(Internal Heat Generation*Wall Thickness)/(2*Convection Heat Transfer Coefficient)+Fluid Temperature
Maximum Temperature Inside Solid Cylinder Immersed in Fluid
Go Maximum Temperature = Fluid Temperature+(Internal Heat Generation*Radius of Cylinder)/(4*Convection Heat Transfer Coefficient*(2+(Convection Heat Transfer Coefficient*Radius of Cylinder)/Thermal Conductivity))
Maximum Temperature in Plane Wall Surrounded by Fluid with Symmetrical Boundary Conditions
Go Maximum Temperature of Plain Wall = (Internal Heat Generation*Wall Thickness^2)/(8*Thermal Conductivity)+(Internal Heat Generation*Wall Thickness)/(2*Convection Heat Transfer Coefficient)+Fluid Temperature
Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions
Go Temperature 1 = -(Internal Heat Generation*Wall Thickness^2)/(2*Thermal Conductivity)*(Thickness/Wall Thickness-(Thickness/Wall Thickness)^2)+Surface Temperature
Temperature Inside Solid Cylinder at given Radius
Go Temperature Solid Cylinder = Internal Heat Generation/(4*Thermal Conductivity)*(Radius of Cylinder^2-Radius^2)+Surface Temperature of wall
Temperature Inside Solid Sphere at given Radius
Go Temperature 2 = Surface Temperature of wall+Internal Heat Generation/(6*Thermal Conductivity)*(Radius of Sphere^2-Radius^2)
Surface Temperature of Solid Cylinder Immersed in Fluid
Go Surface Temperature of wall = Fluid Temperature+(Internal Heat Generation*Radius of Cylinder)/(2*Convection Heat Transfer Coefficient)
Maximum Temperature in Solid Cylinder
Go Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Cylinder^2)/(4*Thermal Conductivity)
Maximum Temperature in Solid Sphere
Go Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Sphere^2)/(6*Thermal Conductivity)
Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions
Go Maximum Temperature = Surface Temperature+(Internal Heat Generation*Wall Thickness^2)/(8*Thermal Conductivity)
Location of Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions
Go Location of Maximum Temperature = Wall Thickness/2

Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions Formula

Maximum Temperature = Surface Temperature+(Internal Heat Generation*Wall Thickness^2)/(8*Thermal Conductivity)
Tmax = T1+(qG*b^2)/(8*k)

What is steady state conduction?

Steady-state conduction is the form of conduction that happens when the temperature difference(s) driving the conduction are constant.

What is internal heat generation?

Internal heat generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium.

How to Calculate Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions?

Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions calculator uses Maximum Temperature = Surface Temperature+(Internal Heat Generation*Wall Thickness^2)/(8*Thermal Conductivity) to calculate the Maximum Temperature, The Maximum temperature in plane wall with symmetrical boundary conditions is the temperature when the temperature at both surfaces of the plane wall is equal. Maximum Temperature is denoted by Tmax symbol.

How to calculate Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions using this online calculator? To use this online calculator for Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions, enter Surface Temperature (T1), Internal Heat Generation (qG), Wall Thickness (b) & Thermal Conductivity (k) and hit the calculate button. Here is how the Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions calculation can be explained with given input values -> 481.8173 = 305+(100*12.601905^2)/(8*10.18).

FAQ

What is Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions?
The Maximum temperature in plane wall with symmetrical boundary conditions is the temperature when the temperature at both surfaces of the plane wall is equal and is represented as Tmax = T1+(qG*b^2)/(8*k) or Maximum Temperature = Surface Temperature+(Internal Heat Generation*Wall Thickness^2)/(8*Thermal Conductivity). Surface Temperature is the temperature at or near a surface. Specifically, it may refer to as Surface air temperature, the temperature of the air near the surface of the earth, Internal Heat Generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium, Wall Thickness is simply the width of the wall that we are taking under consideration & Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
How to calculate Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions?
The Maximum temperature in plane wall with symmetrical boundary conditions is the temperature when the temperature at both surfaces of the plane wall is equal is calculated using Maximum Temperature = Surface Temperature+(Internal Heat Generation*Wall Thickness^2)/(8*Thermal Conductivity). To calculate Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions, you need Surface Temperature (T1), Internal Heat Generation (qG), Wall Thickness (b) & Thermal Conductivity (k). With our tool, you need to enter the respective value for Surface Temperature, Internal Heat Generation, Wall Thickness & Thermal Conductivity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Maximum Temperature?
In this formula, Maximum Temperature uses Surface Temperature, Internal Heat Generation, Wall Thickness & Thermal Conductivity. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Cylinder^2)/(4*Thermal Conductivity)
  • Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Sphere^2)/(6*Thermal Conductivity)
  • Maximum Temperature = Fluid Temperature+(Internal Heat Generation*Radius of Cylinder)/(4*Convection Heat Transfer Coefficient*(2+(Convection Heat Transfer Coefficient*Radius of Cylinder)/Thermal Conductivity))
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