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Ratio of temperature difference for given time elapsed Solution

STEP 0: Pre-Calculation Summary
Formula Used
temperature_ratio = exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity))
Tratio = exp(-(h*SA*t)/(ρ*V*c))
This formula uses 1 Constants, 1 Functions, 6 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
exp - Exponential function, exp(Number)
Variables Used
Convection heat transfer coefficient - Convection heat transfer coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit kellvin. (Measured in Watt per Meter² per K)
Surface Area - The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides. (Measured in Square Meter)
Time elapsed - Time elapsed after a particular task is started. (Measured in Second)
Density - Density is the degree of compactness of a substance. (Measured in Kilogram per Meter³)
Volume - Volume is the amount of space that a substance or object occupies or that is enclosed within a container. (Measured in Cubic Meter)
Specific Heat Capacity - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount. (Measured in Kilojoule per Kilogram per K)
STEP 1: Convert Input(s) to Base Unit
Convection heat transfer coefficient: 1 Watt per Meter² per K --> 1 Watt per Meter² per K No Conversion Required
Surface Area: 50 Square Meter --> 50 Square Meter No Conversion Required
Time elapsed: 1 Second --> 1 Second No Conversion Required
Density: 5.51 Kilogram per Meter³ --> 5.51 Kilogram per Meter³ No Conversion Required
Volume: 63 Cubic Meter --> 63 Cubic Meter No Conversion Required
Specific Heat Capacity: 4.184 Kilojoule per Kilogram per K --> 4184 Joule per Kilogram per K (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tratio = exp(-(h*SA*t)/(ρ*V*c)) --> exp(-(1*50*1)/(5.51*63*4184))
Evaluating ... ...
Tratio = 0.999965574623026
STEP 3: Convert Result to Output's Unit
0.999965574623026 --> No Conversion Required
FINAL ANSWER
0.999965574623026 <-- Temperature Ratio
(Calculation completed in 00.031 seconds)

10+ Transient Heat Conduction Calculators

Instantaneous heat transfer rate
heat_rate = Convection heat transfer coefficient*Surface Area*(Initial Temperature-Fluid temperature)*(exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity))) Go
Temperature after given time elapsed
temperature = ((Initial Temperature-Fluid temperature)*(exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity))))+Fluid temperature Go
Total heat transfer during a time interval
heat_transfer_KJ = Density*Specific heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot number*Fourier Number)))) Go
Ratio of temperature difference for given time elapsed
temperature_ratio = exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity)) Go
Power on exponential of temperature-time relation
constantt = -(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity) Go
Product of Biot and Fourier Number in terms of system properties
constantt = (Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity) Go
Time Constant in unsteady state heat transfer
tau_mi = (Density*Specific Heat Capacity*Volume)/(Convection heat transfer coefficient*Surface Area) Go
Thermal Capacitance
thermal_capacitance = Density*Specific Heat Capacity*Volume Go
Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number
temperature_ratio = exp(-(Biot number*Fourier Number)) Go
Power on exponential of temperature-time relation in terms of Biot and Fourier Number
constantt = -(Biot number*Fourier Number) Go

Ratio of temperature difference for given time elapsed Formula

temperature_ratio = exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity))
Tratio = exp(-(h*SA*t)/(ρ*V*c))

What is Temperature-Time relation?

The temperature-time relationship of unsteady-state heat transfer helps to determine the rate of heat transfer that has been conducted in the lumped system in a given time period.

How to Calculate Ratio of temperature difference for given time elapsed?

Ratio of temperature difference for given time elapsed calculator uses temperature_ratio = exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity)) to calculate the Temperature Ratio, Ratio of temperature difference for given time elapsed formula calculates the exponential term given in the temperature-time relationship for a lumped body. Temperature Ratio is denoted by Tratio symbol.

How to calculate Ratio of temperature difference for given time elapsed using this online calculator? To use this online calculator for Ratio of temperature difference for given time elapsed, enter Convection heat transfer coefficient (h), Surface Area (SA), Time elapsed (t), Density (ρ), Volume (V) & Specific Heat Capacity (c) and hit the calculate button. Here is how the Ratio of temperature difference for given time elapsed calculation can be explained with given input values -> 0.999966 = exp(-(1*50*1)/(5.51*63*4184)).

FAQ

What is Ratio of temperature difference for given time elapsed?
Ratio of temperature difference for given time elapsed formula calculates the exponential term given in the temperature-time relationship for a lumped body and is represented as Tratio = exp(-(h*SA*t)/(ρ*V*c)) or temperature_ratio = exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity)). Convection heat transfer coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit kellvin, The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides, Time elapsed after a particular task is started, Density is the degree of compactness of a substance, Volume is the amount of space that a substance or object occupies or that is enclosed within a container & Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
How to calculate Ratio of temperature difference for given time elapsed?
Ratio of temperature difference for given time elapsed formula calculates the exponential term given in the temperature-time relationship for a lumped body is calculated using temperature_ratio = exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity)). To calculate Ratio of temperature difference for given time elapsed, you need Convection heat transfer coefficient (h), Surface Area (SA), Time elapsed (t), Density (ρ), Volume (V) & Specific Heat Capacity (c). With our tool, you need to enter the respective value for Convection heat transfer coefficient, Surface Area, Time elapsed, Density, Volume & Specific Heat Capacity 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 Temperature Ratio?
In this formula, Temperature Ratio uses Convection heat transfer coefficient, Surface Area, Time elapsed, Density, Volume & Specific Heat Capacity. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • heat_rate = Convection heat transfer coefficient*Surface Area*(Initial Temperature-Fluid temperature)*(exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity)))
  • heat_transfer_KJ = Density*Specific heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot number*Fourier Number))))
  • tau_mi = (Density*Specific Heat Capacity*Volume)/(Convection heat transfer coefficient*Surface Area)
  • constantt = -(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity)
  • constantt = -(Biot number*Fourier Number)
  • temperature_ratio = exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity))
  • temperature_ratio = exp(-(Biot number*Fourier Number))
  • temperature = ((Initial Temperature-Fluid temperature)*(exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity))))+Fluid temperature
  • constantt = (Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity)
  • thermal_capacitance = Density*Specific Heat Capacity*Volume
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